Push and pull search embedded in an M2M framework for solving constrained multi-objective optimization problems

In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations. However, most state-of-the-art MOEAs show poor performance in balancing them, and can cause the working populations to concentrate on part of the Pareto fronts, leading to serious imbalanced searching between preserving diversity and achieving convergence. This paper proposes a method which combines a multi-objective to multi-objective (M2M) decomposition approach with the push and pull search (PPS) framework, namely PPS-M2M. To be more specific, the proposed algorithm decomposes a CMOP into a set of simple CMOPs. Each simple CMOP corresponds to a sub-population and is solved in a collaborative manner. When dealing with constraints, each sub-population follows a procedure of “ignore the constraints in the push stage and consider the constraints in the pull stage”, which helps each working sub-population get across infeasible regions. In order to evaluate the performance of the proposed PPS-M2M, it is compared with the other nine algorithms, including CM2M, MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP, C-MOEA/D, NSGA-II-CDP, MODE-ECHM, CM2M2 and MODE-SaE on a set of benchmark CMOPs. The experimental results show that the proposed PPS-M2M is significantly better than the other nine algorithms. In addition, a set of constrained and imbalanced multi-objective optimization problems (CIMOPs) are suggested to compare PPS-M2M and PPS-MOEA/D. The experimental results show that the proposed PPS-M2M outperforms PPS-MOEA/D on CIMOPs.