A two-phase framework of locating the reference point for decomposition-based constrained multi-objective evolutionary algorithms

A self-organizing map approach for constrained multi-objective optimization problems

There exist many multi-objective optimization problems (MOPs) containing several inequality and equality constraints in practical applications, which are known as CMOPs. CMOPs pose great challenges for existing multi-objective evolutionary algorithms (MOEAs) since the difficulty in balancing the objective minimization and constraint satisfaction. Without loss of generality, the distribution of the Pareto set for a continuous m-objective CMOP can be regarded as a piecewise continuous manifold of dimension (m − 1). According to this property, a self-organizing map (SOM) approach for constrained multi-objective optimization problems is proposed in this article. In the proposed approach, we adopt the strategy of two population evolution, in which one population is evolved by considering all the constraints and the other population is used to assist in exploring the areas. In the evolutionary stage, each population is assigned a self-organizing map for discovering the population distribution structure in the decision space. After the topological mapping, we utilize the extracted neighborhood relationship information to generate promising offspring solutions. Afterwards, the neuron weight vectors of SOM are updated by the objective vectors of the surviving offsprings. Through the proposed approach, we can make the population efficiently converge to the feasible region with suitable levels of diversity. In the experiments, we compare the proposed method with several state-of-the-art approaches by using 48 benchmark problems. The evaluation results indicate that the overwhelmingly superior performance of the proposed method over the other peer algorithms on most of the tested problems. The source code is available at https://github.com/hccccc92918/CMOSMA.