An opposition-based repair operator for multi-objective evolutionary algorithm in constrained optimization problems

In this paper, we design a set of multi-objective constrained optimization problems (MCOPs) and propose a new repair operator to address them. The proposed repair operator is used to fix the solutions that violate the box constraints. More specifically, it employs a reversed correction strategy that can effectively avoid the population falling into local optimum. In addition, we integrate the proposed repair operator into two classical multi-objective evolutionary algorithms MOEA/D and NSGA-II. The proposed repair operator is compared with other two kinds of commonly used repair operators on benchmark problems CTPs and MCOPs. The experiment results demonstrate that our proposed approach is very effective in terms of convergence and diversity.

[1]  Yuping Wang,et al.  Multiobjective programming using uniform design and genetic algorithm , 2000, IEEE Trans. Syst. Man Cybern. Part C.

[2]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[3]  M.M.A. Salama,et al.  Opposition-Based Differential Evolution , 2008, IEEE Transactions on Evolutionary Computation.

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

[5]  Mitsuo Gen,et al.  Specification of Genetic Search Directions in Cellular Multi-objective Genetic Algorithms , 2001, EMO.

[6]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

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

[8]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[9]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

[10]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[11]  Marc Schoenauer,et al.  ASCHEA: new results using adaptive segregational constraint handling , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[12]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[13]  Frank Hoffmeister,et al.  Problem-Independent Handling of Constraints by Use of Metric Penalty Functions , 1996, Evolutionary Programming.

[14]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[15]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[16]  Wang Yong,et al.  Constrained Optimization Evolutionary Algorithms , 2009 .

[17]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[18]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

[19]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

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

[21]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[22]  Raphael T. Haftka,et al.  A Segregated Genetic Algorithm for Constrained Structural Optimization , 1995, ICGA.

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

[24]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[25]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[26]  Yuren Zhou,et al.  Constrained Optimization Evolutionary Algorithms: Constrained Optimization Evolutionary Algorithms , 2009 .

[27]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[28]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[29]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

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

[31]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[32]  David W. Coit,et al.  Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems , 1996, INFORMS J. Comput..

[33]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm for Constrained Optimization , 2009 .