Differential Evolution Algorithm: Foundations and Perspectives

Differential Evolution (DE) has recently emerged as simple and efficient algorithm for global optimization over continuous spaces.DE shares many features of the classical Genetic Algorithms (GA). But it is much easier to implement than GA and applies a kind of differential mutation operator on parent chromosomes to generate the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world, resulting in a lot of variants of the basic algorithm, with improved performance. This chapter begins with a conceptual outline of classical DE and then presents several significant variants of the algorithm in greater details.

[1]  Xiao-Feng Xie,et al.  DEPSO: hybrid particle swarm with differential evolution operator , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[2]  Hamid R. Tizhoosh,et al.  Opposition-Based Reinforcement Learning , 2006, J. Adv. Comput. Intell. Intell. Informatics.

[3]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[4]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[5]  A. Kai Qin,et al.  Self-adaptive differential evolution algorithm for numerical optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[6]  D. E. Goldberg,et al.  Optimization and Machine Learning , 2022 .

[7]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[8]  Janez Brest,et al.  Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems , 2006, IEEE Transactions on Evolutionary Computation.

[9]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[10]  José Neves,et al.  The fully informed particle swarm: simpler, maybe better , 2004, IEEE Transactions on Evolutionary Computation.

[11]  Andries Petrus Engelbrecht,et al.  Self-adaptive Differential Evolution , 2005, CIS.

[12]  Xin Yao,et al.  Making a Difference to Differential Evolution , 2008, Advances in Metaheuristics for Hard Optimization.

[13]  P. N. Suganthan,et al.  Differential Evolution Algorithm With Strategy Adaptation for Global Numerical Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[14]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[15]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[16]  W. Price.  Global optimization by controlled random search , 1983 .

[17]  Hamid R. Tizhoosh,et al.  Opposition-Based Learning: A New Scheme for Machine Intelligence , 2005, International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC'06).

[18]  Wyn L. Price,et al.  A Controlled Random Search Procedure for Global Optimisation , 1977, Comput. J..

[19]  Steven M. Lalonde,et al.  A First Course in Multivariate Statistics , 1997, Technometrics.

[20]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[21]  Jouni Lampinen,et al.  A Fuzzy Adaptive Differential Evolution Algorithm , 2005, Soft Comput..

[22]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[23]  Daniel A. Ashlock,et al.  Evolutionary computation for modeling and optimization , 2005 .

[24]  Amit Konar,et al.  Differential Evolution Using a Neighborhood-Based Mutation Operator , 2009, IEEE Transactions on Evolutionary Computation.

[25]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[26]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[27]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

[28]  Hitoshi Iba,et al.  Accelerating Differential Evolution Using an Adaptive Local Search , 2008, IEEE Transactions on Evolutionary Computation.

[29]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[30]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[31]  Mordecai Avriel,et al.  Nonlinear programming , 1976 .

[32]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[33]  M. Yamamura,et al.  Multi-parent recombination with simplex crossover in real coded genetic algorithms , 1999 .

[34]  Shahryar Rahnamayan,et al.  Opposition-Based Differential Evolution for Optimization of Noisy Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[35]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[36]  Carlos A. Coello Coello,et al.  A comparative study of differential evolution variants for global optimization , 2006, GECCO.

[37]  Dana Petcu,et al.  Adaptive Pareto Differential Evolution and Its Parallelization , 2003, PPAM.

[38]  Andy J. Keane,et al.  Meta-Lamarckian learning in memetic algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[39]  Andries Petrus Engelbrecht,et al.  Binary Differential Evolution , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[40]  Amit Konar,et al.  Improving particle swarm optimization with differentially perturbed velocity , 2005, GECCO '05.

[41]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[42]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[43]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[44]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[45]  Amit Konar,et al.  Two improved differential evolution schemes for faster global search , 2005, GECCO '05.

[46]  Hans-Georg Beyer,et al.  On the Dynamics of EAs without Selection , 1998, FOGA.

[47]  Kevin M. Passino,et al.  Biomimicry of bacterial foraging for distributed optimization and control , 2002 .

[48]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[49]  Zbigniew Michalewicz,et al.  Advances in Metaheuristics for Hard Optimization , 2008, Advances in Metaheuristics for Hard Optimization.

[50]  Jouni Lampinen,et al.  A Trigonometric Mutation Operation to Differential Evolution , 2003, J. Glob. Optim..

[51]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

[52]  Saku Kukkonen,et al.  Real-parameter optimization with differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

[53]  Amit Konar,et al.  Annealed Differential Evolution , 2007, 2007 IEEE Congress on Evolutionary Computation.

[54]  Jason Teo,et al.  Exploring dynamic self-adaptive populations in differential evolution , 2006, Soft Comput..