Memetic Differential Evolution combined with Constraint Consensus method for solving COPs

Reaching feasible solutions in constrained optimization problems is a prime condition that requires the conversion of one or more infeasible individuals to feasible individuals. In this paper, to ensure the effective movement of infeasible individuals towards feasible region, we introduce a Constraint Consensus method within a Differential Evolution (DE) algorithm for solving constrained optimization problems. In addition, we use Sequential Quadratic Programming as a local search algorithm to speed up the convergence of the algorithm. The algorithm has been tested by solving 24 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]  Paul T. Boggs,et al.  Sequential Quadratic Programming , 1995, Acta Numerica.

[2]  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.

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

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

[5]  Andrzej Stachurski,et al.  Parallel Optimization: Theory, Algorithms and Applications , 2000, Parallel Distributed Comput. Pract..

[6]  Ruhul A. Sarker,et al.  Differential evolution combined with constraint consensus for constrained optimization , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

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

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

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

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

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

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

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

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

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

[17]  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.