Differential Evolution With Dynamic Parameters Selection for Optimization Problems

Over the last few decades, a number of differential evolution (DE) algorithms have been proposed with excellent performance on mathematical benchmarks. However, like any other optimization algorithm, the success of DE is highly dependent on the search operators and control parameters that are often decided a priori. The selection of the parameter values is itself a combinatorial optimization problem. Although a considerable number of investigations have been conducted with regards to parameter selection, it is known to be a tedious task. In this paper, a DE algorithm is proposed that uses a new mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate, and the population size) for a problem during the course of a single run. The performance of the algorithm is judged by solving three well known sets of optimization test problems (two constrained and one unconstrained). The results demonstrate that the proposed algorithm not only saves the computational time, but also shows better performance over the state-of-the-art algorithms. The proposed mechanism can easily be applied to other population-based algorithms.

[1]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[2]  Gang Liu,et al.  Self-adaptive Clustering-Based Differential Evolution with New Composite Trial Vector Generation Strategies , 2012 .

[3]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[4]  Karl-Dirk Kammeyer,et al.  Parameter Study for Differential Evolution Using a Power Allocation Problem Including Interference Cancellation , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[5]  Janez Brest,et al.  An improved self-adaptive differential evolution algorithm in single objective constrained real-parameter optimization , 2010, IEEE Congress on Evolutionary Computation.

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

[7]  P. Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2010 Competition on Constrained Real- Parameter Optimization , 2010 .

[8]  Janez Brest,et al.  Differential Evolution with Self-adaptation and Local Search for Constrained Multiobjective Optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

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

[10]  Carlos A. Coello Coello,et al.  Constraint-handling in nature-inspired numerical optimization: Past, present and future , 2011, Swarm Evol. Comput..

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

[12]  Janez Brest,et al.  Population Reduction Differential Evolution with Multiple Mutation Strategies in Real World Industry Challenges , 2012, ICAISC.

[13]  Bruce A. Robinson,et al.  Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces , 2009, IEEE Transactions on Evolutionary Computation.

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

[15]  Mehmet Fatih Tasgetiren,et al.  Differential evolution algorithm with ensemble of parameters and mutation strategies , 2011, Appl. Soft Comput..

[16]  Anne Auger,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions , 2009 .

[17]  Ruhul A. Sarker,et al.  Multi-operator based evolutionary algorithms for solving constrained optimization problems , 2011, Comput. Oper. Res..

[18]  Gary G. Yen,et al.  An Adaptive Penalty Formulation for Constrained Evolutionary Optimization , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[19]  Qingfu Zhang,et al.  Differential Evolution With Composite Trial Vector Generation Strategies and Control Parameters , 2011, IEEE Transactions on Evolutionary Computation.

[20]  André da Motta Salles Barreto,et al.  Using performance profiles to analyze the results of the 2006 CEC constrained optimization competition , 2010, IEEE Congress on Evolutionary Computation.

[21]  Helio J. C. Barbosa,et al.  An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization , 2011 .

[22]  Tetsuyuki Takahama,et al.  Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation , 2010, IEEE Congress on Evolutionary Computation.

[23]  Janez Brest,et al.  Population size reduction for the differential evolution algorithm , 2008, Applied Intelligence.

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

[25]  Lawrence Davis,et al.  Adapting Operator Probabilities in Genetic Algorithms , 1989, ICGA.

[26]  Stefan Janaqi,et al.  Generalization of the strategies in differential evolution , 2004, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings..

[27]  Arthur C. Sanderson,et al.  JADE: Adaptive Differential Evolution With Optional External Archive , 2009, IEEE Transactions on Evolutionary Computation.

[28]  Michèle Sebag,et al.  Comparison-Based Adaptive Strategy Selection with Bandits in Differential Evolution , 2010, PPSN.

[29]  Hui Li,et al.  Adaptive strategy selection in differential evolution for numerical optimization: An empirical study , 2011, Inf. Sci..

[30]  K. Deb An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[31]  Elizabeth A. Peck,et al.  Introduction to Linear Regression Analysis , 2001 .

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

[33]  Ponnuthurai N. Suganthan,et al.  Differential evolution with ensemble of constraint handling techniques for solving CEC 2010 benchmark problems , 2010, IEEE Congress on Evolutionary Computation.

[34]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[35]  A. Kai Qin,et al.  Self-adaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[36]  Gregory W. Corder,et al.  Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach , 2009 .

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

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

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

[40]  Carlos A. Coello Coello,et al.  Modified Differential Evolution for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[41]  Yuren Zhou,et al.  An Adaptive Tradeoff Model for Constrained Evolutionary Optimization , 2008, IEEE Transactions on Evolutionary Computation.

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

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

[45]  Jani Rönkkönen ContinuousMultimodal Global Optimization with Differential Evolution-Based Methods , 2009 .

[46]  Josef Tvrdík,et al.  Competitive differential evolution for constrained problems , 2010, IEEE Congress on Evolutionary Computation.

[47]  P. N. Suganthan,et al.  Ensemble of Constraint Handling Techniques , 2010, IEEE Transactions on Evolutionary Computation.

[48]  Josef Tvrdík Adaptation in differential evolution: A numerical comparison , 2009, Appl. Soft Comput..

[49]  P. Suganthan,et al.  Differential evolution algorithm with ensemble of populations for global numerical optimization , 2009 .

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

[51]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .