A Bibliography of

Differential Evolution

Algorithm

collected by

Jouni Lampinen

GOTO YEAR: 1995  1996  1997  1998  1999  2000  2001  2002

Reference data for this document:

Lampinen, Jouni (2001). A Bibliography of Differential Evolution Algorithm. Technical Report. Lappeenranta University of Technology, Department of Information Technology, Laboratory of Information Processing. Available via Internet  http://www.lut.fi/~jlampine/debiblio.htm. Cited dd/mm/yyyy.

Author:

Jouni Lampinen

Lappeenranta University of Technology,

Department of Information Technology

Laboratory of Information Processing

P.O.Box 20

FIN-53851 LAPPEENRANTA

Finland

E-mail: Jouni.Lampinen@lut.fi

One of the most important issues in any serious scientific research is to be aware about the work done before you by the other researchers. There is no point to invent a wheel again. For that purpose up-to-date bibliographies are of great help as well as they save time making it possible to find all the relevant information in effortless way.

This bibliography contains the references to all articles discussing about Differential Evolution (DE) which are currently known by the author. The items marked with a boldfaced reference symbol [XYZ95] are also in my collection of DE articles. If you find that one or more references are missing, incomplete or erroneous, please inform me about that by E-mail Jouni.Lampinen@lut.fi. I would appreciate even more if you can send me a photocopy of any missing article by surface mail for bibliographical purposes. This is important because I will also forward the information to the world's largest bibliography of evolutionary algorithms [Ala97a] maintained by professor Jarmo Alander from University of Vaasa, Finland. This bibliography [Ala97a] is undoubtedly the most comprehensive bibliography in the field of evolutionary computing. Thus, it can be highly recommended as an excellent source of information. The bibliography documents are available for anyone (without any payment) in PostScript format via anonymous ftp, see the reference below.

[Ala97a] Alander, Jarmo T. (1997). A bibliography collection of evolutionary algorithms. Report Series 94-1-*, University of Vaasa, Department of Information Technology and Production Economics, Vaasa. Available as subbibliographies (PostScript-format) via anonymous ftp from ftp://ftp.uwasa.fi/cs/report94-1/. For further information, see first file ftp://ftp.uwasa.fi/cs/report94-1/README. The bibliography contains currently over 10,000 GA references.

Note

The latest changes and additions to this document are marked with a red coloured reference symbol, for example [XYZ95].

1995

[SP95a] Storn, Rainer and Price, Kenneth (1995). Differential Evolution - a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012, ICSI, March 1995. PostScript-file downloadable from http://www.icsi.berkeley.edu/techreports/1995.abstracts/tr-95-012.html.

[Sto95a] Storn, Rainer (1995). Modeling and Optimization of PET-Redundancy Assignment for MPEG-Sequences. Technical Report TR-95-018, ICSI, May 1995. PostScript-file downloadable from http://www.icsi.berkeley.edu/techreports/1995.abstracts/tr-95-018.html.

[Sto95b]Storn, Rainer (1995). Differential Evolution Design of an IIR-Filter with Requirements for Magnitude and Group Delay. Technical Report TR-95-026, ICSI, May 1995. PostScript-file downloadable from http://www.icsi.berkeley.edu/techreports/1995.abstracts/tr-95-026.html.

[BUM95] Brutovský, B., Ulicný, J. and Miškovský, P. (1995). Application of Genetic Algorithms Based Techniques in the Theoretical Analysis of Molecular Vibrations. In: Ošmera, Pavel (ed.) (1995). Proceedings of MENDEL'95, First International Conference on Genetic Algorithms on the occasion of 130-th anniversary of Mendel's laws in Brno, September 26-28, 1995, Brno, Czech Republic (1995). Technical University of Brno, Faculty of Mechanical Engineering, Institute of Computer Science, Brno (Czech Republic), pp. 29–33. ISBN 80-214-0672-0.

1996

[JS96] Joshi, Rajive and Sanderson, Arthur C. (1996). Multisensor fusion and model selection using a minimal representation size framework. In: Proceedings of the 1996 IEEE/SICE/RSJ International Conference on Multisensor Fusion and Integration for Intelligent Systems, 8-11 December 1996, pp. 25–32. ISBN 0-7803-3700-X. 

Abstract: This paper addresses the problem of statistical model selection for model-based multisensor fusion problems. The minimal representation size (MRS) criterion is used as a basis for the selection of a minimal complexity model among a class of stored models, and in addition enables the selection of parameterization, scaling, and data subsampling. This use of an information-based criterion results in a "universal yardstick" for model selection which is easily adapted to new combinations of sensors and parameters. Each sensor is characterized by a constraint equation defined in the measurement space of observed sensor data. The search for the best model structure is conducted using a polynomial time hypothesize and test algorithm that uses constraining data feature sets (CDFS) to instantiate environment models. Analytical formulation of the minimal representation size model selection for tactile-visual fusion with an anthropomorphic robot hand is presented.

[Pri96] Kenneth V. Price (1996). Differential evolution: a fast and simple numerical optimizer. 1996 Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS, 19–22 June 1996, M. Smith, M. Lee, J. Keller, J. Yen, Eds., pp. 524-527, IEEE Press, New York, NY, 1996. ISBN: 0-7803-3225-3. 

Abstract: Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimizing real-valued multi-modal functions. Function parameters are encoded as floating-point variables and mutated with a simple arithmetic operation. During mutation, a variable-length, one-way crossover operation splices perturbed best-so-far parameter values into existing population vectors. A novel sampling technique adaptively scales the step-size of perturbations as the population evolves. DE's selection criterion demands that improved vectors always be accepted. The performance of DE on a testbed of 15 functions is compared with a variety of recently published results encompassing many different methods. DE converged for all 15 functions and was the fastest method for solving 11 of them. DE's performance on the remaining 4 functions was competitive.

[SP96] Storn, Rainer and Price, Kenneth (1996). Minimizing the real functions of the ICEC'96 contest by Differential Evolution. IEEE International Conference on Evolutionary Computation, Nagoya, May 1996, pp. 842 - 844. IEEE, New York, NY, USA. PostScript-file downloadable from http://www.icsi.berkeley.edu/~storn/litera.html . 

Abstract: Differential Evolution (DE) has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. Besides its good convergence properties and suitability for parallelization, DE's main assets are its conceptual simplicity and ease of use. This paper describes two variants of DE which were used to minimize the real test functions of the ICEC'96 contest.

[Sto96a] Storn, Rainer (1996). On the Usage of Differential Evolution for Function Optimization. In: 1996 Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS 1996), Berkeley, pp. 519–523. IEEE, New York, NY, USA. PostScript-file downloadable from http://www.icsi.berkeley.edu/~storn/litera.html . 

Abstract: Differential evolution (DE) has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. Besides its good convergence properties and suitability for parallelization, DE's main assets are its conceptual simplicity and ease of use. This paper describes several variants of DE and elaborates on the choice of DE's control parameters, which corresponds to the application of fuzzy rules. Finally, the design of a howling removal unit with DE is described to provide a real-world example for DE's applicability.

[Sto96b]Storn, Rainer (1996). System Design by Constraint Adaptation and Differential Evolution. Technical Report TR-96-039, ICSI, November 1996. PostScript-file downloadable from http://www.icsi.berkeley.edu/techreports/1996.abstracts/tr-96-039.html.

[Sto96c] Storn, Rainer (1996). Differential evolution design of an IIR-filter. Proceedings of IEEE International Conference on Evolutionary Computation ICEC'96, 20-22 May 1996, pp. 268–273. ISBN: 0-7803-2902-3. IEEE, New York, NY, USA. See also [Sto95b] . 

Abstract: The task of designing an 18 parameter IIR-filter (IIR=infinite impulse response) which has to meet tight specifications for both magnitude response and group delay is investigated. This problem is usually tackled by specialized design methods and requires an expert in digital signal processing for its solution. The use of the general purpose minimization method differential evolution (DE), however, allows filter design with a minimum knowledge of digital filters.

1997

[Fle97] Fleiner, Claudio (1997). Parallel Optimizations: Advanced Constructs and Compiler Optimizations for a Parallel, Object Oriented, Shared Memory Language running on a Distributed System, Ph. D. Thesis, Faculty of Science, University of Fribourg. Available via Internet: http://www.icsi.berkeley.edu/~fleiner/thesis/.

Description: DE was used in this thesis as an example for a parallel algorithm.

[Haa97] Haataja, Juha (1997). Evoluutiostrategiat Fortran 90:llä. @CSC (CSC–Tieteellinen laskenta Oy:n asiakaslehti) 3/1997 pp. 28–30. ISSN 1238-4798 (Evolution Strategies with Fortran 90. @CSC, Customer Journal of CSC-Scientific Computing, article in Finnish, DE-source code in Fortran 90). Available via Internet: http://www.csc.fi/oppaat/f95/art/f90evol.html .

[JS97a] Joshi, Rajive and Sanderson, Arthur C. (1997). Minimal representation multisensor fusion using differential evolution. Proceedings. 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA'97. Towards New Computational Principles for Robotics and Automation', Monterey, CA, USA, 10-11 July 1997, pp. 266–273. ISBN 0-8186-8138-1.  Available via Internet:  http://computer.org/proceedings/cira/8138/81380266abs.htm . 

Abstract: Fusion of information from multiple sensors is increasingly used in planning and control of robotic systems. The minimal representation approach provides a framework for integrating information from a variety of sources, and uses an information measure as a universal yardstick for fusion. In this paper, we evaluate a differential evolution approach to the search for minimal representation solutions. Experiments in robot manipulation using both tactile and visual sensing demonstrate that this algorithm is effective in solving this difficult search problem, and comparison with a more traditional genetic algorithm shows distinct advantages in both accuracy and efficiency for the differential evolution approach.

[JS97b] Joshi, Rajive and Sanderson, Arthur C. (1997). Multisensor fusion of touch and vision using minimal representation size. In Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS '97, 7-11 September 1997. Pages V4–V5 of volume 3. ISBN 0-7803-4119-8. 

Abstract: Multisensor fusion has emerged as a central problem in the development of robotic systems where interaction with the environment is critical to the achievement of a given task. The Anthrobot five-fingered hand grasps an object, and senses the contact points with the surface of the object using tactile sensors. The tactile sensors extract touch position and approximate surface normal in the kinematic reference frame of the hand. In addition, a CCD camera views the position of the same object and extracts vertex/edge features of the object image. Both the tactile features and the visual features are related to the position and orientation of the object, and in practice we wish to combine these two sources of information to improve robot's ability to accurately manipulate the object. The fusion of the tactile and image feature data is used to derive an improved estimate of the object pose which guides the manipulation.

[JS97c] Joshi, Rajive and Sanderson, Arthur C. (1997). Experimental studies on minimal representation multisensor fusion. In: Proceedings of 8th International Conference on Advanced Robotics, ICAR '97, Monterey, CA, 7-9 July 1997, pp. 603-610. ISBN 0-7803-4160-0. 

Abstract: We describe laboratory experiments, in which tactile data obtained from the finger-tips of a robot hand, while it is holding an object in front of a calibrated camera, is fused with the vision data from the camera, to determine the object identity, pose, and the touch and vision data correspondences. The touch data is incomplete due to required hand configurations, while nearly half of the vision data are spurious due to the presence of the hand in the image. Using either sensor alone results in ambiguous or incorrect interpretations. A minimal representation size framework is used to formulate the multisensor fusion problem, and can automatically select the object class, correspondence (data subsamples), and pose parameters. The experiments demonstrate that it consistently finds the correct interpretation, and is a practical method for multisensor fusion and model selection.

[ML97] Masters, Timothy and Land, Walker (1997). A new training algorithm for the general regression neural network. 1997 IEEE International Conference on Systems, Man, and Cybernetics, Computational Cybernetics and Simulation., Volume: 3, pp. 1990–1994. 

Abstract: The general regression neural network (GRNN) is known to be widely effective for modeling and prediction, especially if separate sigma weights are used for each predictor. However, the significant time requirements for executing the model, combined with the frequent presence of multiple local optima, makes it difficult to train this model in many applications. This paper shows how differential evolution may be enhanced by direct gradient descent to produce a hybrid training algorithm that is both fast and effective.

[MM97]Michael, Christoph and McGraw, Gary (1997). Opportunism and Diversity in Automated Software Test Data Generation. Technical Report RSTR-003-97-13, version 1.3, 8. December 1997. RST Corporation, Sterling, VA, USA. Available via Internet: ftp://ftp.rstcorp.com/pub/techreports/gadget.ps . See also [MMS98] . 

Description: DE was applied here for test data generation to obtain condition/decision coverage of C/C++ programs.

[Pri97] Kenneth V. Price (1997). Differential evolution vs. the functions of the 2nd ICEO. Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97), Indianapolis, IN, USA, 13-16 April 1997, pp. 153–157, (Cat. No.97TH8283) Sponsor(s): IEEE; IEEE Neural Network Council (NNC); Evolutionary Computation (ICEC '97). ISBN 0-7803-3949-5. 

Abstract: Differential evolution (DE) is a simple evolutionary algorithm for numerical optimization whose most novel feature is that it mutates vectors by adding weighted, random vector differentials to them. A new version of the DE algorithm is described and the results of its attempts to optimize the 7 real-valued functions of the 2nd ICEO are tabulated. DE succeeded in finding each function's global minimum, although the number of evaluations needed in one instance was unacceptably high. Despite this lone difficulty, DE's speed of execution across the remaining test bed, in addition to its simplicity, robustness and ease of use, suggest that it is a valuable tool for continuous numerical optimization.

[Rut97a] Rüttgers, M. (1997). Differential Evolution: A Method for Optimization of Real Scheduling Problems. International Computer Science Institute, TR-97-013. PostScript-file downloadable from http://www.icsi.berkeley.edu/techreports/1997.abstracts/tr-97-013.html.

Abstract: A new method for optimizing scheduling problems with nonlinear objective functions and multiple dependent restrictions is presented. This method is based on an Evolutionary Algorithm but has special changing operators for a directed search over the entire solution space. It can be implemented for solving real problems very fast, it requires only few control variables, it is robust, easy to use and lends itself very well to parallel computation. The implementation for solving a model representing a real scheduling problem in foundries is presented. This application shows good results and the comparison to a method based on a stochastic Evolutionary Algorithm, having the reputation for being very powerful, shows that the new method converges faster and with more certainty.

[Rut97b] Rüttgers, M. (1997). Entwicklung eines DV-gestützten Verfahrens zur Maschinenbelegungsplanung in Kernmachereien von Gießereien. In: Differential Evolution: Ein neuer Algorithmus zur Maschinenbelegungsplanung Fortschirtte in der Simulationstechnik, Tagungsband SAIM, November 1997, Hrsg. Kuhn, A.; Wenzel, S., S. 688-694.

[Rut97c] Rüttgers, M. (1997). Design of a New Algorithm for Scheduling in Parallel Machine Shops. In: Proceedings of the 5th European Congress on Intelligent Techniques and Soft Computing 1997, Vol. 3, S. 2182-2187.

[SP97a] Storn, Rainer and Price, Kenneth (1997). Differential Evolution – A simple evolution strategy for fast optimization. Dr. Dobb's Journal 22(4):18–24 and 78, April 97. 

Description: The price to be paid for an efficient numerical optimizer has been mathematical complexity. Differential Evolution, however, is an exceptionally simple evolution strategy that promises to make fast and robust numerical optimization accessible to everyone. Remarkably, DE's main search engine can be easily written in less than 20 lines of C code and involves nothing more exotic than a uniform random-number generator and a few floating-point arithmetic operations.

[SP97b] Storn, R. and Price, K. (1997). Differential Evolution – a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 11(4):341–359, December 1997. Kluwer Academic Publishers.

[TV97] Thomas P. and Vernon, D. (1997). Image Registration by Differential Evolution. Proceedings of the First Irish Machine Vision and Image Processing Conference IMVIP-97, Magee College, University of Ulster, pp. 221-225. PostScript-file available from http://www.cs.may.ie/~pthomas/.

[WC97a] Wang, F. S. and Chiou J. P. (1997). Optimal control and optimal time location problems of differential-algebraic systems by Differential Evolution. Ind. Eng. Chem. Res. 36:5348-5357.

[WC97b] Wang, F. S. and Chiou J. P. (1997). Differential Evolution for Dynamic Optimization of Differential-Algebraic Systems. In: Proceedings of the IEEE International Conference on Evolutionary Computation ICEC'97, Indianapolis, IN, pp. 531-536. IEEE Press. IEEE Cat. No: 97TH8283. 

Description: Modified version of differential evolution is applied to solve an optimal temperature control problem of a chemical reactor system.
Abstract: An efficient method is introduced for solving optimal control and optimal parameter selection problems of nonlinear differential-algebraic systems involving general constraints. These infinite-dimensional problems are first converted into the uncaused optimal parameter selection problems. Differential evolution is then extended to solve such problems. This modified version of differential evolution is applied to solve an optimal temperature control problem of a chemical reactor system.

1998

[Bak98] Baker, Richard (1998). Genetic Algorithms in Search and Optimization. Financial Engineering News, July 1998, Volume 2, Number 3. Available via Internet: http://www.fenews.com/1998/v2n3/ga.htm.

[BAB98] Eva Balsa-Canto, Antonio A. Alonso and Julio R. Banga (1998). Dynamic optimization of bioprocesses: deterministic and stochastic strategies. Proceedings of ACoFoP IV (Automatic Control of Food and Biological Processes), 21-23 Sept., Göteborg, Sweden. Available via ftp from ftp://nautilus.iim.csic.es/pub/jrbanga/do_bio.ps.

[BLS98] Yair Bartal, Gideon Leonard and Zeev Somer (1998). Optimal Seismic Networks in Israel in the Context of the Comprehensive Test Ban Treaty (CTBT) and the Cooperative National Facilities (CNF). Workshop on Advanced Methods in Seismic Analysis, High precision hypocenter location and Seismic Tomography,  January 12-15, 1998, Dead Sea, Israel. Available (an abstract) from http://ndc.soreq.gov.il/WORKSHOP/abstracts.html

Abstract: One of the tools for checking compliance with the Comprehensive Test Ban Treaty (CTBT) is an On-Site Inspection (OSI). The error ellipse calculated as a result of the location procedure may serve as a guideline for the search area. Minimizing the error ellipse will increase the efficiency of the search. This goal can be achieved by optimizing the configuration of the seismic network used for the location. We checked optimal configurations consisting of the two existing auxiliary stations in northern and southern Israel with up to eight additional optimally located Cooperative National Facility (CNF) stations. We used Genetic Algorithms (GA) and Differential Evolution (DE) techniques for the optimization. Optimal configurations were compared to best judgement configurations suggested by three professional seismologists.
    A representative set of 18 events in Israel was checked, using modelling error of 0.20 seconds and measurement error of 0.15 seconds. The optimal configuration for adding 4,5,6,7 and 8 stations to the two existing ones yielded maximal error ellipse areas of 158, 121, 101, 86 and 82 km²  respectively.
    The human best judgement configurations for 6 added stations yielded maximal error ellipse areas of 731, 628 and 251 km², with some singular hypocenters.

[Caf98] Cafolla, A. A. (1998). A new stochastic optimisation strategy for quantitative analysis of core level photoemission data. Surface Science, Volumes 402-404, 15 May 1998, pp. 561-565. 

Abstract: A new procedure is presented for the curve-fitting of core level photoemission energy distribution curves. The algorithm described in this paper is an exceptionally simple Evolutionary Strategy that is both fast and robust. It presents a novel departure from conventional deterministic non-linear least-squares fitting techniques such as the Simplex, and the Levenberg-Marquard methods. A detailed description of the algorithm is presented. The technique is demonstrated by applying it to the curve-fitting of As 3d core level spectra obtained in synchrotron photoemission experiments.

[CC98] Tien-Ting Chang and Hong-Chan Chang (1998). Application of differential evolution to passive shunt harmonic filter planning. 8th International Conference On Harmonics and Quality of Power, 14-16 Oct. 1998, Volume: 1, 1998, pp. 149–153. ISBN 0-7803-5105-3. 

Abstract: This paper presents a refined differential evolution (RDE) for passive shunt harmonic filter planning. The purpose is to minimize total costs while satisfying various practical constraints. The substation harmonic voltage sources and load harmonic current sources are considered simultaneously. In addition, practical constraints such as the voltage magnitude limit, total harmonic distortion and the commercially available discrete sizes of the capacitors can be accounted for. The RDE approach together with evolutionary programming (EP) were tested on a 9-bus distribution system. Results obtained show that the proposed RDE method can provide a highly optimal solution within a reasonable time.

[CH98] Cheng, S.-L and Hwang, C. (1998). Designing PID Controllers With A Minimum IAE Criterion By A Differential Evolution Algorithm. Chemical engineering communications 170():83. ISSN 0098-6445.

[CW98] Chiou, Ji-Pyng and Wang, Feng-Sheng (1998). A hybrid method of differential evolution with application to optimal control problems of a bioprocess system. The 1998 IEEE International Conference on Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence, 1998 , pp. 627–632. IEEE, New York, NY, USA. 

Abstract: A hybrid method of differential evolution is developed in this study. Two additional operations, accelerated phase and migrating phase, are embedded into the original version of differential evolution. These two phases are used for the improvement of the convergence speed without decreasing the diversity among the individuals. The method of multiplier updating incorporated in the proposed method is introduced to solve the constrained optimization problems. The method is then extended to apply for solving the simultaneous optimal control and optimal parameter selection problems of a bioprocess system.

[Joh98] Johnson, R. Colin (1998). Differential Evolution Underwrites Java Applet. Electronic Engineering Times 05/11/98, Issue 1006, p. 42. ISSN 0192-1541. 

Description: A half-page article. Announces a Java implementation of the Differential Evolution.

[DC98] Kalyanmoy Deb and Nirupam Chakraborti (1998). A Combined Heat Transfer and Genetic Algorithm Modeling of an Integrated Steel Plant Bloom Re-Heating Furnace. In: proceedings of EUFIT ´98, 6th European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, September 7-10, 1998. Vol. 1, pp.439-443. Verlag Mainz, Aachen, Germany. ISBN 3-89653-500-5. 

Abstract: This paper presents a modeling study of preheating of blooms in a fuel fired furnace using a combined GA and heat transfer formulation. A re-heating furnace containing three asymmetrically placed burners are considered in this study, which is a typical configuration used in many integrated steel plants. This study shows that the the GA is an ideally suited tool for studying such complex problems.

[LZ98] Jouni Lampinen – Ivan Zelinka (1998). Mechanical Engineering Design Optimization by Differential Evolution. Internal Report. University of Vaasa, department of information technology and production economics. 

Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. An optimization method based on using the differential evolution algorithm for optimization of the object function and on using the soft-constraint approach for constraint handling is described. Also the required handling techniques for integer, discrete and continuous variables are described. Three mechanical engineering design related numerical examples, design of a gear train, design of a pressure vessel and design of a coil spring, are given to illustrate the capabilities and the practical use of the described method. The results are compared with the previous results found in literature, which are obtained by using other optimization methods. It is shown that the described approach is capable of obtaining high quality solutions. The novel method described is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.

[MMS98]Gary McGraw, Christoph Michael and Michael Schatz (1998). Generating Software Test Data by Evolution. Technical Report RSTR-018-97-01, 9. February 1998. RST Corporation, Sterling, VA, USA. Available via Internet: ftp://ftp.rstcorp.com/pub/techreports/journal.ps . See also [MM97]. 

Description: DE was applied here for automated software test data generation.

[PSV98] Plagianakos, V. P. , Sotiropoulos, D.G. and Vrahatis, M. N. (1998). Integer weight training by differential evolution algorithms. In: Mastorakis, N.E. (ed.) (1998). Recent Advances in Circuits and Systems. World Scientific. 

Description: Training of Neural Networks with integer weights applying Differential Evolution algorithm was under investigations.

[PWC98] Power, J. R., Weightman,  P. and Cafolla, A. A. (1998). The initial stages of Ge-GaAs(100) interface formation studied by reflectance anisotropy spectroscopy and low-energy electron diffraction. Surface Science, Volumes 402-404, 15 May 1998, pp. 566-570. 

Description: DE was applied for solving a parameter fitting problem with seven parameters. However, DE itself was not subject to investigations.

[RP98] Rae, Allan and Parameswaran, Sri (1998). Application-specific heterogeneous multiprocessor synthesis using differential-evolution. Proceedings of the 11th International Symposium on System Synthesis, 2–4 December, 1998, pp. 83–88. IEEE Comput. Soc., Los Alamitos (CA, USA). ISBN: 0-8186-8623-5. 

Abstract: This paper presents an application-specific, heterogeneous multiprocessor synthesis system, named HeMPS, that combines a form of Evolutionary Computation known as Differential Evolution with a scheduling heuristic to search the design space efficiently. We demonstrate the effectiveness of our technique by comparing it to similar existing systems. The proposed strategy is shown to be faster than recent systems on large problems while providing equivalent or improved final solutions.

[Rog98] Rogalsky, T. (1998). Aerodynamic Shape Optimization of Fan Blades. M.Sc. Thesis. University of Manitoba. Department of Applied Mathematics. 1998.

[SA98] Schmitz, G. P. J. and Aldrich, C. (1998).  Neurofuzzy modeling of chemical process systems with ellipsoidal radial basis function neural networks and genetic algorithms. Computers & Chemical Engineering, Vol. 22, Supplement 1, pp. S1001-S1004, May 1998. 

Abstract: Non-parametric methods for the construction of empirical process models have been used successfully in a variety of contexts in the field of process engineering. Despite their ability to form accurate representations of chemical process systems, non-parametric models are usually difficult to interpret. This is a serious hindrance where a premium is placed on model reliability and transparency. In this paper it is shown that by making use of radial basis function neural networks with arbitrarily oriented ellipsoidal basis functions, more parsimonious process models can be constructed. As with other radial basis function neural networks, the radial basis kernels also lend themselves to the construction of fuzzy rules. The methodology is illustrated by means of a case study on induced aeration in agitated vessels.

[TK98] Tvrdík, Josef and Krivý, Ivan (1998). Experimental Comparison of Some Evolutionary Algorithms. In: Ošmera, Pavel (ed.) (1998). Proceedings of MENDEL'98, 4th International Mendel Conference on Genetic Algorithms, Optimization Problems, Fuzzy Logic, Neural Networks, Rough Sets. June 24-26, 1998, Brno, Czech Republic (1998). Technical University of Brno, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 220–225. ISBN 80-214-1199-6.

[WJT98] Wang, Feng-Sheng, Jing, Chang-Huei and Tsao, George T. (1998). Fuzzy-Decision-Making Problems of Fuel Ethanol Production Using a Genetically Engineered Yeast. Industrial & Engineering Chemistry Research, 37(8):3434–3443, August 1998. ACS, Washington, DC, USA. ISSN 0888-5885. 

Description: A hybrid differential evolution was used to solve a fuel ethanol production planning problem.
Abstract: A fuzzy-decision-making procedure is applied to find the optimal feed policy of a fed-batch fermentation process for fuel ethanol production using a genetically engineered Saccharomyces yeast 1400 (pLNH33). The policy consisted of feed flow rate, feed concentration, and fermentation time. The recombinant yeast 1400 (pLNH33) can utilize glucose and xylose simultaneously to produce ethanol. However, the parent yeast utilizes glucose only. A partially selective model is used to describe the kinetic behavior of the process. In this study, this partially selective fermentation process is formulated as a general multiple-objective optimal control problem. By using an assigned membership function for each of the objectives, the general multiple-objective optimization problem can be converted into a maximizing decision problem. In order to obtain a global solution, a hybrid method of differential evolution is introduced to solve the maximizing decision problem. A simple guideline is introduced in the interactive programming procedures to find a satisfactory solution to the general multiple-objective optimization problem.

1999

[BS99] Babu, B.V. and Sastry, K.K.N. (1999). Estimation of heat transfer parameters in a trickle-bed reactor using differential evolution and orthogonal collocation. Computers & Chemical Engineering 23(3):327–339, 28 Feb 1999. Elsevier Science Ltd. (Engl.). ISSN 0098-1354. Available via Internet:  http://www.icsi.berkeley.edu/~storn/Tbrde.pdf or http://www.bvbabu.50megs.com/about.html . 

Abstract: A new non-sequential technique is proposed for the estimation of effective heat transfer parameters using radial temperature profile measurements in a gas-liquid co-current downflow through packed bed reactors (often referred to as trickle bed reactors). Orthogonal collocation method combined with a new optimization technique, differential evolution (DE) is employed for estimation. DE is an exceptionally simple, fast and robust, population based search algorithm that is able to locate near-optimal solutions to difficult problems. The results obtained from this new technique are compared with that of radial temperature profile (RTP) method. Results indicate that orthogonal collocation augmented with DE offer a powerful alternative to other methods reported in the literature. The proposed technique takes less computational time to converge when compared to the existing techniques without compromising with the accuracy of the parameter estimates. This new technique takes on an average 10 s on a 90 MHz Pentium processor as compared to 30 s by the RTP method. This new technique also assures of convergence from any starting point and requires less number of function evaluations.

[Ber99] Bergey, P.K. (1999). An agent enhanced intelligent spreadsheet solver for multi-criteria decision making. Proceedings of AIS AMCIS 99: 1999 Americas Conference on Information Systems, 13-15 August 1999; Milwaukee (USA), pp. 966-968. 

Abstract: Recently, a great deal of research interest has been spawned in the use of evolutionary algorithms (EAs) for the multi-criteria decision making (MCDM) problem because of the EA's unique ability to provide multiple Pareto optimal solutions in a single run. This can be accomplished without any prerequisite information about preferences from the decision maker (DM). To this end, the author is developing a decision support system (DSS) that provides the DM with a set of Pareto optimal (non-dominated) solutions to constrained MCDM problems. The search procedure used to generate the Pareto set is based upon a recently introduced algorithm known as Differential Evolution (DE). DE has shown considerable promise for global optimization of a single, continuous space objective function. The author has made several enhancements to DE to address multiple objective functions. The DSS provides the DM with a set of alternative non-dominated solutions from which to choose. The enhanced algorithm is referred to as Pareto Differential Evolution (PDE). PDE is implemented as a general-purpose spreadsheet solver designed as an add-in for Microsoft Excel. The primary objective of PDE is to help the DM with making better decisions. To accomplish this task PDE provides an interface that is intuitive to use and simple to map MCDM problems into. While EAs generally require specified control parameters to search efficiently, PDE shields the DM from such tasks to the extent that the DM is completely unaware that an EA is even used in the optimization process.

[CFRS99] Candela, R., Fileccia Scimemi, G., Romano, P. and Sanseverino, E.R. (1999). Analysis of Partial Discharge activity at different temperatures through an Heuristic Algorithm. In: 1999 Annual Report Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), October 17–20, 1999. Vol. 1 , pp.202–205. IEEE, Piscataway, NJ, USA. ISBN 0-7803-5414-1. 

Abstract: Partial discharge, PD, activity is strongly influenced by the temperature. The analysis of PD phenomenon in a void embedded in an insulating material is a difficult problem because such voids are physically inaccessible. On the basis of a numerical model for the simulation of PD activity, it is possible to give a good interpretation of the physical parameters values. The developed model is stochastic and it depends on these parameters, which need to be optimised as the temperature changes. On this purpose, an Evolutionary Algorithm has been used for the parameters optimisation. This algorithm is a Differential Evolution strategy for non-linear optimisation with mixed continuous and discrete variables. For this application, it has proved to be more efficient as compared to other enhanced evolutionary algorithms. In the search algorithm, the objective function has been calculated by means of the Weibull distribution, which is used to extract valuable information from a set of stochastic data. In this way, it is possible to compare the cumulative probability distribution of the experimental data and of the calculated data.

[CXQ99] Chang, C.S., Xu, D.Y. and Quek, H.B. (1999). Pareto-optimal set based multiobjective tuning of fuzzy automatic train operation for mass transit system. IEE Proceedings on Electric Power Applications, 146(5):577–583, September 1999. 

Description: A novel approach of differential evolution (DE) by incorporating the Pareto-optimal set is presented for optimising train movement through tuning fuzzy membership functions in mass transit systems.

[CD99] Chang, C.S. and Du, D. (1999). Further improvement of optimisation method for mass transit
signalling block-layout design using differential evolution. IEE Proceedings on Electric Power Applications, 146(5):559–569, September 1999. 

Description: The paper describes the ongoing development of optimisation methods for the layout design of equi-block n-aspect mass transit signalling systems.

[CL99] Cheong, F. and Lai R. (1999). Designing a hierarchical fuzzy logic controller using differential evolution. In: Proceedings of 1999 IEEE International Fuzzy Systems Conference, FUZZ-IEEE'99, August 22.–25. 1999, Seoul, Korea. Vol.1, pp.277–282.  IEEE, Piscataway, NJ, USA.

[CW99] Ji-Pyng Chiou and Feng-Sheng Wang (1999). Hybrid method of evolutionary algorithms for static and dynamic optimization problems  with application to a fed-batch fermentation process. Computers and Chemical Engineering 23(9):1277–1291, November 1999. ISSN 0098-1354. 

Abstract: A hybrid algorithm of evolutionary optimization, called hybrid differential evolution (HDE), is developed in this study. The acceleration phase and migration phase are embedded into the original algorithm of differential evolution (DE). These two phases are used to improve the convergence speed without decreasing the diversity among individuals. With some assumptions, this hybrid method is shown as a method using N_p parallel processors of the two member evolution strategy, where N_p is the number of individuals in the solution space. The multiplier updating method is introduced in the proposed method to solve the constrained optimization problems. The topology of the augmented Lagrange function and the necessary conditions for the approach are also inspected. The method is then extended to solve the optimal control and optimal parameter selection problems. A fed-batch fermentation example is used to investigate the effectiveness of the proposed method. For comparison, several alternate methods are also employed to solve this process.

[Chi99] Chisholm, K.J. (1999). Co-evolving Draughts Strategies with Differential Evolution. In: David Corne, Marco Dorigo and Fred Glover (editors) (1999). New Ideas in Optimization. McGraw-Hill, London (UK), pp. 147–158. ISBN 007-709506-5.

[DCC99a] Doyle, S., Corcoran, D. and Connell, J. (1999). Automated mirror design using an evolution strategy. Optical Engineering 38(2):323–333, February 1999. SPIE - The International Society for Optical Engineering. ISSN 0091-3286. 

Abstract: We describe how an evolution strategy is used to automate the design of luminaire reflectors. In particular, we outline a computer simulation, consisting of a 2-D optical reflector with point light source, which is implemented for this purpose. The reflector shape is modeled using a Bezier curve representation, and photometric distributions are calculated in the near, middle and far fields using a ray-tracing approach. The automation of the design process is achieved through the use of a novel evolution strategy, termed differential evolution. For the effective operation of differential evolution, a merit function specific to luminaire reflector design is presented. Finally, we describe our investigation into the validity of the evolution strategy approach to reflector design. Based on our results, we propose that the technique is not only valid but also feasible.

[DCC99b] Doyle, S., Corcoran, D. and Connell, J. (1999). Automated mirror design for an extented light source. Proceedings of SPIE – The International Society for Optical Engineering 3781, pp. 94-102. Nonimaging Optics: Maximum Efficiency Light Transfer V., 21.–22 July 1999, Denver, CO, USA. SPIE Society of Photo-Optical Instrumentation Engineers. 

Abstract: A computer package, Automated Mirror Design, has been developed by us to automate the design of luminaire reflectors. In this paper, new improvements to the algorithm for Automated Mirror Design are presented. We have previously reported a study on a series of point-light source luminaire problems. We now report on the operation of Automated Mirror Design for non-trivial light sources. In particular, reflector designs are presented for an extended light source, which produce limited Lambertian output and return no radiation to the source. Finally, the operation of differential evolution relies on the use of an appropriate merit function to determine the quality of proposed mirror designs. Merit functions specific to the Lambertian output design problem are discussed.

[EM99] Robert F. Engle and Simone Manganelli (1999). CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. UCSD Economics Discussion Paper 99-20, University of California, San Diego, Department of Economics. October 1999. Available via Internet: http://www.socialsciences.ucsd.edu/Depts/Econ/Wpapers/dp99.html#99-20 . 

Abstract: Value at Risk (VaR) has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. VaR is defined as the value that a portfolio will lose with a given probability, over a certain time horizon (usually one or ten days). Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting the VaR as the quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Autoregressive Value-at-Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We specify the evolution of the quantile over time using a special type of autoregressive process and use the regression quantile framework introduced by Koenker and Bassett to determine the unknown parameters. Since the objective function is not differentiable, we use a differential evolutionary genetic algorithm for the numerical optimization. Utilizing the criterion that each period the probability of exceeding the VaR must be independent of all the past information, we introduce a new test of model adequacy, the Dynamic Quantile test. Applications to simulated and real data provide empirical support to this methodology and illustrate the ability of these algorithms to adapt to new risk environments.

[FHR99a] Manfred M. Fischer, Katerina Hlavackova-Schindler and Martin Reismann (1999). A global search procedure for parameter estimation in neural spatial interaction modelling. Papers in Regional Science 78(2):119–134, 1999. ISSN 1056–8190. Available via Internet: http://wigeo.wu-wien.ac.at/~reismann/fhr99a.pdf.

Abstract: Parameter estimation is one of the central issues in neural spatial interaction modelling. Current practice is dominated by gradient based local minimization techniques. They find local minima efficiently and work best in unimodal minimization problems, but can get trapped in multimodal problems. Global search procedures provide an alternative optimization scheme that allows to escape from local minima. Differential evolution has been recently introduced as an efficient direct search method for optimizing real-valued multi-modal objective functions (Storn and Price 1997). The method is conceptually simple and attractive, but little is known about its behavior in real world applications. This article explores this method as an alternative to current practice for solving the parameter estimation task, and attempts to assess its robustness, measured in terms of in-sample and out-of-sample performance. A benchmark comparison against backpropagation of conjugate gradients is based on Austrian interregional telecommunication traffic data.

[FHR99b] Manfred M. Fischer, Katerina Hlavackova-Schindler and Martin Reismann (1999). An evolutionary mutation-based algorithm for weight training in neural networks for telecommunication flow modelling. In: M. Mohammadian (ed.), Computational Intelligence for Modelling, Control and Automation. Evolutionary Computation and Fuzzy Logic for Intelligent Control, Knowledge Acquisition and Information Retrieval, 17.-19. February 1999; Vienna, Austria. Concurrent Systems Engineering Series Vol.55, pp. 54–59. IOS Press, Amsterdam, Netherlands. 

Abstract:  The training of perceptron networks with sigmoidal activation functions is executed by a new evolutionary algorithm, DE (differential evolution) (Storn and Price, (1997)). On this evolutionary optimization method, we apply a search space reduction algorithm and compare this approach to training by standard DE and training by the conjugate gradient method. The testbed is Austrian interregional telecommunication traffic data. In our experiments, DE with only mutation was able to achieve better suboptimal solutions than DE together with crossover and search space reduction. DE with mutation only outperforms the conjugate gradient method in terms of in-sample and out-of-sample performance. The experimental results support the hypothesis that mutation-based evolutionary algorithms (like DE) tend to be more suitable methods for training perceptron networks than crossover-based evolutionary algorithms and gradient-based methods (Fogel, 1995).

[FRH99c] Manfred M. Fischer, Martin Reismann and Katerina Hlavackova-Schindler (1999). Parameter estimation in neural spatial interaction modelling by a derivative free global optimization method. The IV International Conference on GeoComputation, Mary Washington College, Fredericksburg, VA, USA, 25-28 July 1999. Available via Internet: http://www.geovista.psu.edu/sites/geocomp99/Gc99/007/gc_007.htm . 

Abstract: Parameter estimation is one of the central issues in neural spatial interaction modelling. Current practice is dominated by gradient-based local minimization techniques. They find local minima efficiently and work best in unimodal minimization problems, but can get trapped in multimodal problems. Global search procedures provide an alternative optimization scheme that allows to escape from local minima. Differential Evolution has been recently introduced as an efficient direct search method for optimizing real-valued multi-modal objective functions (Storn and Price 1996). The method is conceptually simple and attractive, but little is known about its behaviour in real world applications. This paper explores this method as an alternative to current practice for solving the parameter estimation task, and attempts to assess its robustness, measured in terms of in-sample and out-of-sample performance. A benchmark comparison with backpropagation of conjugate gradients illustrates the superiority of Differential Evolution.

[JS99] Joshi, Rajive and Sanderson, Arthur C. (1999). Minimal representation multisensor fusion using differential evolution. IEEE Transactions on Systems, Man and Cybernetics, Part A 29(1):63–76, Jan. 1999. ISSN: 1083-4427. 

Abstract: Fusion of information from multiple sensors is required for planning and control of robotic systems in complex environments. The minimal representation approach is based on an information measure as a universal yardstick for fusion and provides a framework for integrating information from a variety of sources. In this paper, we describe the principles of minimal representation multisensor fusion and evaluate a differential evolution approach to the search for solutions. Experiments in robot manipulation using both tactile and visual sensing demonstrate that this algorithm is effective in finding useful and practical solutions to this problem for real systems. Comparison of this differential evolution algorithm with more traditional genetic algorithms shows distinct advantages in both accuracy and efficiency.

[KB99] Kasemir, K.-U. and Betzler, K. (1999). Characterization of photorefractive materials by spontaneous noncolinear frequency doubling. Applied Physics B, Lasers and Optics, 68(5):763-766, 1999. Springer-Verlag. ISSN 0946-2171. 

Abstract: "Spontaneous" noncolinear frequency doubling (SNCFD) is a type of optical second-harmonic generation (SHG) that uses scattered light to provide additional fundamental beams in order to accomplish noncolinear phase matching. Based on a novel algorithm for the automated evaluation of the resulting ring patterns, we present an easy-to-apply, sensitive, and non-destructive method for the characterization of photorefractive materials, yielding two-dimensional spatial resolution. As applications of the technique, examples for the characterization of lithium niobate crystals are presented.

[KR99]Michal Kvasnicka and Bohuslav Ruzek (1999). Earthquake relocation in Corinth Gulf. Inco-Copernicus COME Final Research Report, Charles University, Prague (Czech Republic). Available at http://karel.troja.mff.cuni.cz/Greece/come/relrep.html.

[Lam99a] Jouni Lampinen (1999). Differential Evolution – new naturally parallel approach for engineering design optimization. In: Topping, B.H.V. (ed.), Euroconference: Parallel and Distributed Computing for Computational Mechanics 1999 EURO-CM-PAR99 – Abstracts, Lecture and Research Presentations, Weimar, Germany, 20–25 March 1999, pp. 35–36, Civil-Comp Press, Edinburgh (Scotland). 

Description: This abstract discusses shortly parallel implementation of DE. A cluster of workstations connected via LAN is used as a platform for parallel computation.

[Lam99b] Jouni Lampinen (1999). Differential Evolution – New Naturally Parallel Approach for Engineering Design Optimization. In: Barry H.V. Topping (ed.) (1999). Developments in Computational Mechanics with High Performance Computing. Civil-Comp Press, Edinburgh (Scotland), pp. 217–228. ISBN 0-948749-59-8. Available via Internet: http://www.lut.fi/~jlampine/ECMPAR99.ps . 

Abstract: In this article a parallel implementation of a quite recently introduced Differential Evolution algorithm for stochastic non-linear optimization is discussed. A new approach for efficient parallel implementation of Differential Evolution using a cluster of workstations connected via Local Area Network is suggested and the topics involved are discussed. This approach provides the required speed-up for optimization of computationally expensive objective functions such as computer simulation models of various technical systems.
    Shared disk files are used for introducing an asynchronous communication channel between the master and slave processes. The use of disk files makes it possible to implement the program without any special programming tools, like PVM or MPI. Furthermore, no special hardware is required. For example the most widely available platform, a cluster of PCs connected via Ethernet, can be used.
    Because the master process and slave processes are coupled only loosely via the shared interface files, the number of slave processes can be altered even during the optimization run. Both steady-state and generational reproduction of individuals can be used. Unlike than standard approach for parallelizing evolutionary optimization algorithms, the maximum number of involved slave processes is not limited by the population size of the master process.
    The other major advantages of the suggested parallel computing approach are easy implementation, flexibility, robustness and low idle times of slave processes resulting in a high efficiency of parallelization.

[Lam99c] Lampinen, Jouni (1999). A Bibliography of Differential Evolution Algorithm. Technical Report. Lappeenranta University of Technology, Department of Information Technology, Laboratory of Information Processing, 16th October 1999. Available via Internet  http://www.lut.fi/~jlampine/debiblio.htm.

Description: This document. A bibliography containing references to various publications discussing about Differential Evolution algorithm. Includes a short description or an abstract of each article.

[LZ99a] Jouni Lampinen – Ivan Zelinka (1999). Mechanical Engineering Design Optimization by Differential Evolution. In: David Corne, Marco Dorigo and Fred Glover (editors) (1999). New Ideas in Optimization. McGraw-Hill, London (UK), pp. 127–146. ISBN 007-709506-5. 

Description: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. An optimization method based on using the differential evolution algorithm for optimization of the object function and on using the soft-constraint approach for constraint handling is described. Also the required handling techniques for integer, discrete and continuous variables are described. Three mechanical engineering design related numerical examples, design of a gear train, design of a pressure vessel and design of a coil spring, are given to illustrate the capabilities and the practical use of the described method. The results are compared with the previous results found in literature, which are obtained by using other optimization methods. It is shown that the described approach is capable of obtaining high quality solutions. The novel method described is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.

[LZ99b] Jouni Lampinen – Ivan Zelinka (1999). Mixed Integer-Discrete-Continuous Optimization By Differential Evolution, Part 1: the optimization method. In: Ošmera, Pavel (ed.) (1999). Proceedings of MENDEL'99, 5th International Mendel Conference on Soft Computing, June 9.–12. 1999, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 71–76. ISBN 80-214-1131-7. Available via Internet: http://www.lut.fi/~jlampine/MEND99p1.ps (article) and http://www.lut.fi/~jlampine/MEND99tr.ps (presentation transparencies). 

Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The Part 1 of the article describes a novel optimization method based on Differential Evolution algorithm. The required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. In Part 2 of the article a mechanical engineering design related numerical example, design of a coil spring, is given to illustrate the capabilities and the practical use of the method. It is demonstrated that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.

[LZ99c] Jouni Lampinen – Ivan Zelinka (1999). Mixed Integer-Discrete-Continuous Optimization By Differential Evolution, Part 2: a practical example. In: Ošmera, Pavel (ed.) (1999). Proceedings of MENDEL'99, 5th International Mendel Conference on Soft Computing, June 9.–12. 1999, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 77–81. ISBN 80-214-1131-7. Available via Internet: http://www.lut.fi/~jlampine/MEND99p2.ps (article) and http://www.lut.fi/~jlampine/MEND99tr.ps (presentation transparencies). 

Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The Part 1 of the article describes a novel optimization method based on Differential Evolution algorithm. The required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. In Part 2 of the article a mechanical engineering design related numerical example, design of a coil spring, is given to illustrate the capabilities and the practical use of the method. It is demonstrated that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems.

[LZ99d] Jouni Lampinen – Ivan Zelinka (1999).Mixed Variable Non-Linear Optimization by Differential Evolution.In: Zelinka, Ivan (ed.) (1999). Proceedings of Nostradamus'99, 2nd International Prediction Conference, October 7.–8. 1999, Zlin, Czech Republic. Technical University of Brno, Faculty of Technology Zlin, Department of Automatic Control, Zlin (Czech Republic), pp. 45–55. ISBN 80-214-1424-3. Available via Internet: http://www.lut.fi/~jlampine/NOSTRA99.ps . 

Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. A novel mixed integer-discrete-continuous, non-linear optimization method based on Differential Evolution algorithm is described. Also the required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. Previous experiments and comparisons with other methods for mixed integer-discrete-continuous non-linear optimization have suggested that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use. It is found to be effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical problems in the field of prediction.

[LHC99] Lee, M. H., Han, C. and Chang, K. S. (1999). Dynamic Optimization of a Continuous Polymer Reactor Using a Modified Differential Evolution Algorithm. Industrial & Engineering Chemistry Research 38(12):4825-4831.

[LTT99] Li Gang, Tu Yiqing and Tong Fu (1999). A Fast Evolutionary Algorithm for Neural Network Training Using Differential Evolution. In: Luo, J., Xu, B., Wang, Y., Li, X and Lu, J. (editors) (1999). Proceedings of ICYCS'99, Fifth International Conference for Young Computer Scientists. vol.1. 17-20 August 1999; Nanjing, China. Volume 1, pp. 507–511. Int. Acad. Publishers, Beijing, China. 

Abstract: A new evolutionary algorithm for determining the weights in a neural network is proposed. This algorithm is based on differential evolution, a powerful yet simple evolutionary optimization approach over continuous space, and it is easy to use and capable of evolving the network weights simultaneously. Experimental results show that this algorithm is faster than traditional evolutionary approaches such as genetic algorithms when training a neural network.

[LWH99] Yung-Chien Lin, Feng-Sheng Wang and Kao-Shing Hwang (1999). A hybrid method of evolutionary algorithms for mixed-integer nonlinear optimization problems. Proceedings of the 1999 Congress on Evolutionary Computation, CEC'99, Vol. 3, pp.2159–2166. IEEE, Piscataway, NJ, USA. ISBN 0-7803-5536-9. 

Description: A hybrid method of evolutionary algorithms, called mixed-integer hybrid differential evolution (MIHDE), is proposed in this study.

[PH99] Pahner, U. and Hameyer, K. (1999). Adaptive coupling of differential evolution and multiquadrics approximation for the tuning of the optimization process.  In: Proceedings of 12th Conference on the Computation of Electromagnetic Fields-COMPUMAG, Sapporo, Japan, October 25-28, 1999, Vol.1, OB-3, pp.116-117.

[PV99a] Plagianakos, V. P. and Vrahatis, M. N. (1999). Neural Network Training with Constrained Integer Weights. Proceedings of the 1999 Congress on Evolutionary Computation, CEC'99, Vol. 3, pp.2007–2013. IEEE, Piscataway, NJ, USA. ISBN 0-7803-5536-9. 

Description: Training of Neural Networks with integer weights applying Differential Evolution algorithm was under investigations.

[PV99b] Plagianakos, V. P. and Vrahatis, M. N. (1999). Training Neural Networks with 3-bit Integer Weights. In: Banzhaf, W,. Daida J., Eiben A.E., Garzon M.H., Honavar V., Jakiela M., Smith R.E. (editors) (1999). Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, Orlando, USA, 13-17 July 1999, Vol. 1, pp. 910–915. Morgan Kaufmann Publishers, San Francisco, CA, USA. 

Abstract: We present neural network training algorithms, which are based on the differential evolution (DE) strategies introduced by R. Storn and K. Price (1997). These strategies are applied to train neural networks with 3-bit integer weights. Integer weight neural networks are better suited for hardware implementation than their real weight analogous. Moreover, we constrain the weights and biases in the range [-3, 3], thus, they can be represented by just 3 bits. This property reduces the amount of memory required and simplifies the digital multiplication operation. Our intention is to present a broad picture of the behavior of this class of evolution algorithms in this difficult task. Simulation results from classical benchmarks show that these methods are promising, fast, and reliable.

[Pri99] Price, Kenneth V. (1999). An Introduction to Differential Evolution. In: David Corne, Marco Dorigo and Fred Glover (editors) (1999). New Ideas in Optimization. McGraw-Hill, London (UK), pp. 79–108. ISBN 007-709506-5.

[RSR99] Richardson, T., Shokrollahi, A. and Urbanke, R. (1999). Design of provably good low-density parity-check codes. Available via Internet: http://www.wavelet.org/cm/ms/who/amin/pub.html .

[RM99] Rigling, B.D. and Moore, F.W. (1999). Exploitation of sub-populations in evolution strategies for improved numerical optimization. In: Proceedings of the Tenth Midwest Artificial Intelligence and Cognitive Science Conference (MAICS-99), pp. 80–88. AAAI Press, Menlo Park, CA, USA. 

Description: This paper describes the use of a modified differential evolution strategy that identifies multiple solutions to the numerical optimization of multidimensional objective functions.

[RDK99a] Rogalsky, T., Derksen, R.W. and Kocabiyik, S. (1999). Differential Evolution in Aerodynamic Optimization. In: Proceedings of the 46th Annual Conference of the Canadian Aeronautics and Space Institute, May 2-5 1999, pp 29-36. Available via Internet: http://home.cc.umanitoba.ca/~umrogal1/publications.html.

Abstract: Aerodynamic design algorithms require an optimization strategy to search for the best design. The object of this paper is to compare the performance of some different strategies when used by an aerodynamic shape optimization routine which designs fan blade shapes. A recently developed genetic algorithm, Differential Evolution, outperforms more traditional techniques.

[RDK99b] Rogalsky, T., Derksen, R.W. and Kocabiyik, S. (1999). An Aerodynamic Design Technique for Optimizing Fan Blade Spacing. In: Proceedings of the 7th Annual Conference of the Computational Fluid Dynamics Society of Canada, May 30–June 1 1999, pp 2-29 – 2-34. Available via Internet: http://home.cc.umanitoba.ca/~umrogal1/publications.html.

Abstract: Aerodynamic shape optimization involves designing the most efficient shapes of bodies that move through fluids. An optimization algorithm perturbs the shape of an airfoil until it finds the shape which best exhibits a given design objective. For an inverse design technique, this objective is a prescribed aerodynamic distribution, usually the surface pressure distribution. Liebeck pressure distributions, for example, have been demonstrated to generate airfoils with high lift to drag ratios.
    When designing fans, consideration must be given not only to the shape of the fan blades, but also to the distance separating the fan blades. This spacing is defined by the pitch/chord ratio t/l, where the pitch, t, is the distance between fan blades, and the chord, 1, is the length of each fan blade. In this work, an inverse algorithm is developed, then used to design fan blade shapes and to find the optimal blade spacing.

[RDK99c] Rogalsky, T., Derksen, R.W. and Kocabiyik, S. (1999). Optimal Optimization in Aerodynamic Design. In: Proceedings of the 17th Canadian Congress of Applied Mechanics, May 30–June 3 1999.

[SBN99] K. K. N. Sastry, L. Behera, I. J. Nagrath (1999). Differential Evolution Based Fuzzy Logic Controller for Nonlinear Process Control. Fundamenta Informaticae 37(1–2):121–136, January 1999. ISSN 0169-2968. 

Abstract: This paper presents an unconventional approach to adaptive fuzzy logic controller (FLC) design wherein a new evolution strategy, Differential Evolution (DE) is used in the simultaneous design of membership functions and rule sets for fuzzy logic controllers. Differential Evolution is an exceptionally simple, fast, and robust population based search algorithm that is able to locate near-optimal solutions to difficult problems. This technique, which is similar to genetic algorithms, has been applied to the control of pH, which is a requirement in many chemical industries. Control of pH poses a difficult problem because of inherent nonlinearities and frequently changing process dynamics. This technique has been successfully implemented on a laboratory scale pH plant setup. The results have been compared with a simple GA based adaptive FLC where we have incorporated a search space smoothing function for achieving faster convergence and for ascertaining a global optimum. Results indicate that FLC's augmented with DE's offer a powerful alternative to GA based FLC's. Results also show that the search space smoothing function helps in faster convergence of a GA.

[Sch99]Gregor P.J. Schmitz (1999). Combinatorial Evolution of Feedforward Neural Network Models for Chemical Processes. Ph.D. Thesis, University of Stellenbosch, June 1999.  Available via Internet: http://www.lut.fi/~jlampine/schmitz.zip. See also [SA99]. 

Summary: The proposed combinatorial selection scheme was able to make an existing evolutionary algorithm significantly faster for neural network optimisation. This made it computationally competitive with traditional gradient descent based techniques. Being an evolutionary algorithm, the proposed technique does not require a gradient and can therefore optimise a larger set of parameters in comparison to traditional techniques.

[SA99]Gregor P.J. Schmitz and ChrisAldrich (1999). Combinatorial evolution of regression nodes in feedforward neural networks. Neural Networks 12(1):175-189, 1999. See also [Sch99]. 

Abstract: A number of techniques exist with which neural network architectures such as multilayer perceptrons and radial basis function networks can be trained. These include backpropagation, k-means clustering and evolutionary algorithms. The latter method is particularly useful as it is able to avoid local optima in the search space and can optimise parameters for which no gradient information exists. Unfortunately, only moderately sized networks can be trained by this method, owing to the fact that evolutionary optimisation is very computationally intensive In this paper a novel algorithm (CERN) is therefore proposed which uses a special form of combinatorial search to optimise groups of neural nodes. Oriented, ellipsoidal basis nodes optimised with CERN achieved significantly better accuracy with fewer nodes than spherical basis nodes optimised by k-means clustering. Multilayer perceptrons optimised by CERN were found to be as accurate as those trained by advanced gradient descent techniques. CERN was also found to be significantly more efficient than a conventional evolutionary algorithm that does not use a combinatorial search.

[She99] Shepherd, Ross (2000). Implementing breeding programs tactically – the origin of total genetic resource management. In: Proceedings of the Breeding Technologies Workshop, 10th November 1999, Tropical Beef Centre, North Rockhampton, Queensland (Australia). See also [She00].

Abstract: A tactical approach to the design of breeding programs is presented which integrates technical, logistical and cost issues facing animal breeders. It is opportunistic in that it uses actual animals and prevailing costs and resources to produce better outcomes than a static approach using preset breeding rules. It involves developing a Mate Selection Index (MSI) which describes net economic merit in terms of selection and mating decisions, and then implementing a mate selection algorithm which searches for the best mating solution in terms of the MSI. Total Genetic Resource Management (TGRM) is a new service for breeders offering a tactical mate selection approach to the implementation of their breeding programs. The paper discusses TGRM in detail, focussing on the inputs required and the output generated, in addition to how decisions (eg. on advanced reproductive technology) are made. Future developments, with genetic markers and in Total Resource Management, are briefly discussed.

[SS99] Shokrollahi, Amin M. and Storn, Rainer (1999). Design of Efficient Erasure Codes with Differential Evolution. Available via Internet: http://www.wavelet.org/cm/ms/who/amin/pub.html . 

Abstract: The design of practical and highly powerful codes for protection against erasures in digital communication can be reduced to optimizing solutions of a highly nonlinear constraint satisfaction problem. In this paper we will attack this problem using the Differential Evolution approach and significantly improve results previously obtained using classical optimization procedures.

[Sto99a] Storn, Rainer (1999). System Design by Constraint Adaptation and Differential Evolution. IEEE Transactions on Evolutionary Computation, 3(1):22–34, April 1999. ISSN 1089-778X.  See also [Sto96b].

Abstract: A simple optimization procedure for constraint-based problems is described which works with a simplified cost function or even without one. The simplification of the problem formulation makes this method particularly attractive. The new method lends itself to parallel computation and is well suited for constraint satisfaction, constrained optimization, and design centering problems. A further asset is its self-steering property which makes the new method easy to use.

[Sto99b] Storn, Rainer (1999). Designing Digital Filters with Differential Evolution. In: David Corne, Marco Dorigo and Fred Glover (editors) (1999). New Ideas in Optimization. McGraw-Hill, London (UK), pp. 109–125. ISBN 007-709506-5.

[Sto99c] Storn, Rainer (1999). DeApp – An Application in Java for the Usage of Differential Evolution. Technical report. Available via Internet: http://http.icsi.berkeley.edu/~storn/code.html#java.

Abstract: This document contains a brief overview of the Java based application DeApp. The latter is set out to provide an easily extendable and plattform independent-framework to solve function optimization problems with Differential Evolution (DE).

[SDPH99] Stumberger, G., Dolinar, D., Pahner, U. and Hameyer, K. (1999). Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm. In: Proceedings of 12th Conference on the Computation of Electromagnetic Fields-COMPUMAG, Sapporo, Japan, October 25-28, 1999, Vol.2, PE3-5, pp.508-509.

[SDSPH99] Gorazd Stumberger, Drago Dolinar, Bojan Stumberger, Uwe Pahner and Kay Hameyer (1999). Optimiranje radialnega aktivnega magnetnega lezaja. Elektrotehniski Vestnik/Electrotechnical Review 66(4-5):307-313, 1999. Elektrotehniska Zveza Slovenije. ISSN 0013-5852. In Slovenian. 

Abstract: The numerical optimization of a radial active magnetic bearing using a direct stochastic search algorithm is presented. The aim is to achieve a maximum force at a maximum mass of the entire construction. The optimization is carried out in a special environment tuned for finite element method based numerical optimization. The obtained results make it possible to evaluate the robustness of the control algorithm. Moreover, they can be approximated by a continuous function, which is further used for the linearization in the entire operating range, and altogether applied in the synthesis of the nonlinear bearing control.

[Tho99] P. Thomas (1999). Genetic Algorithms and Inverse Fractal Problem. Available from http://www.cs.may.ie/~pthomas/inv_frac_ga/index.html.

Description: This www-page describes some research done in using a GA to tackle the inverse fractal problem.

[TK99a] Tvrdík, Josef and Krivý, Ivan (1999). Evolutionary Heuristics in Nonlinear Regression. In: Ošmera, Pavel (ed.) (1999). Proceedings of MENDEL'99, 5th International Mendel Conference on Soft Computing, June 9.–12. 1999, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 59–64. ISBN 80-214-1131-7.

[TK99b] Tvrdík, Josef and Krivý, Ivan (1999). SimpleEvolutionary Heuristics for Global Optimization. Computational Statistics & Data Analysis, 30(3):345–352, 28 May 1999. 

Description: The paper deals with the empirical comparison of five evolutionary algorithms. One of them is closely related to the controlled random search, another two are based on evolutionary search and remaining two on differential evolution. The testbed consists of six functions widely used for testing of optimization algorithms.

[WGJ99] Watson, G.H., Gilholm K. and Jones, J.G. (1999). A wavelet-based method for finding inputs of given energy which maximize the outputs of nonlinear systems. International Journal of Systems Science 30(12):1297–1307, December 1999. 

Abstract: In this paper we describe an algorithm designed to find those deterministic inputs, subject to an energy constraint, which maximize the outputs of nonlinear systems. One of the main applications of the algorithm is in finding the most likely causes of system failure. In such situations, the input energy is related to the probability of occurrence of the inputs, and the aim is to determine those inputs with the highest probability of occurrence that cause the output to exceed a specified failure threshold. To find the desired inputs, the proposed algorithm employs a wavelet packet representation of system inputs and uses a search method based on the differential evolution according to Storn and Price (1997). The performance of the algorithm is demonstrated upon three different systems and compared with two other approaches described in the literature. The first two systems are configurations of a realistic model of a commercial wide-body aircraft where structural failure in extreme air turbulence is of interest, while the third system concerns the noise-induced escape of a particle from a potential well. There are a large number of other potential applications, including false alarms in signal processing and pattern recognition, the nonlinear response of buildings to seismic disturbances, the response of ships and off-shore structures to sea waves and the study of metastable states of system equilibrium.

[WC99] Wang, F-S; Cheng, W-M (1999). Simultaneous Optimization of Feeding Rate and Operation Parameters for Fed-Batch Fermentation Processes. Biotechnology Progress 15(5):949–952, October 1999. ISSN 8756-7938. 

Abstract: An efficient method is introduced for simultaneously determining optimal polices of feeding rate and operation parameters for a fermentation process. Such an optimization problem is converted into the finite dimensional optimization problem using the control parametrization technique. The hybrid differential evolution is introduced to solve the converted problem. The optimal production rate obtained by the simultaneous optimization approach could be significantly improved with comparison to a simplified optimization problem, which is considered the optimal feed control only, as observed from the simulation results.

[WPMB99] M. Wormington, C. Panaccione, K. M. Matney and D. K. Bowen (1999). Characterization of structures from X-ray scattering data using genetic algorithms. The Royal Society, Philosophical Transactions: Mathematical, Physical and Engineering Sciences 357(1761):2827–2848, 15 October 1999. London, UK. 

Abstract: We have developed a procedure for fitting experimental and simulated X-ray reflectivity and diffraction data in order to automate and to quantify the characterization of thin-film structures. The optimization method employed is a type of genetic algorithm called `differential evolution'. The method is capable of rapid convergence to the global minimum of an error function in parameter space even when there are many local minima in addition to the global minimum. We show how to estimate the pointwise errors of the optimized parameters, and how to determine whether the model adequately represents the structure. The procedure is capable of fitting some tens of adjustable parameters, given suitable data.

[Zel99] Ivan Zelinka (1999). Applikovaná informatika. Brno University of Technology, Faculty of Technology, Zlín, Czech Republic. ISBN 80-214-1423-5. 

Description: A stydying book on fractal geometry, evolutionary algorithms, neural networks, etc. A detailed discussion about differential evolution algorithm is included with practical examples. In Czech language.

[ZL99a] Ivan Zelinka and Jouni Lampinen (1999). Inverse Fractal Problem by Means of Evolutionary Algorithms. In: Ošmera, Pavel (ed.) (1999). Proceedings of MENDEL'99, 5th International Mendel Conference on Soft Computing, June 9.–12. 1999, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 430–435. ISBN 80-214-1131-7. 

[ZL99b] Ivan Zelinka and Jouni Lampinen (1999).DELA – an Evolutionary Learning Algorithms for Neural Networks. In: Ošmera, Pavel (ed.) (1999). Proceedings of MENDEL'99, 5th International Mendel Conference on Soft Computing, June 9.–12. 1999, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 410–414. ISBN 80-214-1131-7. 

[ZL99c] Ivan Zelinka and Jouni Lampinen (1999).Evolutionary Identification of Predictive Models.In: Zelinka, Ivan (ed.) (1999). Proceedings of Nostradamus'99, 2nd International Prediction Conference, October 7.–8. 1999, Zlin, Czech Republic. Technical University of Brno, Faculty of Technology Zlin, Department of Automatic Control, Zlin (Czech Republic), pp. 114–122. ISBN 80-214-1424-3.

2000

[AHHJL00] Ainslie, E.A., Hamson, R.M., Horsley G.D., James A.R., Laker R.A., Lee, M.A., Miles, D.A., Richards, S.D. (2000). Deductive multi-tone inversion of seabed parameters. Journal of Computational Acoustics 8(2):274-284, June 2000. 

Abstract: An iterative matched field processing scheme is described for efficient inversion of geoacoustic parameters in shallow water using a vertical receiving array at three frequencies in the range 50-500 Hz. The method relies on the assumption that the acoustic data are sensitive to different geoacoustic parameters at different frequencies. First an exhaustive 2D search is carried out at high frequency to determine initial estimates for density and sound speed. A second 2D search follows at an intermediate frequency to determine sediment attenuation and sound speed gradient. An iteration is carried out over these first two phases until these four parameters converge. In a third phase, the low frequency data are used to search for the remaining unknown parameters (primarily sediment thickness, substrate density and substrate sound speed) with a differential evolution algorithm. Finally all three phases are repeated iteratively, in principle until a complete converged solution (a self-consistent set of all inverted parameters) is found, although for practical reasons the search is terminated before convergence is demonstrated. Tests on synthetic data are reported demonstrating the accuracy and stability of the method. Initial results for measured data are also presented.

[BC00] Babu, B.V. and Chaturvedi, Gaurav (2000). Evolutionary Computation strategy for optimization of an Alkylation Reaction. Proceedings of International Symposium & 53rd Annual Session of IIChE (CHEMCON-2000), Science City, Calcutta, December 18-21, 2000. Available via Internet: http://bvbabu.50megs.com/custom.html/#31.

[BM00a] Babu, B.V. and Munawar, S.A. (2000). Optimal Design of Shell-and-Tube Heat Exchangers by Different Strategies of Differential Evolution. Available via Internet: http://www.bvbabu.50megs.com/about.html . 

Abstract: This paper presents the application of Differential Evolution (DE) for the optimal design of shell-and-tube heat exchangers. The main objective in any heat exchanger design is the estimation of the minimum heat transfer area required for a given heat duty, as it governs the overall cost of the heat exchanger. Lakhs of configurations are possible with various design variables such as outer diameter, pitch, and length of the tubes; tube passes; baffle spacing; baffle cut etc. Hence the design engineer needs an efficient strategy in searching for the global minimum. In the present study for the first time DE, an improved version of Genetic Algorithms (GAs), has been successfully applied with different strategies for 1,61,280 design configurations using Bell’s method to find the heat transfer area. In the application of DE 9680 combinations of the key parameters are considered. For comparison, GAs are also applied for the same case study with 1080 combinations of its parameters. For this optimal design problem, it is found that DE, an exceptionally simple evolution strategy, is significantly faster compared to GA and yields the global optimum for a wide range of the key parameters.

[BM00b] Babu, B.V. and Munawar, S.A. (2000). Differential Evolution for the Optimal Design of Heat Exchangers. Proceedings of All India Seminar on Chemical Engineering Progress on Resource Development: A Vision 2010 and Beyond, organized by IE (I), Orissa State Centre Bhuvaneshwar, March 13, 2000. Available via Internet: http://bvbabu.50megs.com/custom.html/#28.

[BVI00] Banga, Julio R., Karina J. Versyck and van Impe, Jan F. (2000). Numerical strategies for optimal experimental design for parameter identification of non-linear dynamic (bio-)chemical processes. In: S. Pieruci (Ed.) (2000). Computer-Aided Chemical Engineering, Vol. 8,  pp. 37-43. Elsevier, Amsterdam. ISBN 0-444-50520-2. Available via Internet: http://www.iim.csic.es/~julio/conferen.html . 

Abstract: The problem of optimal experimental design (OED) for parameter estimation of non-linear dynamic systems is considered. It is shown how this problem can be formulated as a dynamic optimization (optimal control) problem where the performance index is usually a scalar function of the Fisher information matrix. Numerical solutions can be obtained using direct methods, which transform the original problem into a nonlinear programming (NLP) problem via discretizations. However, due to the frequent non-smoothness of the cost functions, the use of gradient-based methods to solve this NLP might lead to local solutions. Stochastic methods of global optimization are suggested as robust alternatives. A case study considering the OED for parameter estimation in a fed-batch bioreactor is used to illustrate the performance and advantages of two selected stochastic algorithms.

[BSLSH00] Yair Bartal, Zeev Somer, Gideon Leonard, David M. Steinberg and Yochai Ben Horin (2000). Optimal Seismic Networks in Israel in the Context of the Comprehensive Test Ban Treaty. Bulletin of the Seismological Society of America 90(1):151-165, February 2000. Abstract available via Internet: http://www.seismosoc.org/publications/BSSA_html/bssa_90-1/98164.htm . 

Abstract: The International Monitoring System (IMS) location capability in the Eastern Mediterranean region is limited by the network sparseness. The addition of Cooperating National Facility (CNF) stations is one way to enhance location capability. The sites for such stations should be located so as to minimize the area of the 90% confidence-error ellipse. In this study, configurations of potential CNF stations in Israel are optimized, based on a representative set of seismic events. Appropriate total error variance comprised of model and measurement errors is estimated based on 1997 regional events. A genetic algorithm (GA) technique is used for the optimization. It is compared to the differential evolution (DE) technique and to random search (RS) and found superior but not by a great margin, which indicates that the optimization problem is not hard to solve. Configurations proposed by expert seismologists are compared to the computerized solution and are found inferior. Adding a few potential CNF stations in Jordan improves the location capability significantly.

[CM00] Chakraborti N. and Mukherjee A. (2000). Optimisation of continuous casting mould parameters using genetic algorithms and other allied techniques. Ironmaking and Steelmaking 27(3):243-247. ISSN 0301-9233. Institution of Materials, London (UK). 

Abstract: A rigorous optimisation has been carried out for the mould region of the continuous caster, using genetic algorithms, differential evolution, simulated annealing, and the traditional steepest descent method. The optimised predictions of some important casting parameters such as negative strip time, flux pool depth, and vitrification ratio are compared with current industrial practice.

[CDJ00] Nirupam Chakraborti, Kalyanmoy Deb and Avinash Jha (2000). Genetic algorithm based heat transfer analysis of a bloom re-heating
furnace. Steel Research, 71(10):396-402, October 2000. ISSN 0177-4832. 

Abstract: A heat transfer model, coupled with an optimization scheme has been presented in designing a re-heating furnace typically used in the integrated steel plants. Numerical solution of the pertinent differential equations were coupled with the optimal settings of the burner and the velocity of the bloom, using biologically inspired genetic algorithms (GAs) and differential evolution (DE), which led to optimized temperature profiles satisfying bloom dropout temperature constraints. The ease of application and efficiency of solution methodology demonstrated in this paper suggest further application of GAs and DE to more complex engineering design problems.

[CC00] Tien-Ting Chang and Hong-Chan Chang (2000). An efficient approach for reducing harmonic voltage distortion in distribution systems with active power line conditioners. IEEE Transactions on Power Delivery 15(3):990–995, July 2000. ISSN: 0885-8977. 

Abstract: This paper presents a combined differential evolution/multiple gradient summation approach for reducing harmonic distortion with active power line conditioners (APLC's). The purpose of this approach is to minimize the total injection currents of APLC's while satisfying harmonic standards and practical constraints such as the individual harmonic voltage distortion, total harmonic voltage distortion limits, and the commercially available discrete sizes of the APLCS. The proposed approach was tested on an 18-bus radial distribution system. Results obtained show that the proposed approach can effectively solve the APLC installation problem.

[CX00] Chang, C.S. and Xu, D. (2000). Differential evolution based tuning of fuzzy automatic train operation for mass rapid transit system. IEE Proceedings on Electric Power Applications, 147(3):206–212, May 2000. 

Abstract: Train performance of mass rapid transit systems can be improved with the use of fuzzy controllers in automatic train operation (ATO) systems. The tuning of these fuzzy controllers is presented using the algorithm of differential evolution (DE). The basic DE algorithm is modified to optimise a multiobjective function comprising punctuality, riding comfort and energy usage. Using this algorithm, the fuzzy ATO controller is tuned for each interstation train run. In operation, the controller adjusts each train's control according to the current operating conditions. A fuzzy ATO controller model was previously developed by the authors and is used to demonstrate the effectiveness of the tuning scheme.

[FGR00] Fileccia Scimemi, G., Giambanco, G. and Rizzo, S. (2000). Rate dependent interface laws for the analysis of cementitious joints. In: European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2000, 11-14 September 2000, Barcelona, Spain. Available via Internet: http://www.imamod.ru/jour/conf/ECCOMAS_2000/PDF/882.pdf

Abstract. The present paper is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the behavior of cementitious joints at long term. The interface laws are formulated in the framework of viscoplasticity for non standard materials in order to simulate the time-dependent softening response which occurs along the decohesion process in presence of shear and tension tractions. The interface laws are expressed both in rate and discrete incremental form. Details regarding the numerical implementation are presented and the consistent tangent matrix is derived leading to asymptotic quadratic convergence of the Newton-Raphson global procedure. The interface model parameters identification is discussed on the base of experimental data reported in the literature. The optimization problem related to the parameters evaluation is approached by a heuristic algorithm. Finally some numerical calculations are presented which show the capabilities of the proposed model and the effectiveness of the computational strategy herein presented.

[FVG00] Francken, K.; Vancorenland, P. and Gielen, G. (2000). DAISY: a simulation-based high-level synthesis tool for Delta Sigma modulators. In: Proceedings of IEEE/ACM International Conference on Computer Aided Design. ICCAD-2000, 5-9 November 2000; San Jose, CA, USA. Pp.188-192. ISBN 07803-6448-1. Available via Internet: http://www.sigda.org/Archives/ProceedingArchives/Iccad/Iccad2000/papers/2000/iccad00/pdffiles/04b_2.pdf

Abstract: An integrated tool called DAISY (Delta-Sigma Analysis and Synthesis) is presented for the high-level synthesis of Delta Sigma modulators. The approach determines both the optimum modulator topology and the required building block specifications, such that the system specifications mainly accuracy and signal bandwidth-are satisfied at the lowest possible power consumption. A genetic-based differential evolution algorithm is used in combination with a fast dedicated behavioral simulator that includes the major nonidealities of the building blocks to realistically analyze and optimize the modulator performance. Experimental results illustrate the effectiveness of the approach. Also, an overview of optimized topologies as a function of the modulator specifications for a wide range of values shows the capabilities and performance range covered by the tool.

[KoR00] Korczak, J. and Roger, P. (2000). Portfolio optimization using differential evolution. Prace Naukowe-Akademii Ekonomicznej Imienia Oskara Langego We Wroclawiu 855():302-319. Wydawnictwo Akademii Ekonomicznej we Wroclawiu, Wroclaw.

[KGWHB00] Kyprianou A., Giacomin J., Worden K., Heidrich M., Böcking J. (2000). Differential evolution based identification of automotive hydraulic engine mount model parameters. Proceedings of the Institution of Mechanical Engineers, Journal of Automobile Engineering (Part D) 214(3): 249–264, April 2000. Professional Engineering Publishing. ISSN 0954-4070. 

Abstract: Hydraulic engine mounts are commonly used in automotive applications, and numerical models exist for performing full-vehicle noise, vibration and harshness (NVH) studies by means of multibody simulation. The parameters of these models are usually determined by the manufacturer from first-principle numerical calculations, or by means of direct testing of the individual components. This paper describes, instead, a four-step identification method developed to determine the parameter values of a specific hydromount numerical model, the Freudenberg hydromount equations, a set of highly non-linear piecewise-continuous differential equations. The identification procedure is based on two concepts, the first being the use of the differential evolution algorithm for determining optimal parameter values, while the second is the use of data obtained from a series of experimental tests of progressively higher displacement amplitude. Identified parameters provide models whose mean square errors between the calculated output force time history and the experimentally measured force time history are typically of the order of 1–2 per cent.

[LTWL00] Tamzin Lafford, Mark Taylor, John Wall and Neil Loxley (2000). Rapid high-resolution X-ray diffraction measurement and analysis of MOVPE pHEMT structures using a high-brilliance X-ray source and automatic pattern fitting. Journal of Crystal Growth, 221(1-4):520-524, December 2000. 

Abstract: A novel micro-focus X-ray tube in combination with a focusing optic that uses total external reflection has been used to
enhance the diffracted intensity in a double-crystal experiment, whilst simultaneously reducing the beam footprint on the sample. The increased intensity allows data to be collected more quickly. Advances in auto-fitting using the full dynamical theory of X-ray diffraction mean that sample material parameters can be extracted quickly and objectively, opening the way to automatic data analysis. Both features are attractive for non-destructive quality control of semiconductor device structures, as well as for process development and research purposes.

[LWEMSL00] Jelveh Lameh, Paul Wang, David Elgart, David Meredith, Steven L. Shafer and Gilda H. Loew (2000). Unraveling the identity of benzodiazepine binding sites in rat hipppocampus and olfactory bulb. European Journal of Pharmacology, 400(2-3):167-176, 21 July 2000. 

Description: In this article DE was applied for solving a curve fitting problem. However, DE itself was not subject to investigations.

[LWMSL00] Jelveh Lameh, Paul Wang, David Meredith, Steven L. Shafer and Gilda H. Loew (2000). Characterization of Benzodiazepine Receptors in the Cerebellum. Progress in Neuro-Psychopharmacology and Biological Psychiatry, 24(6):979-991, August 2000.

Description: In this article a combination of Marguardt minimization and DE was applied for solving a curve fitting problem. However, DE itself was not subject to investigations.

[LZ00] Jouni Lampinen and Ivan Zelinka (2000). On Stagnation of the Differential Evolution Algorithm. In: Ošmera, Pavel (ed.) (2000). Proceedings of MENDEL 2000, 6th International Mendel Conference on Soft Computing, June 7.–9. 2000, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 76–83. ISBN 80-214-1609-2. Available via Internet: http://www.lut.fi/~jlampine/MEND2000.ps . 

Abstract: This article discusses the stagnation of an evolutionary optimization algorithm called Differential Evolution. Stagnation problem refers to a situation in which the optimum seeking process stagnates before finding a globally optimal solution. Typically, stagnation occurs virtually without any obvious reason. The stagnation differs from the premature convergence so that the population remains diverse and unconverged after stagnation, but the optimization process does not progress anymore. The reasons for this problem have remained unknown so far. This article uncovers this problem describing the basic nature of stagnation phenomena, a mechanism behind it and some reasons for stagnation. Advices for reducing the risk of stagnation are concluded on basis of the new findings.

[LHW00] Yung-Chien Lin, Kao-Shing Hwang and Feng-Sheng Wang (2000). Plant scheduling and planning using mixed-integer hybrid differential evolution with multiplier updating. In: Proceedings of the CEC00, 2000 Congress on Evolutionary Computation, Vol.1, pp. 593-600. IEEE, Piscataway, NJ, USA. ISBN 0-7803-6375-2. 

Abstract: Plant scheduling and planning are two of the most important decision-making problems in manufacturing industry. In general, these two decision-making problems are complex, due to the features of combinatorial nature for production-strategy selection and coupling properties for constrained requirements. In this paper, we have developed two general mixed-integer nonlinear programming models to formulate the scheduling and planning problems. In order to obtain a global solution, mixed-integer hybrid differential evolution with a multiplier updating method is introduced to solve both constrained problems. The proposed method can use parameters to obtain a feasible solution as compared with the penalty function approach.

[Mer00] Vesa Meriläinen (2000). Diskreetin optimoinnin käyttö mekatronisen koneen virtuaalisuunnittelussa. M.Sc. thesis,  Lappeenranta University of Technology, Department of Mechanical Engineering, October 2000. In Finnish, abstract in English (The Use of Discrete Optimization in Coupled Simulation of Mechatronic Machines). Available via Internet: http://www.lut.fi/~jlampine/dippa.pdf . 

Abstract: The objective of the work was to find out the suitability of an optimization program for optimizing virtual prototypes. Furthermore, the objective was to find out restrictions and possibilities of using virtual prototypes to optimization by real optimization problems. In this thesis the optimization program Optimaze was merged to simulation software ADAMS using sign files and internal macros of the simulation software. Designed optimization environment was tested by two optimization problems of a real hydromechanical system. The results indicate that the optimization program can be used to optimize virtual prototypes. Anyhow heavy simulation models were found to be too slow to be optimized in reasonable time. That’s why more research and development was recommended.

[Mic00] Michalski, K.A. (2000). Electromagnetic imaging of circular-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave and Optical Technology Letters 27(5):330-334, December 2000. 

Abstract: A technique is developed for the electromagnetic reconstruction of the location and radius of buried circular-cylindrical conductors or tunnels based on a differential evolution (DE) algorithm. Simulation results are presented which demonstrate that DE can offer a simple, yet an efficient and robust method for the imaging of buried objects.

[Myd00] Ravicharan Mydur (2000). Application of Evolutionary Algorithms & Neural Networks to Electromagnetic Inverse Problems.  M.Sc. thesis, Texas A&M University, Texas, USA. 

Abstract: This research investigates the imaging of buried two-dimensional objects (conducting cylinders and air tunnels) of various shapes, by processing the scattered electromagnetic field under Transverse Magnetic (TM) and Transverse Electric (TE) illumination. A technique is developed for the novel application of the Differential Evolution (DE) algorithm to electromagnetic imaging of buried objects. A hybrid of the DE and Powell method is also developed to further accelerate the DE’s performance. Both plane wave and line source excitations are employed for a circular and cross-borehole configuration of receivers. The effect of noise and the simultaneous recovery of shape and location of the objects are also investigated. Simulation results are presented which show that this technique is efficient and robust compared to state-of-the-art methods. A significant achievement in the area of real time inversion is made possible by training a neural network for recovery of shape and location. Test results presented indicate high reliability of the network.

[NGH00] Neelaveni, R., Gurusamy, G and Hemavathy, L. (2000). Adaptive genetic algorithm and differential evolution based backpropagation neural network for epileptic pattern recognition. Vivek. 13(4):15-23, October 2000. 

Abstract: This paper aims at developing a signal detector that detects the presence of epileptic patterns in electroencephalograph (EEG) waveforms using the conventional backpropagation network and compares the performance with an adaptive genetic algorithm (AGA) based neural network. EEGs are recordings of the minute electrical potentials produced by the brain. Epilepsy is a symptom of brain damage and is characterized by synchronous discharges of large groups of neurons, often including the whole brain. A neural network based epileptic pattern detector trained using backpropagation has been developed. The EEG signal is split into segments and linear predictor coefficients are extracted as features of the segment. These features are fed as input to a three layered neural network for detection of epileptic patterns. The convergence of the network depends on parameters like learning rate, momentum factor, slope of activation function etc. Improper selection of these parameters will slow down the convergence of the network. This paper seeks to improve the performance of the neural network by determining the structure and parameters of the network using an adaptive genetic algorithm (AGA) and differential evolution (DE) strategies.

[PH00] Pahner, U. and Hameyer, K. (2000). Adaptive coupling of differential evolution and multiquadrics approximation for the tuning of the optimization process. IEEE Transactions on Magnetics 36(4):1047–1051, July 2000. ISSN: 0018-9464. 

Abstract: Recently, the combination of global convergent stochastic search methods with approximation schemes based on radial basis functions has been introduced. This paper presents a new approach: instead of a procedural sequencing of the approximation algorithm and optimization algorithm, this optimization scheme is characterized by a direct and adaptive coupling of both algorithms. An approximation of the feasible space is constructed and updated during the progress of the evolutionary search. If the approximation fulfils particular accuracy criteria, the evolutionary search algorithm starts sampling the approximation (indirect search) instead of directly sampling the objective function. This can lead to a significant reduction of function calls, which is desirable if the function evaluation is computational expensive (e.g. involving finite element analysis steps).

[PV00] Plagianakos, V. P. and Vrahatis, M. N. (2000). Training Neural Networks with Threshold Activation Functions and Constrained Integer Weights. In: Proceedings of the IEEE International Joint Conference on Neural Networks (IJCNN'2000), Como, Italy, 24-27 July 2000, vol. 5, pp. 161-166. ISBN 0-7695-0619-4. 

Abstract: Evolutionary neural network training algorithms are presented. These algorithms are applied to train neural networks with weight values confined to a narrow band of integers. We constrain the weights and biases in the range [-2^(k-1)+1 , 2^(k-1)-1], for k=3,4,5 , thus they can be represented by just k bits. Such neural networks are better suited for hardware implementation than the real weight ones.
   Mathematical operations that are easy to implement in software might often be very burdensome in the hardware and therefore more costly. Hardware-friendly algorithms are essential to ensure the functionality and cost effectiveness of the hardware implementation. To this end, in addition to the integer weights, the trained neural networks use threshold activation functions only, so hardware implementation is even easier. These algorithms have been designed keeping in mind that the resulting integer weights require less bits to be stored and the digital arithmetic operations between them are easier to be implemented in hardware. Obviously, if the network is trained in a constrained weight
  space, smaller weights are found and less memory is required. On the other hand, as we have found here, the network training procedure can be more effective and efficient when larger weights are allowed. Thus, for a given application a trade off between effectiveness and memory consumption has to be considered.
   Our intention is to present results of evolutionary algorithms on this difficult task. Based on the application of the proposed class of methods on classical neural network benchmarks, our experience is that these methods are effective and reliable.

[RD00] Rogalsky, T. and Derksen, R.W. (2000). Hybridization of Differential Evolution for Aerodynamic Design. In: Proceedings of the 8th Annual Conference of the Computational Fluid Dynamics Society of Canada, June 11–13, 2000, pp 729–736. Available via Internet: http://home.cc.umanitoba.ca/~umrogal1/publications.html.

Abstract: Differential Evolution is a genetic algorithm which has been shown to be a robust but inefficient optimizer for aerodynamic design problems, requiring thousands of function evaluations to converge. Differential Evolution is combined with a local search engine to create a new hybridized algorithm. The optimizers are then used to design several fan blade shapes, in order to compare their performances. The new algorithm is shown to have a better convergence rate, without sacrificing robustness.

[RKD00] Rogalsky, T., Kocabiyik, S. and Derksen, R.W. (2000). Differential evolution in aerodynamic optimization. Canadian Aeronautics and Space Journal, 46(4):183-190, December 2000. CASI, Ottawa (Canada). ISSN 0008-2821. 

Abstract: Aerodynamic design algorithms require an optimization strategy to search for the best design. The object of this paper is to compare the performance of Differential Evolution, a recently developed genetic algorithm, with other more traditional optimization strategies. An inverse design technique is developed to design fan blade profiles. The design objective in this case is the surface pressure distribution. Three different optimizers are integrated into the inverse design algorithm in order to compare their performance. Differential Evolution is shown to be the most effective of the three - finding solutions even when the other optimizers are unable to do so. However, genetic algorithms are not efficient, and Differential Evolution requires a high number of function evaluations to converge to a solution.

[Sal00] Salomon, Michel (2000). Parallélisation de l'évolution différentielle pour le recalage rigide d'images médicales volumiques. RenPar'2000, 12ème Rencontres Francophones du Parallélisme, Besançon (France), 19-22 Juin 2000. 6 pages. Available via Internet: http://icps.u-strasbg.fr/~salomon/ .  In French language. See also [Sal01].

[SPH00] M. Salomon, G.-R. Perrin and F. Heitz (2000). Parallelizing differential evolution for 3D medical image registration. Rapport de Recherche 00-06, Septembre 2000. 10 pages. Available via Internet: http://icps.u-strasbg.fr/~salomon/ . In English language.

[She00] Shepherd, Ross (2000). Beef Breeding Technologies: 6. Implementing breeding programs tactically – the origin of total genetic resource management. Available via Internet: http://www2.dpi.qld.gov.au/dpinotes/animals/cattle/breeding/bi00145.html. See also [She99]. 

Abstract: A tactical approach to the design of breeding programs is presented which integrates technical, logistical and cost issues facing animal breeders. It is opportunistic in that it uses actual animals and prevailing costs and resources to produce better outcomes than a static approach using preset breeding rules. It involves developing a Mate Selection Index (MSI) which describes net economic merit in terms of selection and mating decisions, and then implementing a mate selection algorithm which searches for the best mating solution in terms of the MSI. Total Genetic Resource Management (TGRM) is a new service for breeders offering a tactical mate selection approach to the implementation of their breeding programs. The paper discusses TGRM in detail, focussing on the inputs required and the output generated, in addition to how decisions (eg. on advanced reproductive technology) are made. Future developments, with genetic markers and in Total Resource Management, are briefly discussed.

[SS00] Shokrollahi, Amin and Storn, Rainer (1999). Design of Efficient Erasure Codes with Differential Evolution. In: Proceedings of ISIT 2000, International Symposium on Information Theory, 25-30 June 2000, Sorrento, Italy. Page 5. IEEE. ISBN 0-7803-5857-0. See also [SS99].

Abstract: The design of practical and highly powerful codes for protection against erasures can be reduced to optimizing solutions of a highly nonlinear constraint satisfaction problem. In this paper we will attack this problem using the Differential Evolution approach and significantly improve results previously obtained using classical optimization procedures.

[SDPH00] Stumberger, G., Dolinar, D., Pahner, U. and Hameyer, K. (2000). Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm. IEEE Transactions on Magnetics 36(4):1009–1013, July 2000. ISSN 0018-9464. 

Abstract: An optimization of radial active magnetic bearings is presented in the paper. The radial bearing is numerically optimized, using differential evolution - a stochastic direct search algorithm. The nonlinear solution of the magnetic vector potential is determined, using the 2D finite element method. The force is calculated by Maxwell's stress tensor method. The parameters of the optimized and nonoptimized bearing are compared. The force, the current gain, and the position stiffness are given as functions of the control current and rotor displacement.

[TZB00] Thompson A.V.,  Zhu T.C., Bjärngard B.E. (2000). Quality assurance of measured depth dose for megavoltage photon beams. In: Proceedings of the 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 23-28 July 2000, Chigago, Vol. 4, pp. 3108-3111. IEEE, Piscataway, NJ, USA.

[TK00] Tvrdík, Josef and Krivý, Ivan (2000). Evolutionary search revisited. In: Ošmera, Pavel (ed.) (2000). Proceedings of MENDEL 2000, 6th International Mendel Conference on Soft Computing, June 7.–9. 2000, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 165–170. ISBN 80-214-1609-2. 

Abstract: The aim of this paper is to compare the efflciency of several stochastic algorithms in the global optimization. The algorithms were tested on three multimodal functions (Shekel, Griewangk, Corana). The reliability of finding the true global minimum was investigated. The algorithms are discussed from the standpoint of the algorithms convergence as well as from the standpoint of their applicability in solving practical problems

[VRSG00] Vancorenland, P., De Ranter, C., Steyaert, M. and Gielen, G. (2000). Optimal RF Design Using Smart Evolutionary Algorithms. Proceedings of 37th Design Automation Conference, June 5 - 9, 2000, Los Angeles, CA. ISBN (CD-ROM) 1-58113-188-7. Available via Internet: http://www.sigda.org/Archives/ProceedingArchives/Dac/Dac2000/papers/2000/dac00/pdffiles/01_2.pdf

Abstract: This paper presents an optimization algorithm that is able to significantly increase the speed of RF circuit optimizations. The algorithm consists of a series of consecutive evolutionary optimizations of the circuit itself and of a modeled version thereof. The speed increase arises from the difference in evaluation time between the real simulation and the fit evaluation. As circuit approximation, behavioral models are used instead of polynomial expressions, allowing to put some "design knowledge" into the optimization. gaRFeeld is a tool implementing this smart evolutionary algorithm for RF circuits. Finally some experiments performed with gaRFeeld are illustrated for the optimization of a Low Noise Amplifier.

[WJi00] Wang, F.-S. and Jing, C.-H. (2000). Application of Hybrid Differential Evolution to Fuzzy Dynamic Optimization of a Batch Fermentation. Journal of Chinese Institute of Chemical Engineers 31(5):443-454. Chinese Institution of Chemical Engineers. ISSN 0368-1653.

[WJ00] Wang, Feng-Sheng and Jang, Horng-Jhy (2000). Parameter estimation of a bioreaction model by hybrid differential evolution. In: Proceedings of the CEC00, 2000 Congress on Evolutionary Computation, Vol.1, pp. 410-417. IEEE, Piscataway, NJ, USA. ISBN 0-7803-6375-2. 

Abstract: Hybrid differential evolution is applied to estimate the kinetic model parameters of batch fermentation for ethanol and glycerol production using Saccharomyces diastaticus LORRE 316. In this study, we consider the worst observed error for all experiments as an objective function so that the parameter estimation problem becomes a min-max estimation problem. Several methods have been employed to solve the min-max estimation problem for comparison. The proposed method can use a small population size to obtain a more satisfactory solution as compared from these computations. In order to validate the kinetic model, we have carried out the fedbatch experiments with an optimal feed rate. The experimental data can fit the computed results satisfactorily.

[WS00] Wang, Feng-Sheng and Sheu, Jyh-Woei (2000). Multiobjective parameter estimation problems of fermentation processes using a high ethanol tolerance yeast. Chemical Engineering Science 55(18):3685–3695, 15 September 2000. Elsevier Science. ISSN 0009-2509. 

Abstract: A multiobjective optimization approach is applied to estimate the kinetic model parameters of batch and fed-batch fermentation processes for ethanol production using Saccharomyces diastaticus (LORRE 316), which is a high ethanol tolerance yeast. Both batch and fed-batch experimental observations are simultaneously employed to formulate the parameter estimation problem. Consequently, the estimation problem becomes a multiobjective optimization problem. The hybrid differential evolution is introduced to solve the multiobjective parameter estimation problem to obtain a global Pareto solution. Optimality test is inferred in this study to guarantee to obtain the unique solution. Various experimental data obtained from a fermenter with the working volume of 5L are used to evaluate the proposed method. The validated kinetic model could fit for both batch and fed-batch fermentation processes as observed from the experimental results.

[WH00] Wu Huapeng and Heikki Handroos (2000). Utilization of differential evolution in inverse kinematics solution of a parallel redundant manipulator. In: Howlett, R.J., Jain, L.C. (eds.)(2000). Proceedings of Fourth International Conference on Knowledge-Based Intelligent Engineering Systems and Allied Technologies, 2000, 30th August–1st September 2000, Brighton, UK. Vol.2, pp. 812–815. ISBN 0-7803-6400-7. 

Abstract: A novel type of redundant parallel manipulator is presented and studied. The inverse kinematics model of the manipulator is postulated. The static stiffness of the manipulator is discussed. To achieve a minimum deflection in the solution of the inverse kinematics problem the differential evolution method is used. In the inverse kinematics solution also the appropriate link motions to avoid collision and joint limits are selected.

[ZL00] Ivan Zelinka and Jouni Lampinen (2000).Evolutionary Identification of Predictive Models. In: Ošmera, Pavel (ed.) (2000). Proceedings of MENDEL 2000, 6th International Mendel Conference on Soft Computing, June 7.–9. 2000, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 171–176. ISBN 80-214-1609-2.

2001

[ASN01] Abbass, Hussein A., Sarker, Ruhul and Newton, Charles (2001). PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the 2001 Congress on Evolutionary Computation, 27-30 May 2001, Seoul, South Korea, Vol. 2, pp. 971-978. IEEE, Piscataway, NJ, USA. ISBN 0-7803-6657-3. 

Description: A modified DE for solving multiobjective optimization problems is proposed in this article.

[BG01] Babu, B.V. and Gautam, K. (2001). Evolutionary Computation for Scenario-Integrated Optimization of Dynamic Systems. Proceedings of International Symposium & 54th Annual Session of IIChE (CHEMCON-2001), CLRI, Chennai, December 19-22, 2001. Available via Internet: http://bvbabu.50megs.com/custom.html/#39.

[BA01a] Babu, B.V. and Angira, Rakesh (2001). Optimization of Non-Linear Functions Using Evolutionary Computation. Proceedings of 12th ISME Conference on Mechanical Engineering, Crescent Engineering College, Chennai, January 10-12, 2001. Paper No. CT07, pp.153-157. Available via Internet: http://bvbabu.50megs.com/custom.html/#34.

[BA01b] Babu, B.V. and Angira, Rakesh (2001). Optimization of Thermal Cracker Operation using Differential Evolution. Proceedings of International Symposium & 54th Annual Session of IIChE (CHEMCON-2001), CLRI, Chennai, December 19-22, 2001. Available via Internet: http://bvbabu.50megs.com/custom.html/#38.

[BLWS01] W. G. Booty, D. C. L. Lam, I. W. S. Wong and P. Siconolfi (2001). Design and implementation of an environmental decision support system. Environmental Modelling and Software 16(5):453-458, July 2001. 

Description: An environmental decision support system is a specific version of an environmental information system that is designed to help decision makers, managers, and advisors locate relevant information and carry out optimal solutions to problems using special tools and knowledge. The optimization module is used in conjunction with running the various modelling scenarios. Both linear programming and genetic algorithm (based on DE) methods are available to help to determine the most effective (both environmentally and financially) solutions to reducing and eliminating toxic chemicals of concern from the different lakes and their components.

[CMBBP01] Chakraborti, N., Misra, K., Bhatt, B., Barman, N. and Prasad, R. (2001). Tight-Binding Calculations of Si-H Clusters Using Genetic Algorithms and Related Techniques: Studies Using Differential Evolution. Journal of Phase Equilibria 22(5):525-530, October 2001. 

Abstract: A nonorthogonal tight-binding model has been developed for the system containing Si and H, where the energy functional included the contributions of both electronic and pairwise interaction between the atoms. In order to calculate the ground state structures of various clusters, energy minimization was carried out using Differential Evolution: a very recently developed biologically inspired computing technique, belonging, in general, to the family of Genetic Algorithms (GAs), but having a number of advantages over its conventional forms.

[CC01] Hong-Chan Chang and Tien-Ting Chang (2001). Optimal installation of three-phase active power line conditioners in unbalanced distribution systems. Electric Power Systems Research 57(3):163-171, 20 April 2001. 

Abstract: In this paper, a new solution algorithm based on a multiple gradient summation (MGS) and differential evolution (DE) approach for optimal three-phase active power line conditioners (APLCs) installation in unbalanced distribution systems is proposed. The active power line conditioners installation problem considers the individual and total harmonic voltage distortions as well as the commercially available discrete sizes of the APLCs limits to minimize the total sizes of three-phase APLCs. The imbalance of systems resulting from using asymmetrical connection transformers was taken into account. The effectiveness of the proposed method was demonstrated by its application to a 23-bus unbalanced radial distribution system.

[CH01]Shih-Lian Cheng and Chyi Hwang (2001). Optimal approximation of linear systems by a Differential Evolution Algorithm. IEEE Transactions on Systems, Man and Cybernetics, Part A, 31(6):698-707, November 2001. ISSN 1083-4427.

Abstract: The problem of optimally approximating linear systems is solved by a differential evolution algorithm (DEA) incorporating a search-space expansion scheme. The optimal approximate rational model with/without a time delay for a system described by its rational or irrational transfer function is sought such that a frequency-domain L/sup 2/-error criterion is minimized. The distinct feature of the proposed model approximation approach is that the search-space expansion scheme can enhance the possibility of converging to a global optimum in the DE search. This feature and the chosen frequency-domain error criterion make the proposed approach quite efficacious for optimally approximating unstable and/or nonmimimum-phase linear systems. The simplicity and robustness of the modified DEA in terms of easy implementation and minimum assumptions on search space are demonstrated by two numerical examples .

[CW01] J.-P. Chiou and F.-S. Wang (2001). Estimation of Monod model parameters by hybrid differential evolution. Bioprocess and Biosystems Engineering, 13 April 2001. Springer-Verlag. ISSN 1615-7605 (electronic version of the journal).

Abstract:A hybrid method based on evolutionary algorithms is developed in this study. Two additional operations, an acceleration operation and a migration operation, are embedded into the original version of differential evolution. These two operations are used for the improvement of the convergence speed without decreasing the diversity among the individuals. The acceleration operation is used to speed up convergence. However, the migration operation is used to increase the diversity among the individuals. The hybrid method is applied to estimate the parameters of the Monod model of a recombinant fermentation process. The model profiles based on +/- 50% variations of the initial concentrations of glucose can fit the experimental observations satisfactorily.

[DS01] Mark R. DiSilvestro and Jun-Kyo Francis Suh (2001). A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression. Journal of Biomechanics, 34(4):519-525, April 2001. 

Description: The biphasic poroviscoelastic (BPVE) model was curve fit to the simultaneous relaxation of reaction force and lateral displacement exhibited by articular cartilage in unconfined compression. DE was applied here for determining the BPVE model parameters. DE itself was not subject to investigations.

[GVJM01] Gómez-Skarmeta, A.F., Valdés, M., Jiménez, F. and  Marín-Blázquez, J.G. (2001). Approximative fuzzy rules approaches for classification with hybrid-GA techniques. Information Sciences 136(1-4):193-214, August 2001. 

Abstract: In this paper the use of different methods from the fuzzy modeling field for classification tasks is evaluated and the potential of their integration in producing better classification results is investigated. The methods considered, approximative in their nature, consider different integrations of techniques with an initial rule generation step and a following rule tuning approach using different evolutionary algorithms. We analyse the adaptation of existing techniques in the fuzzy modeling context for the classification problem, and the integration of these techniques in order to improve the classifiers performance. Finally a genetic algorithm (GA) for translation from approximative rules to similar descriptive ones trying to preserve the accuracy of the approximative classifier is presented. The classical Iris and Cancer data set are used throughout the evaluation process to form a common ground for comparison and performance analysis.

[HAS01] Dollena S. Hawkins, David M. Allen and Arnold J. Stromberg (2001). Determining the number of components in mixtures of linear models. Computational Statistics & Data Analysis 38():15-48. 

Abstract: Methods for determining the number of components in normal mixtures are extended to mixtures of linear regression models. This simulation study evaluates the influence of component separation and mixing proportions on the performance of 22 approximations of measures for determining the number of components in mixtures of linear regression models. Estimated measures based on the maximized log likelihood of the observed data are compared to estimated measures based on the maximized log likelihood of the complete data. Approximations of measures which previously required the convergence rate of the EM algorithm are presented which have no such restriction for their implementation. As an alternative to the EM algorithm, which is known to be sensitive to starting values, differential evolution was the implemented optimization algorithm. This study is further set apart in that the performances of the approximated component measures are explored without assuming the mixing proportions to be equal or assuming equal component variances. Based on the results of the k=1 and 2 component model simulations, the minimum description length, MDL, is the recommended criterion for choosing between one and two component mixtures of linear regression models.

[Hen01] Hendtlass, Tim (2001). A Combined Swarm Differential Evolution Algorithm for Optimization Problems. Lecture Notes in Computer Science, no. 2070, pp. 11-18. Springer-Verlag. ISSN 0302-9743. 

Abstract: An algorithm that is a combination of the particle swarm and differential evolution algorithms is introduced. The results of testing this on a graduated set of trial problems is given. It is shown that the combined algorithm out performs both of the component algorithms under most conditions, in both absolute and computational load weighted terms.

[HSM01] Jilei Hou, Paul H. Siegel and Lawrence B. Milstein (2001). Performance analysis and code optimization of low density parity-check codes on Rayleigh fading channels. IEEE Journal on Selected Areas in Communications 19(5):924-934, May 2001. ISSN 0733-8716. Available via Internet: http://cwc.ucsd.edu/~psiegel . 

Abstract: A numerical method has been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we apply the technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimize irregular LDPC codes for such a channel. The thresholds of the optimized irregular LDPC codes are very close to the Shannon limit for this channel. For example, at rate one-half, the optimized irregular LDPC code has a threshold only 0.07 dB away from the capacity of the channel. Furthermore, we compare simulated performance of the optimized irregular LDPC codes and turbo codes on a land mobile channel, and the results indicate that at a block size of 3072, irregular LDPC codes can outperform turbo codes over a wide range of mobile speeds.

[KWP01] Kyprianou, A., Worden, K. and Panet, M. (2001). Identification of hysteretic systems using the differential evolution algorithm. Journal of Sound and Vibration 248(2):289-314, November 2001. ISSN 0022-460X. 

Abstract:A widely used model in the field of hysteretic or memory-dependent vibrations is that of Bouc (1967) and Wen (1976). Different parameter values extend its use to various areas of mechanical vibrations. As a consequence an identification method is required to identify the parameter values relevant to its application. Its structure, however, includes internal states and non-linear terms. This rules out the conventional identification methods, such as least squares and maximum likelihood because they require derivative calculations of the prediction error with respect to the parameters. In this paper we present some results for Bouc-Wen model identification, using simulated noise-free data, simulated noisy data and experimental data obtained from a nuclear power plant. The method used to achieve this is the differential evolution algorithm. Differential evolution is an optimization method developed to perform a direct search in a continuous parameter space without requiring any derivative estimation.

[Lam01a] Jouni Lampinen (2001). Solving Problems Subject to Multiple Nonlinear Constraints by the Differential Evolution. In: Radek Matoušek and Pavel Ošmera (eds.) (2001). Proceedings of MENDEL 2001, 7th International Conference on Soft Computing, June 6.–8. 2001, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 50-57. ISBN 80-214-1894-X. Available via Internet: http://www.lut.fi/~jlampine/MEND01.pdf (article) and http://www.lut.fi/~jlampine/MEND01tr.pdf (presentation transparencies). 

Abstract: In this article an extension for the Differential Evolution algorithm is proposed for handling nonlinear constraint functions. From the user point of view, the proposed method allows solving multi-constrained nonlinear global optimization problems virtually as easily as unconstrained problems or only boundary constrained ones. The proposed approach is straightforward to implement and use. User is not assumed to provide a feasible solution as a starting point for searching, as required by many other methods. Furthermore, the user is not required to set any penalty function parameters, weighting factors for individual constraint functions, or any other additional search parameters, as in cases for most penalty function methods. In comparison with the original Differential Evolution algorithm, only the selection operation was modified with a new selection criteria for handling the constraint function values. The effectiveness of the proposed method is demonstrated by solving a suite of four well-known and difficult test problems.

[Lam01b] Jouni Lampinen (2001).Multi-Constrained Nonlinear Optimization by the Differential Evolution Algorithm. 6th On-line World Conference on Soft Computing in Industrial Applications (WSC6), September 10.–24. 2001. On the Internet (World Wide Web), http://vision.fhg.de/wsc6 . 

Abstract: In this article an extension for the Differential Evolution algorithm is proposed for handling nonlinear constraint functions. From the user point of view, the proposed method allows solving multi-constrained nonlinear global optimization problems virtually as easily as unconstrained problems or only boundary constrained ones. Also constraint satisfaction problems with multiple constraint functions, but without objective function, can be solved by applying the proposed method. The proposed approach is both straightforward to implement and use. User is not assumed to provide a feasible solution as a starting point for searching, as required by many other methods. Furthermore, the user is not required to set any penalty parameters, any weighting factors for individual constraints, or any other additional search parameters, as in cases for most penalty function methods. In comparison with the original Differential Evolution algorithm, only the selection operation was modified with a new selection criteria for handling the constraint functions. The proposed method is demonstrated by an illustrative constraint satisfaction example and by solving a suite of seven well-known and difficult test problems.

[Lam01c] Jouni Lampinen (2001).Multi-Constrained Optimization By The Differential Evolution. In: M.H. Hamza (ed.) (2001). Proceedings of the IASTED International Conference Artificial Intelligence and Applications (AIA 2001), 4-7 September 2001, Marbella, Spain, pp. 177-184. ACTA Press, Anaheim (USA). ISBN 0-88986-301-6. 

Abstract: In this article an extension for the Differential Evolution algorithm is proposed for handling nonlinear constraint functions. From the user point of view, the proposed method allows solving multi-constrained nonlinear global optimization problems virtually as easily as unconstrained problems or only boundary constrained ones. The pro-posed approach is both straightforward to implement and use. User is not assumed to provide a feasible solution as a starting point for searching, as required by many other methods. Furthermore, the user is not required to set any penalty function parameters, weighting factors for indi-vidual constraint functions, or any other additional search parameters, as in cases for most penalty function methods. In comparison with the original Differential Evolution algorithm, only the selection operation was modified with a new selection criteria for handling the constraint func-tion values. The effectiveness of the proposed method is demonstrated by solving a suite of four well-known and difficult test problems.

[Lam01d] Jouni Lampinen (2001). Solving Engineering Optimization Problems By Applying Differential Evolution. In: Kesheng Wang, Janis Grundspenkis and Anatoly Yerofeyev (eds.). Applied Computational Intelligence to Engineering and Business, Lecture Notes of the Nordic, Baltic and Northwest Russian Summer School NBR’2000, June 4 – 11, 2000, St. Petersburg, Russia, pp. 92–115. Riga Technical University, Riga, Latvia. ISBN 9984-681-83-1.

Abstract: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The article describes a novel optimisation method based on a recently introduced evolutionary algorithm called Differential Evolution. The required handling techniques for integer, discrete and continuous variables are described, including the techniques needed to handle boundary constraints as well as those needed to deal simultaneously with several non-linear and non-trivial constraint functions. Three mechanical engineering design related numerical examples, design a gear train, design of a pressure vessel and design of a coil spring, are given to illustrate the capabilities and practical use of the method. Since these classical examples have been used by a number of other researchers, it was possible to compare results between no less than 20 alternative optimization methods. In each single problem the described method was able to provide a better or equal solution than any of the compared methods. Thus, the described approach is shown to be capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it an attractive and widely applicable approach for solving practical engineering design problems.

[LHW01]Lin, Yung-Chien, Hwang, Kao-Shing and Wang, Feng-Sheng (2001). Co-Evolutionary Hybrid Differential Evolution for Mixed-Integer Optimization Problems. Engineering Optimization 33(6):663-682. ISSN 0305-215X.

Abstract: Evolutionary algorithms are promising candidates for obtaining global optimum. Hybrid differential evolution is one of the evolutionary algorithms, which has been successfully applied to many real-world nonlinear programming problems. This paper proposes a co-evolutionary hybrid differential evolution to solve mixed-integer nonlinear programming (MINLP) problems. The key ingredients of the algorithm consist of an integer-valued variable evolution and a real-valued co-evolution, so that the algorithm can be used to solve MINLP problems or pure integer programming problems. Furthermore, the algorithm combines a local search heuristic (called acceleration) and a widespread search heuristic (called migration) to promote search for a global optimum. Some numerical examples are tested to illustrate the performance of the proposed algorithm. Numerical examples show that the proposed algorithm converges to better solutions than the conventional MINLP optimization methods.

[LiLa01] Miika Lindfors – Jouni Lampinen (2001). Training MLP Networks by Differential Evolution Algorithm. 6th Online World Conference on Soft Computing in Industrial Applications (WSC6), September 10.–24. 2001. On the Internet (World Wide Web), http://vision.fhg.de/wsc6 . 

Abstract: In this article feasibility of training multilayer perceptron networks by ap-plying a recently introduced evolutionary algorithm, called Differential Evolution, was investigated. The Differential Evolution algorithm was compared with four variations of the Back-Propagation algorithm on training the network. The initial results of our experiments suggested that the Back-Propagation typically finds a good solution relatively fast, but cannot improve the solution further on, when more iterations are per-formed. Consequently, the Differential Evolution algorithm did not, in the early stages of the training process, provide solutions as good as those obtained with the Back-Propagation.  However, after the Back-Propagation got stuck on a locally optimal so-lution, the Differential Evolution finally overtook it due to its global optimization capabilities. Our results suggest that it depend on the time available for training, which of the compared algorithms provide the best training result. However, the conclusions are preliminary and limited by the problems studied so far. For example, until now, only relatively small networks have been used for experimentation.

[LWS01] Lopez Cruz I.L., Van Willigenburg L.G., Van Straten, G. (2001). Parameter Control Strategy in Differential Evolution Algorithm for Optimal Control. In: M.H. Hamza (ed.) (2001). Proceedings of the IASTED International Conference Artificial Intelligence and Soft Computing (ASC 2001), May 21-24, 2001, Cancun , Mexico, pp. 211-216. ACTA Press, Calgary (Canada). ISBN 0-88986-283-4, ISSN: 1482-7913. 

Abstract: Most optimal control algorithms are not capable of finding the global solution among local ones. Because of this we recently proposed the use of a Differential Evolution algorithm to solve multimodal optimal control problems. The DE algorithm is efficient compared to most other evolutionary algorithms. Still, when applied to optimal control problems, the algorithm is significantly less efficient than other, non-global, optimal control algorithms. In this paper the efficiency of the DE algorithm for optimal control is improved significantly through parameter control. In the DE algorithm three main parameters have to be set by the user. The parameter values all constitute a compromise between the efficiency of the algorithm and the capability of finding the global minimum. Instead of keeping these parameters constant, which is common practice, these parameters are changed during the optimization. Roughly speaking in the beginning of the optimization it is important to search the whole space, while after some time, to improve the efficiency, the search must be more local. Based on the diversity of intermediate computations, our algorithm makes this transition, i.e. the change of the parameters, more quickly or slowly. The algorithm is illustrated through numerical solutions of two multimodal optimal control problems.

[LW01] Lu, J.-C. and Wang, F.-S. (2001). Optimization of Low Pressure Chemical Vapour Deposition Reactors Using Hybrid Differential Evolution. Canadian Journal of Chemical Engineering 79(2):246-254. Chemical Institute of Canada. ISSN 0008-4034.

[MPV01] Magoulas, G.D., Plagianakos, V.P., Vrahatis, M.N. (2001). Hybrid methods using evolutionary algorithms for on-line training. Proceedings of IJCNN'01, International Joint Conference on Neural Networks, 15-19 July 2001, Washington, DC. Vol 3 pp.2218-2223. 

Abstract: A novel hybrid evolutionary approach is presented in this paper for improving the performance of neural network classifiers in slowly varying environments. For this purpose, we investigate a coupling of differential evolution strategy and stochastic gradient descent, using both the global search capabilities of evolutionary strategies and the effectiveness of online gradient descent. The use of differential evolution strategy is related to the concept of evolution of a number of individuals from generation to generation and that of online gradient descent to the concept of adaptation to the environment by learning. The hybrid algorithm is tested in two real-life image processing applications. Experimental results suggest that the hybrid strategy is capable to train online effectively leading to networks with increased generalization capability.

[MW01]Manson, G. and Worden, K. (2001). Lamb Wave Sensor Optimization Using Differential Evolution. In: Proceedings of the SPIE. The International Society for Optical Engineering, Vol. 4326, pp. 570-580.

Abstract: Recent work investigating the use of Lamb-wave propagation to detect and localize damage in composite structures has produced some very encouraging results. Lamb-waves are launched form piezoceramic actuators and the resulting signals are recorded at piezoceramic sensors at various locations on the structure. When damage is introduced into the structure, the Lamb-wave will be modified in some potentially complicated matter. The extent of this modification will be dependent upon the proximity of the damage location to the relevant actuator/sensor path. The purpose of this paper is to propose a strategy for the location of piezoceramic actuators and sensors so as to provide optimum damage detection coverage of the structure. The method used is a differential evolution algorithm constructed so as to minimize a cost function based on either an angular of Lamb-wave propagation distance approach. More complicated effects such as attenuation, edge reflection, orientation of fibers in the structure may be taken into account using this approach. Known trouble spots in the structure may also be given greater priority in a straightforward manner and also components known to cause propagation problems, such as stringers or riveted joints, can be accommodated.

[Mic01] Michalski, K.A. (2001). Electromagnetic imaging of elliptical-cylindrical conductors and tunnels using a differential evolution algorithm. Microwave and Optical Technology Letters 28(3):164-169, February 2001. 

Abstract: A technique is developed for the electromagnetic reconstruction of the location and shape of buried elliptical-cylindrical conductors or tunnels based on a differential evolution (DE) algorithm. Simulation results are presented which demonstrate that DE can offer a simple, yet efficient and robust method for the imaging of buried objects and voids.

[NGH01] Neelaveni R., Gurusamy G., Hemavathy L. (2001). Adaptive genetic algorithm and differential evolution based backpropagation neural network for epileptic pattern recognition. In: Proceedings of the National Conference on Technology Convergence for Information, Communication and Entertainment, NICE 2001, 23-24 February 2001, Cochin, India, pp.26-30. Instn. Electron. & Telecommun. Eng. (IETE). 

Abstract: This paper aims at developing a signal detector that detects the presence of epileptic pattern in electroencephalograph (EEG) waveforms using the conventional backpropagation network and compares the performance with adaptive genetic algorithm (AGA) and differential evolution based neural network. EEGs are recordings of the minute electrical potentials produced by the brain. Epilepsy is a symptom of brain damage and is characterized by synchronous discharges of large groups of neurons, often including the whole brain EEG signal is split into segments and linear predictor coefficients are extracted as features of the segment. These features are fed as input to a three layered neural network for detection of epileptic pattern. Training of neural network is achieved through backpropagation (BP) algorithm. The convergence of the network depends on parameters like learning rate, momentum factor, slope of activation function etc. Improper selection of these parameters will slow down the convergence of the network. This paper seeks to improve the performance of neural network by determining the structure and parameters of the network using adaptive genetic algorithm (AGA) and differential evolution (DE) strategies. Simulation results show that for the same number of training samples and test samples the recognition accuracy of AGANN and DENN is higher than that of conventional backpropagation.

[PMV01]Plagianakos V.P., Magoulas G.D., Vrahatis M.N. (2001). Learning in Multilayer Perceptrons Using Global Optimization Strategies. Nonlinear Analysis Theory, Methods and Applications 47(5):3431-3436, August 2001. ISSN 0362-546X.

Abstract: Learning algorithms for multiplayer perceptrons are usually based on local minimization methods that can be often trapped in a local minimum of the error function. In this work, the use of global optimization strategies for training multiplayer perceptrons is investigated. These methods are expected to lead to “optimal” or “near-optimal” weight configurations by allowing the network to escape local minima during training. The paper reviews the fundamentals of a recently proposed deflection procedure, simulated annealing, genetic and evolutionary algorithms, and introduces a new differential evolution strategy. Simulations and comparisons are presented. 

[RuM01] Rumpler, James A. and Moore, Frank W. (2001). Automatic selection of sub-populations and minimal spanning distances for improved numerical optimization. In: Proceedings of the 2001 Congress on Evolutionary Computation, 27-30 May 2001, Seoul, South Korea, Vol. 1, pp. 38-43. IEEE, Piscataway, NJ, USA. ISBN 0-7803-6657-3. 

Abstract: This paper presents a modified differential evolution algorithm that is capable of automatically discovering an arbitrarily large number of global optima in an arbitrarily complex solution space. Previous research is extended in two ways: first, the algorithm automatically determines the number of sub-populations that are necessary to maximize the number of optimal solutions found. Second, the algorithm automatically determines the appropriate minimal spanning distance between elements from each sub-population. These extensions greatly increase the overall power and efficiency of the DE algorithm for the numerical optimization of multidimensional objective functions. Results for several benchmark problems are described.

[RP01]Rae, Allan and Parameswaran, Sri (2001). Synthesising Application-Specific Heterogenous Multiprocessors Using Differential Evolution. In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E84-A, no.12, December 2001, pp. 3125-3131. ISSN 0916-8508.

Abstract: This paper presents an application-specific, heterogeneous multiprocessor synthesis system, named HeMPS, that combines a form of evolutionary computation known as Differential Evolution with a scheduling heuristic to search the design space efficiently. We demonstrate the effectiveness of our technique by comparing it to similar existing systems. The proposed strategy is shown to be faster than recent systems on large problems while providing equivalent or improved final solutions.

[RSU01] Richardson, T.J., Shokrollahi, M.A. and Urbanke, R.L (2001). Design of Capacity-Approaching Irregular Low-Density Parity-Check Codes. IEEE Transactions on Information Theory 47(2):619 - 637, February 2001. ISSN 0018-9448

Abstract: We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on the work of Richardson and Urbanke (see ibid., vol.47, no.2, p.599-618, 2000). Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph possess a certain symmetry. Using this symmetry property we then show that, under the assumption of no cycles, the message densities always converge as the number of iterations tends to infinity. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief-propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution. Our codes are found by optimizing the degree structure of the underlying graphs. We develop several strategies to perform this optimization. We also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds.

[RK01] Bohuslav Ruzek and Michal Kvasnicka (2001). Differential evolution algorithm in the earthquake hypocenter location. Pure and Applied Geophysics 158(4):667-693. Birkhäuser Verlag, Basel. ISSN 0033-4553. See also [KR99]. 

Abstract: A novel global optimizing algorithm - Differential Evolution (DE) - has appeared recently. This method is easy and advantageous when used for kinematic location of the earthquake hypocenter. The motivation for implementing a robust (i.e. global and nonlinear) optimizing algorithm for the location problem is to obtain better results than those from the classical (i.e. linearized) approach (such as the FASTHYPO, HYPOELLIPSE, HYPOCENTER solutions, among others). Better solutions have lower final misfits expressed as L2 norm. The features of the DE algorithm are studied on a set of synthetic location problems. The DE procedure is controlled by 3 internal parameters, which are easy to adjust, and the convergence properties are very good. Location results using DE are compared with the HYPO71 solutions for real earthquake data from the Gulf of Corinth region, Greece. The DE results are significantly better. The DE optimizing algorithm seems to be very promising both for the location problem as well as for other problems in geophysics.

[Sal01] Salomon, Michel (2001). Parallélisation de l'évolution différentielle pour le recalage rigide d'images médicales volumiques. Technique et science informatiques, 20(5):605-627 (Numéro thématique RenPar'2000). In French language. ISSN 0752-4072. See also [Sal00] . 

Description: In this article parallelizing DE for 3D image registration is discussed.

[SPH01] M. Salomon, G.-R. Perrin and F. Heitz (to appear 2001). Differential evolution for medical image registration. In: 2001 International Conference on Artificial Intelligence (IC-AI 2001), Las Vegas, USA, June 25-28, 2001. 7 pages. See also [SPH00].

[SB01] Anatoly Sukov and Arkady Borisov (2001). A Study of Search Technique in Differential Evolution. In: Radek Matoušek and Pavel Ošmera (eds.) (2001). Proceedings of MENDEL 2001, 7th International Conference on Soft Computing, June 6.–8. 2001, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 144-148. ISBN 80-214-1894-X. 

Abstract: The aim of this paper is to investigate the algorithm of differential evolution. This algorithm is a comparatively non-complicated technique of solution search as applied to multiparameter optimization tasks. Nevertheless there are two essential factors that do not allow to widely apply the considered solution search technique. One of them is the principle of coding variables that constitute a population the algorithm works with. The second problem is of pure technical character: in the process of search, stagnation occurs when there is no optimal solution in the population and the vectors available are not heterogeneous. Besides studying search possibilities of the differential evolution, some ways to cope with the problem of stagnation so as to raise the performance of the algorithm are also suggested.

[TWLWL01] Mark Taylor, John Wall, Neil Loxley, Matthew Wormington and Tamzin Lafford (2001). High resolution X-ray diffraction using a high brilliance source, with rapid data analysis by auto-fitting. Materials Science and Engineering B, 80(1-3):95-98, 22 March 2001. 

Abstract: In a production environment in particular, fast data collection and analysis, which are also highly reliable, are desirable. Measurement can be speeded up by increasing the diffracted intensity, thus reducing the time required to measure it reliably. Increased intensity with a smaller beam footprint at the sample have been achieved in a double-crystal diffractometer by the use of a novel ellipsoidal mirror working by total external reflection, positioned before the reference crystal. To optimise the performance of the mirror and provide high brightnesses, an X-ray source with a very small focal spot is required. Such a high brightness source has been made that uses electromagnetic focusing of the electron beam onto the target. Rapid data analysis is achieved by the use of an auto-fitting program that employs a genetic algorithm and the full dynamical theory of X-ray diffraction. Choice of an appropriate error function produces a deep global minimum while the genetic algorithm avoids convergence on local minima. From the model that produces the best fit, samples parameters such as layer thickness and alloy composition are extracted with quantified goodness of fit.

[TKM01] Josef Tvrdik, Ivan Krivy and Ladislav Misik (2001). Evolutionary Algorithm with Competing Heuristics. In: Radek Matoušek and Pavel Ošmera (eds.) (2001). Proceedings of MENDEL 2001, 7th International Conference on Soft Computing, June 6.–8. 2001, Brno, Czech Republic. Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science, Brno (Czech Republic), pp. 58-64. ISBN 80-214-1894-X. 

Abstract: The aim of this paper is to study the efficiency of different heuristics for generating new trial points in evolutionary algorithms. More than twenty heuristics were implemented and their role in the evolutionary process were followed up. The optimization experiments were done with several test functions. The influence of competing heuristics on reliability and number of objective function evaluations was studied by statistical analysis of the experimental data. Evolutionary algorithm with competing heuristics was found more reliable and effective in most multimodal functions under testing.

[VM01] Jan Vondras and Pravoslav Martinek (2001). New Approach to Analog Filters and Group Delay Equaliser Transfer Function Design. In: The International Conference onElectronics, Circuits and Systems, ICECS 2001, Malta, 2-5 September 2001, Vol.1., pp. 157-160. ISBN 0-7803-7057-0. 

Abstract: The starting point for filters and group delay equalisers design is the appropriate solution of the approximation problem. Through the presented technique is possible to design a transfer function standard even no standard filters with respect to their poles and zeros quality and group delay responses. The technique was also used for transfer function design of group delay equaliser. In this case there were prescribed requirements on group delay response and quality of poles and zeros as well. To solve these large constraint problems, modifying Differential Evolution (DE) is used, as an effective way for penalty function minimization .

[WSJ01] Wang, F.-S., Su, T.-L. and Jang, H.-J. (2001). Hybrid Differential Evolution for Problems of Kinetic Parameter Estimation and Dynamic Optimization of an Ethanol Fermentation Process. Industrial and Engineering Chemistry Research 40(13):2876-2885. ACS American Chemical Society. ISSN 0888-5885.

[YHK01] Jinn-Moon Yang, Jorng-Tzong Horng and Cheng-YanKao (2001). Integrating adaptive mutations and family competition with differential evolution for flexible ligand docking. In: Proceedings of the 2001 Congress on Evolutionary Computation, 27-30 May 2001, Seoul, South Korea, Vol. 1, pp. 473-480. IEEE, Piscataway, NJ, USA. ISBN 0-7803-6657-3. 

Abstract: A flexible ligand docking protocol based on evolutionary algorithms is investigated. The proposed approach integrates decreasing-based mutations and self-adaptive mutations with differential evolution. This approach possesses global and local search strategies to balance the trade-off between exploitation and exploration of the search. The proposed approach is applied to a dihydrofolate reductase enzyme with the anti-cancer drug methotrexate and two analogues of antibacterial drug trimethoprim. Numerical results indicate that the new approach is very robust.

[ZVL01] Ivan Zelinka, Vladimir Vasek and Jouni Lampinen (2001). Nové algoritmy globální optimalizace. Automatizace 44(10): 628-634, October 2001. ISSN 0005-125X. (in Czech language).

2002

[Ab02a] Hussein A. Abbass (2002). An Evolutionary Artificial Neural Networks Approach for Breast Cancer Diagnosis. Artificial Intelligence in Medicine 25():265-281.

Abstract: This paper presents an evolutionary artificial neural network (EANN) approach based on the pareto-differential evolution (PDE) algorithm augmented with local search for the prediction of breast cancer. The approach is named memetic pareto artificial neural network (MPANN). Artificial neural networks (ANNs) could be used to improve the work of medical practitioners in the diagnosis of breast cancer. Their abilities to approximate nonlinear functions and capture complex relationships in the data are instrumental abilities which could support the medical domain. We compare our results against an evolutionary programming approach and standard backpropagation (BP), and we show experimentally that MPANN ahs better generalization and much lower computational cost. 

[Ab02b] Hussein A. Abbass (2002). The Self-Adaptive Pareto Differential Evolution Algorithm. Proceedings of the 2002 Congress on Evolutionary Computation, CEC'02, Honolulu, Hawaii, May 12-17, 2002. Vol.1, pp.831–836. ISBN 0-7803-7282-4. 

Abstract: The Pareto Differential Evolution (PDE) algorithm was introduced last year and showed competitive results. The behavior of PDE, as in many other evolutionary multiobjective optimization (EMO) methods, varies according to the crossover and mutation rates. In this paper, we present a new version of PDE with self-adaptive crossover and mutation. We call the new version Self-adaptive Pareto Differential Evolution (SPDE). The emphasis of this paper is to analyze the dynamics and behavior of SPDE. The experiments will also show that the algorithm is very competitive to other EMO algorithms.

[Ab02c]Hussein A. Abbass (2002). A Memetic Pareto Evolutionary Approach to Artificial Neural Networks. In: Lecture Notes in Artificial Intelligence, Vol. 2256. Springer-Verlag..

Abstract: Evolutionary Artificial Neural Networks (EANN) have been a focus of research in the areas of Evolutionary Algorithms (EA) and Artificial Neural Networks (ANN) for the last decade. In this paper, we present an EANN approach based on pareto multi-objective optimization and differential evolution augmented with local search. We call the approach Memetic Pareto Artificial Neural Networks (MPANN). We show empirically that MPANN is capable to overcome the slow training of traditional EANN with equivalent or better generalization.

[CZ02] Crutchley D.A and Zwolinski M. (2002). Using Evolutionary and Hybrid Algorithms for DC Operating Point Analysis of Nonlinear Circuits. Proceedings of the 2002 Congress on Evolutionary Computation, CEC'02, Honolulu, Hawaii, May 12-17, 2002. Vol.1, pp.753–758. ISBN 0-7803-7282-4. 

Abstract: Traditionally the DC operating points of a nonlinear electronic circuit are found using the Newton-Raphson method. It has known problems. It is not globally convergent; it can frequently diverge and cannot find multiple solutions in a single pass. We will discuss the use of Evolutionary Algorithms to overcome these problems.

[FL02] Fan H.-Y., Lampinen J. (2002). A Trigonometric Mutation Approach to Differential Evolution. In: Giannakoglou K.C., Tsahalis D.T., Periaux J., Papailiou K.D. and Fogarty T. (eds.) (2002). Evolutionary Methods for Design, Optimization and Control (Proceedings of the EUROGEN2001 Conference, Athens, Greece, September 19-21, 2001), pp. 65–70. CIMNE, Barcelona (Spain). ISBN 84-89925-97-6.

Abstract: An attempt to accelerate the convergence velocity of the differential evolution (DE) algorithm has been done recently by authors through introducing a trigonometric mutation operator into the DE. This article describes a preliminary study of this mutation strategy. The mechanism of the trigonometric mutation operator is initially presented and analyzed, and demonstrated by minimizing some benchmark functions.

[GMW02] Goswami J.C., Mydur R. and Wu P. (2002). Application of Differential Evolution Algorithm to Model Based WellLog-Data Inversion. In: Antennas and Propagation Society International Symposium, June 16-21, 2002, Vol. 1, pp. 318-321. ISBN 0-7803-7330-8.

[KHH02] Kilkki J., Huapeng W. and Handroos H. (2002). Applying the Differential Evolution Algorithm to the Optimisation of the Redundant Parallel Manipulator. In: Giannakoglou K.C., Tsahalis D.T., Periaux J., Papailiou K.D. and Fogarty T. (eds.) (2002). Evolutionary Methods for Design, Optimization and Control (Proceedings of the EUROGEN2001 Conference, Athens, Greece, September 19-21, 2001), pp. 223–228. CIMNE, Barcelona (Spain). ISBN 84-89925-97-6.

Abstract: This paper describes the design and optimisation of the new industrial product. The design object was a large-scale redundant parallel manipulator. Parallel manipulators have found wide use in industrial robots in the last years, because of their significant advantages over conventional serial link manipulations. The advantages are high stiffness, a better accuracy, and improved dynamic characteristics. The optimisation problem is modelled and solved by the Optimaze-optimisation program which uses the Differential Evolution algorithm as the optimisation algorithm. Finite element analysis is linked to the optmisation. The discrete optimisation parameters are the thicknesses of the steel plates, the diameters of the hydraulic cylinders and the dimensions of the telescopes. The dimensions of the manipulator are used as continuous optmisation variables. The multi objective function consists of the total mass and the working envelope of the structure. The buckling of the hydraulic cylinders, the fatigue life and the static strength of the steel structure are considered as constraints of the optimisation problem. The optimised structure is presented and the problems met during the optimisation process are reported. The Differential Evolution algorithm was found to be suitable for the mixed number optimisation of the current structure. The feasible are was not easy to achieve without optimisation.

[Lam02a] Lampinen Jouni (2002). A Constraint Handling Approach for the Differential Evolution Algorithm. Proceedings of the 2002 Congress on Evolutionary Computation, CEC'02, Honolulu, Hawaii, May 12-17, 2002. Vol.2, pp.1468–1473. ISBN 0-7803-7282-4.

Abstract: An extension for the Differential Evolution algorithm is proposed for handling nonlinear constraint functions. In comparison with the original algorithm, only the replacement criterion was modified for handling the constraints. In this article the proposed method is described and demonstrated by solving a suite of ten well-known test problems.

[Lam02b] Lampinen Jouni (2002). A Constraint Handling Method for the Differential Evolution Algorithm. In: Sincak P., Vascak J., Kvasnicka V. and Pospichal J. (eds.) (2002). Intelligent Technologies – Theory and Applications, pp. 152–158. ISBN 1-58603-256-9 (IOS Press). ISBN 4-274-90512-8-C3055 (Ohmsha).

Abstract: An extension for the Differential Evolution algorithm is proposed for handling nonlinear constraint functions. In comparison with the original algorithm, only the replacement criterion was modified for handling the constraints. Therefore the proposed approach is straightforward to implement and use. The user is not required to set any penalty parameters or any other additional search parameters. Furthermore, the user is not assumed to provide a feasible solution as a starting point for searching. In this article the proposed method is described and demonstrated by solving a suite of ten well-known test problems.

[LHW02] Yung-Chien Lin, Kao-Shing Hwang and Feng-Sheng Wang (2002). Hybrid Differential Evolution with Multiplier Updating Method for Nonlinear Constrained Optimization. Proceedings of the 2002 Congress on Evolutionary Computation, CEC'02, Honolulu, Hawaii, May 12-17, 2002. Vol.1, pp.872–877. ISBN 0-7803-7282-4. 

Abstract: In this paper, we introduce hybrid differential evolution with a multiplier updating method to solve constrained optimization problems. An adaptive scheme for penalty parameters is involved in the proposed algorithm so that smaller penalty parameters can be used and does not affect the final search results. Computational examples reveal that nearly identical minimum solutions can be obtained using the proposed algorithm even under wide variation of the initial penalty parameters.

[LiuLa02a] Junhong Liu and Jouni Lampinen (2002). On Setting the Control Parameter of the Differential Evolution Method. In: Matoušek, Radek and Ošmera, Pavel (eds.) (2002). Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, June 5.–7. 2002, Brno, Czech Republic, pp. 11–18. Brno University of Technology, Faculty of Mechanical Engineering, Brno (Czech Republic). ISBN 80-214-2135-5.

Abstract: The Differential Evolution is a floating-point encoded evolutionary algorithm for global optimization over continuous spaces. The determination of its control parameters could be complicated for some real applications; several trials are typically needed to define those parameters. This situation motivates studying the influence of control variables on the performance of the Differential Evolution algorithm. In this article, the performance of the Differential Evolution algorithm has been investigated with different settings of control variables. Utilizing the formers’ suggestions about ranges of control variables, three sets of experiments have been realized to investigate the influence of control variables on the performance of the algorithm. Effectiveness, efficiency and robustness of Differential Evolution algorithm are sensitive to the setting of the control variables. Experimental results have demonstrated that the best setting for the control variables can be different for different functions and the same functions with different requirements for consumption time and accuracy.

[LiuLa02b] Junhong Liu and Jouni Lampinen (2002). Adaptive Parameter Control of Differential Evolution. In: Matoušek, Radek and Ošmera, Pavel (eds.) (2002). Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, June 5.–7. 2002, Brno, Czech Republic, pp. 19–26. Brno University of Technology, Faculty of Mechanical Engineering, Brno (Czech Republic). ISBN 80-214-2135-5.

Abstract: Recently the Differential Evolution algorithm, a branch of Evolutionary algorithms, has gained increasing popularity and is used in many practical cases as a robust method as well. However choosing suitable valuables for it’s control parameters can sometimes be difficult. Preferably the values should be set automatically, rather than by the user. Currently the trial-and-error method has to be used for finding good control parameters. In some cases, the time taken for finding suitable values for control parameters by trial-and-error takes too long to be accepted.This fact degrades the applicability of the algorithm since the user should have a substantial amount of knowledge about performing a control parameter setting process. This article discusses a new automatic method for control parameter setting. We propose an adaptive Differential Evolution algorithm with fuzzy logic controlled search parameters. Utilizing a fuzzy model, based on human knowledge and expertise, an adaptive control parameter setting process is applied to accelerate the convergence velocity of the Differential Evolution algorithm. The feedback of the Fuzzy Logic effectiveness, efficiency and robustness of the Adaptive Differential Evolution method has been described to be superior to those of the traditional Differential Evolution algorithm using all the constant control variables. Experimental results demonstrate that the Adaptive Differential Evolution technique is a novel and potentially powerful approach.

[LPV02] Laskari E.C., Parsopoulos K.E., Vrahatis M.N. (2002).Evolutionary Operators in Global Optimization with Dynamic Search Trajectories. Technical Report T.R 02-05, 2002. Department of Mathematics, University of Patras. 

Abstract: One of the most common approaches for solving Unconstrained Global Optmization problems is the application of multi-start algorithms. These algorithms usually combine already found minimizers and previously selected initial points, to generate new starting points, at which, local search methods are applied to detect new minimizers. Multi-start algorithms are usual terminated once a stochastic criterion is satisfied. In this paper, operators used in Differential Evolution algorithms, are utilized to generate the starting points of the Global Optimization with Dynamic Search Trajectories method. Result for different well-known test functions are reported, supporting the claim that the proposed approach improves drastically the performance of the algorithm, in terms of the total number of function evaluations required.

[Mad02] Madavan, Nateri K. (2002). Multiobjective Optimization Using a Pareto Differential Evolution Approach. Proceedings of the 2002 Congress on Evolutionary Computation, CEC'02, Honolulu, Hawaii, May 12-17, 2002. Vol.2, pp.1145–1150. ISBN 0-7803-7282-4. 

Abstract: Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

[MPE02]Mynick H.E., Pomphrey N. and Ethier S. (2002). Exploration of Stellarator Configuration Space with Global Search Methods. Physics of Plasmas 9(3): 869-876, March, 2002. ISSN 1070-664X.

Abstract: An exploration of stellarator configuration space z for quasi-axisymmetric stellarator (QAS) designs is discussed, using methods which provide more global view of that space. To this end, a “differential evolution” search algorithm has been implemented in an existing stellarator optimizer, which is much less prone to become trapped in local, suboptimal minima of the cost function chithat the local search methods used previously. This search algorithm is complemented by mapping studies of chi over z aimed at gaining insight into the results of the automated searches. It is found that a wide range of attractive QAS configurations previously found fall into a small number of classes, with each class corresponding to a basin of chi(z). Maps are developed on which these earlier stellarators can be placed, the relations among them seen, and understanding gained into the physics differences between them. It is also found that, while still large, the region of z space containing practically realizable QAS configurations is much smaller than earlier supposed.

[Smu02] Tomislav Šmuc (2002). Improving Convergence Properties of the Differential Evolution Algorithm. In: Matoušek, Radek and Ošmera, Pavel (eds.) (2002). Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, June 5.–7. 2002, Brno, Czech Republic, pp. 80–86. Brno University of Technology, Faculty of Mechanical Engineering, Brno (Czech Republic). ISBN 80-214-2135-5.

Abstract: Differential evolution is a relatively novel evolutionary algorithm for solving general type of numeric optimization problems. Its simplicity and good convergence properties have been the reason for its broad application in practical scientific engineering problems. Although convergence properties of differential evolution algorithm for modestly dimensioned problems reported in the literature were judged as excellent, analyses of algorithm’s performance are still rather elementary. This work presents results of the study in dynamics of the algorithm on a set of constrained optimization problems. Results and insight gained in the numerical experiments suggested introduction of population refreshment mechanism into the basic differential evolution algorithm, in order to prevent stagnation but also to improve the convergence speed of the algorithm.

[TKM02] Josef Tvrdík, Ivan Krivý and Ladislav Misik (2002). Competing Heuristic – Experimental Study . Matoušek, Radek and Ošmera, Pavel (eds.) (2002). Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, June 5.–7. 2002, Brno, Czech Republic, pp. 74–79. Brno University of Technology, Faculty of Mechanical Engineering, Brno (Czech Republic). ISBN 80-214-2135-5.

Abstract: The aim of this paper is to study the properties of evolutionary algorithms with competing heuristics in dependence on several factors like the number of heuristics in competition, the values of their tuning parameters, the rules of competition and so on. Thirty six heuristics were implemented and their role in the evolutionary process was investigated. The optimization experiments were done with several well-known test functions (DeJong 1 and 2, Ackley, Griewangk). The main variables measured in experiments were the number of the objective function evaluations needed for reaching the stopping condition and the reliability of finding a point very near to the global minimum. The evolutionary algorithms with competing heuristics were more efficient than other evolutionary algorithms in some tasks.

[TMK02] Josef Tvrdík, Ladislav Misik and Ivan Krivý (2002). Competing Heuristics in Evolutionary Algorithms. In: Sincak P., Vascak J., Kvasnicka V. and Pospichal J. (eds.) (2002). Intelligent Technologies – Theory and Applications, pp. 159–165. ISBN 1-58603-256-9 (IOS Press). ISBN 4-274-90512-8-C3055 (Ohmsha).

Abstract: The paper deals with a class of evolutionary algorithms (EAs) for the global optimization. Special attention is paid to the controlled random search (CRS). Generalization of the EA is proposed with several heuristics competing with each other when generating new trial points. The condition for asymptotic convergence of the algorithm are briefly discussed. Two instances of the EA with competing heuristics were implemented and the experimental results obtained on several test functions are presented.

[Zah02] Daniela Zaharie (2002). Critical Values for the Control Parameters of Differential Evolution Algorithms. In: Matoušek, Radek and Ošmera, Pavel (eds.) (2002). Proceedings of MENDEL 2002, 8th International Mendel Conference on Soft Computing, June 5.–7. 2002, Brno, Czech Republic, pp. 62–67. Brno University of Technology, Faculty of Mechanical Engineering, Brno (Czech Republic). ISBN 80-214-2135-5.

Abstract: The population diversity plays an important role in the behavior of evolution strategies. This paper analyzes, both from a theoretical and an empirical viewpoint, the relationship between the control parameters of differential evolution algorithms and the evolution of population variance. Using this relationship, values of the control parameters for which premature convergence can be prevented are obtained.

[ZVKL02]Ivan Zelinka, Vladimir Vasek, Vojtech Kresalek and Jouni Lampinen (2002). Nové algoritmy globální optimalizace. Jemná Mechanika a Optika (Fine Mechanics and Optics) 47(4):112-118, 128, April 2002. (in Czech language).ISSN 0447-6441.

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