A Self-adaptive Interior Penalty Based Differential Evolution Algorithm for Constrained Optimization

A self-adaptive interior penalty method is proposed for the constrained optimization problems by using interior penalty method to handle constraints. A set of interior penalty rules are designed to evaluate feasible solutions and infeasible solutions separately. A self-adaptive penalty factor method is proposed to prevent the interior penalty method from being sensitive to the values of penalty factor and to minimize the interior penalty function value of the optimal solution. As an instance of implementation, a different evolution algorithm is improved by means of the method proposed in this paper, based on which 10 benchmark problems are tested. The numerical solution results indicate that the performance of the method is better than four existing state-of-the-art techniques.

[1]  Jacek M. Zurada,et al.  Swarm and Evolutionary Computation , 2012, Lecture Notes in Computer Science.

[2]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[3]  N. Hansen,et al.  Markov Chain Analysis of Cumulative Step-Size Adaptation on a Linear Constrained Problem , 2015, Evolutionary Computation.

[4]  Efrn Mezura-Montes,et al.  Constraint-Handling in Evolutionary Optimization , 2009 .

[5]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[6]  Luis Enrique Sucar,et al.  MICAI 2004: Advances in Artificial Intelligence , 2004, Lecture Notes in Computer Science.

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

[8]  Carlos A. Coello Coello,et al.  Simple Feasibility Rules and Differential Evolution for Constrained Optimization , 2004, MICAI.

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

[10]  Oliver Kramer,et al.  A Review of Constraint-Handling Techniques for Evolution Strategies , 2010, Appl. Comput. Intell. Soft Comput..

[11]  Margaret H. Wright,et al.  The interior-point revolution in constrained optimization , 1998 .

[12]  M. H. Wright.  The interior-point revolution in optimization: History, recent developments, and lasting consequences , 2004 .

[13]  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.

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

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