Exploring Constraint Handling Techniques in Real-world Problems on MOEA/D with Limited Budget of Evaluations

TL;DR

This paper investigates how different constraint handling techniques affect MOEA/D's performance on constrained multi-objective problems, introducing a new technique called Three Stage Penalty that shows competitive results especially on complex real-world problems.

Contribution

The paper introduces the Three Stage Penalty constraint handling technique and evaluates its effectiveness within MOEA/D on various simulated and analytic MOPs.

Findings

Three Stage Penalty performs well on complex real-world problems.

Best CHTs are problem-dependent.

Three Stage Penalty achieves competitive hypervolume results.

Abstract

Finding good solutions for Multi-objective Optimization (MOPs) Problems is considered a hard problem, especially when considering MOPs with constraints. Thus, most of the works in the context of MOPs do not explore in-depth how different constraints affect the performance of MOP solvers. Here, we focus on exploring the effects of different Constraint Handling Techniques (CHTs) on MOEA/D, a commonly used MOP solver when solving complex real-world MOPs. Moreover, we introduce a simple and effective CHT focusing on the exploration of the decision space, the Three Stage Penalty. We explore each of these CHTs in MOEA/D on two simulated MOPs and six analytic MOPs (eight in total). The results of this work indicate that while the best CHT is problem-dependent, our new proposed Three Stage Penalty achieves competitive results and remarkable performance in terms of hypervolume values in the hard simulated car design MOP.