Multiobjective Optimization Differential Evolution Enhanced with Principle Component Analysis for Constrained Optimization

TL;DR

This paper introduces PCA-projection, a new search operator for multiobjective evolutionary algorithms that uses principal component analysis to adapt to fitness landscapes, improving constrained optimization performance.

Contribution

The paper proposes PCA-projection as a novel operator for MOEAs, demonstrating its effectiveness in constrained optimization through two enhanced algorithms, PMODE and HECO-PDE.

Findings

PCA-projection improves algorithm performance on benchmark problems.

HECO-PDE ranks first in IEEE CEC 2017 constrained optimization competition.

Decomposition-based MOEAs outperform non-dominance-based MOEAs in constrained settings.

Abstract

Multiobjective evolutionary algorithms (MOEAs) have been successfully applied to a number of constrained optimization problems. Many of them adopt mutation and crossover operators from differential evolution. However, these operators do not explicitly utilise features of fitness landscapes. To improve the performance of algorithms, this paper aims at designing a search operator adapting to fitness landscapes. Through an observation, we find that principle component analysis (PCA) can be used to characterise fitness landscapes. Based on this finding, a new search operator, called PCA-projection, is proposed. In order to verify the effectiveness of PCA-projection, we design two algorithms enhanced with PCA-projection for solving constrained optimization problems, called PMODE and HECO-PDE, respectively. Experiments have been conducted on the IEEE CEC 2017 competition benchmark suite in constrained optimisation. PMODE and HECO-PDE are compared with the algorithms from the IEEE CEC 2018 competition and another recent MOEA for constrained optimisation. Experimental results show that an algorithm enhanced with PCA-projection performs better than its corresponding opponent without this operator. Furthermore, HECO-PDE is ranked first on all dimensions according to the competition rules. This study reveals that decomposition-based MOEAs, such as HECO-PDE, are competitive with best single-objective and multiobjective evolutionary algorithms for constrained optimisation, but MOEAs based on non-dominance, such as PMODE, may not.