Differential Evolution with automatic population injection scheme for constrained problems

Over the last few years, Differential Evolution (DE) algorithms have shown brilliant performance in solving a wide variety of complex optimization problems. However, there is no guarantee that these algorithms will not be trapped in local optima for some problems. In this paper, a DE algorithm is proposed that uses a new mechanism to escape from local optima, during the evolution process by injecting new individuals, when the algorithm gets stuck in local optima. The performance of the algorithm is analyzed by solving a well-known set of constrained optimization problems. The algorithm shows consistent performance, and is superior to several state-of-the-art algorithms.

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

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

[3]  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.

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

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

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

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

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

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

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

[11]  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.

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

[13]  Xiaodong Li,et al.  Efficient differential evolution using speciation for multimodal function optimization , 2005, GECCO '05.

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

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

[16]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[18]  Ruhul A. Sarker,et al.  Self-adaptive differential evolution incorporating a heuristic mixing of operators , 2013, Comput. Optim. Appl..

[19]  Tapabrata Ray,et al.  Parameters adaptation in Differential Evolution , 2012, 2012 IEEE Congress on Evolutionary Computation.

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

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

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

[23]  Efrén Mezura-Montes,et al.  Differential evolution in constrained numerical optimization: An empirical study , 2010, Inf. Sci..

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

[25]  Ruhul A. Sarker,et al.  On an evolutionary approach for constrained optimization problem solving , 2012, Appl. Soft Comput..

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

[27]  René Thomsen,et al.  Multimodal optimization using crowding-based differential evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[28]  Z. Dong,et al.  A Modified Differential Evolution Algorithm With Fitness Sharing for Power System Planning , 2008, IEEE Transactions on Power Systems.

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

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

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

[32]  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.