On the importance of isolated solutions in constrained decomposition-based many-objective optimization

Abstract

During the few past years, decomposition has shown a high performance in solving Multi-objective Optimization Problems (MOPs) involving more than three objectives, called as Many-objective Optimization Problems (MaOPs). The performance of most of the existing decomposition-based algorithms has been assessed on the widely used DTLZ and WFG unconstrained test problems. However, the number of works that have been devoted to tackle the problematic of constrained many-objective optimization is relatively very small when compared to the number of works handling the unconstrained case. Recently there has been some interest to exploit infeasible isolated solutions when solving Constrained MaOPs (CMaOPs). Motivated by this observation, we firstly propose an IS-update procedure (Isolated Solution-based update procedure) that has the ability to: (1) handle CMaOPs characterized by various types of difficulties and (2) favor the selection of not only infeasible solutions associated to isolated sub-regions but also infeasible solutions with smaller Constraint Violation (CV) values. The IS-update procedure is subsequently embedded within the Multi-Objective Evolutionary Algorithm-based on Decomposition (MOEA/D). The new obtained algorithm, named ISC-MOEA/D (Isolated Solution-based Constrained MOEA/D), has been shown to provide competitive and better results when compared against three recent works on the CDTLZ benchmark problems.