An Improved Epsilon Constraint-handling Method in MOEA/D for CMOPs with Large Infeasible Regions

TL;DR

This paper introduces MOEA/D-IEpsilon, an improved constraint-handling method for multi-objective evolutionary algorithms, which dynamically adjusts epsilon levels to effectively solve constrained problems with large infeasible regions, outperforming existing methods.

Contribution

The paper presents a novel epsilon constraint-handling mechanism integrated with MOEA/D, specifically designed for CMOPs with large infeasible regions, demonstrating superior performance over existing algorithms.

Findings

MOEA/D-IEpsilon outperforms four other decomposition-based CMOEAs on benchmark problems.

MOEA/D-IEpsilon achieves better solutions on a real-world robot gripper optimization problem.

Dynamic epsilon adjustment improves convergence and feasibility handling in CMOPs.

Abstract

This paper proposes an improved epsilon constraint-handling mechanism, and combines it with a decomposition-based multi-objective evolutionary algorithm (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). The proposed constrained multi-objective evolutionary algorithm (CMOEA) is named MOEA/D-IEpsilon. It adjusts the epsilon level dynamically according to the ratio of feasible to total solutions (RFS) in the current population. In order to evaluate the performance of MOEA/D-IEpsilon, a new set of CMOPs with two and three objectives is designed, having large infeasible regions (relative to the feasible regions), and they are called LIR-CMOPs. Then the fourteen benchmarks, including LIR-CMOP1-14, are used to test MOEA/D-IEpsilon and four other decomposition-based CMOEAs, including MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP and C-MOEA/D. The experimental results indicate that MOEA/D-IEpsilon is significantly better than the other four CMOEAs on all of the test instances, which shows that MOEA/D-IEpsilon is more suitable for solving CMOPs with large infeasible regions. Furthermore, a real-world problem, namely the robot gripper optimization problem, is used to test the five CMOEAs. The experimental results demonstrate that MOEA/D-IEpsilon also outperforms the other four CMOEAs on this problem.