A Study of Adaptive Decomposition-based Multiobjective Evolutionary Algorithms for Solving Constrained Problems

Abstract

Many optimization tasks in the real world can be regarded as Multiobjective Optimization Problems (MOPs) that have multiple objectives to be optimized. Due to trade-off relationships among objectives, MOPs usually have the Pareto-optimal solution set (PS) instead of a single optimal solution. In addition, there is the Pareto-optimal front (PF) which is the image of the PS in the objective space. Decomposition-based Multiobjective Evolutionary Algorithms (MOEAs) are one of the most popular categories of algorithms for MOPs. In the previous study, we introduced CIM-based Adaptive resonance theory (CA), a topological clustering algorithm, into a decomposition-based MOEA to realize the adaptive decomposition according to the PF shape and proposed RVEA-CA. Although several studies show that adaptive decomposition-based MOEAs, including RVEA-CA, have high search performance on MOPs with a large number of objectives and high versatility on the various PF shapes, the effect of adaptive decomposition on constrained MOPs has not yet been investigated, to our knowledge. Hence, this paper introduces a constraint-handling method into RVEA-CA and investigates the search performance on constrained MOPs. The computational experiments showed that the proposed method has search performance equal to or better than those of four state-of-the-art constrained MOEAs and discussed the effectiveness of the adaptive decomposition on constrained MOPs.