A Fitness-assignment Method for Evolutionary Constrained Multi-objective Optimization

TL;DR

This paper introduces IcSDE+, a simple yet effective fitness-assignment method for constrained multi-objective evolutionary algorithms that improves exploration of feasible regions and outperforms existing state-of-the-art algorithms.

Contribution

The paper proposes IcSDE+, a novel single-population fitness assignment approach combining constraint violation, density estimation, and objective summation for better constrained optimization.

Findings

IcSDE+ outperforms 9 state-of-the-art CMOEAs on benchmark tests.

IcSDE+ effectively explores different feasible regions.

The method simplifies constrained multi-objective optimization without sacrificing performance.

Abstract

The effectiveness of Constrained Multi-Objective Evolutionary Algorithms (CMOEAs) depends on their ability to reach the different feasible regions during evolution, by exploiting the information present in infeasible solutions, in addition to optimizing the several conflicting objectives. Over the years, researchers have proposed several CMOEAs to handle Constrained Multi-objective Optimization Problems (CMOPs). However, most of the proposed CMOEAs with scalable performance are too complex because they are either multi-staged or multi-population-based algorithms. Consequently, to ensure the simplicity of CMOEAs, researchers have proposed different fitness-assignment-based CMOEAs by combining different fitness-assignment-based methods used to solve unconstrained multi-objective problems with information regarding the feasibility of each solution. The main performance drawback of such methods is that it is difficult to design a fitness assignment method that can account for constraint violation in addition to convergence and diversity. Hence in this paper, we propose an effective single-population fitness assignment-based CMOEA referred to as IcSDE+ that can explore different feasible regions in the search space. IcSDE+ is a fitness assignment-based algorithm, that is an efficient fusion of constraint violation (c), Shift-based Density Estimation (SDE), and sum of objectives (+). The performance of IcSDE+ is favorably compared against 9 state-of-the-art CMOEAs on 6 different benchmark suites with diverse characteristics.