MOEA/D using covariance matrix adaptation evolution strategy for complex multi-objective optimization problems

Multi-objective optimization is a blooming research area since many real-world problems comprise multiple objectives. Multi-objective evolutionary algorithms (MOEAs) have been widely used to solve the multi-objective optimization problems. In particular, the decomposition based MOEA (MOEA/D) has achieved considerable successes in tackling multi-objective optimization problems. The covariance matrix adaptation evolution strategy (CMAES) is known for its effectiveness in solving complex numerical optimization problems. This study integrates CMAES into MOEA/D as the MOEA/D-CMAES for the merits of MOEA/D framework in multi-objective optimization and CMAES in complex numerical optimization. In MOEA/D-CMAES, each subproblem is handled with one CMAES. To avoid the drastic increase in the number of offspring generated and their fitness evaluations, MOEA/D-CMAES generates only one offspring in each subproblem. The multivariate normal distribution in each CMAES is updated by the collaboration of the offspring generated in the present subproblem and those of other subproblems. Experimental results show that MOEA/D-CMAES outperforms MOEA/D using differential evolution in terms of hypervolume and convergence speed, which validate the effectiveness and efficiency of MOEA/D-CMAES in multi-objective optimization.

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

[2]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

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

[4]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[5]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

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

[7]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[8]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[9]  Ponnuthurai Nagaratnam Suganthan,et al.  Problem Definitions and Evaluation Criteria for the CEC 2014 Special Session and Competition on Single Objective Real-Parameter Numerical Optimization , 2014 .

[10]  Petros Koumoutsakos,et al.  Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) , 2003, Evolutionary Computation.

[11]  Qingfu Zhang,et al.  Stable Matching-Based Selection in Evolutionary Multiobjective Optimization , 2014, IEEE Transactions on Evolutionary Computation.