Differential evolution combined with constraint consensus for constrained optimization

Solving a Constrained Optimization Problem (COP) is much more challenging than its unconstrained counterpart. In solving COPs, the feasibility of a solution is a prime condition that requires the conversion of one or more infeasible individuals to feasible individuals. In this paper, to encourage the effective movement of infeasible individuals towards a feasible region, we introduce a Constraint Consensus (CC) method within the Differential Evolution (DE) algorithm for solving COPs. The algorithm has been tested by solving 13 well-known benchmark problems. The experimental results show that the solutions are competitive, if not better, as compared to the state of the art algorithms.

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

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

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

[4]  Walid Ibrahim,et al.  Improving solver success in reaching feasibility for sets of nonlinear constraints , 2008, Comput. Oper. Res..

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

[6]  Ruhul A. Sarker,et al.  A Three-Strategy Based Differential Evolution Algorithm for Constrained Optimization , 2010, ICONIP.

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

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

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

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

[11]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

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

[13]  Jing J. Liang,et al.  Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constraint-Handling Mechanism , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[14]  John W. Chinneck The Constraint Consensus Method for Finding Approximately Feasible Points in Nonlinear Programs , 2004, INFORMS J. Comput..

[15]  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.

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

[17]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[18]  Y. Censor,et al.  Parallel Optimization: Theory, Algorithms, and Applications , 1997 .

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

[20]  Yair Censor,et al.  The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy , 2003, Ann. Oper. Res..

[21]  Yair Censor,et al.  Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems , 2001, Parallel Comput..

[22]  Y. Censor,et al.  Parallel Optimization:theory , 1997 .

[23]  C. Coello,et al.  Cultured differential evolution for constrained optimization , 2006 .

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

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

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

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

[28]  Riccardo Poli,et al.  Particle Swarm Optimisation , 2011 .

[29]  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 .

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

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

[32]  John W. Chinneck,et al.  Feasibility and Infeasibility in Optimization:: Algorithms and Computational Methods , 2007 .

[34]  R. Storn,et al.  On the usage of differential evolution for function optimization , 1996, Proceedings of North American Fuzzy Information Processing.