MOEA/D with Adaptative Number of Weight Vectors

TL;DR

This paper introduces an adaptive mechanism for MOEA/D that dynamically adjusts the number of weight vectors, improving performance across different multi-objective problems by filling empty objective space areas.

Contribution

We propose a novel adaptive method for MOEA/D that automatically adjusts weight vectors based on the Consolidation Ratio, enhancing flexibility and performance.

Findings

Adaptive MOEA/D matches fine-tuned vector performance

Outperforms poorly chosen vector sets

Reduces stagnation and improves objective space coverage

Abstract

The Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) is a popular algorithm for solving Multi-Objective Problems (MOPs). The main component of MOEA/D is to decompose a MOP into easier sub-problems using a set of weight vectors. The choice of the number of weight vectors significantly impacts the performance of MOEA/D. However, the right choice for this number varies, given different MOPs and search stages. Here we adaptively change the number of vectors by removing unnecessary vectors and adding new ones in empty areas of the objective space. Our MOEA/D variant uses the Consolidation Ratio to decide when to change the number of vectors, and then it decides where to add or remove these weighted vectors. We investigate the effects of this adaptive MOEA/D against MOEA/D with a poorly chosen set of vectors, a MOEA/D with fine-tuned vectors and MOEA/D-AWA on the DTLZ and ZDT benchmark functions. We analyse the algorithms in terms of hypervolume, IGD and entropy performance. Our results show that the proposed method is equivalent to MOEA/D with fine-tuned vectors and superior to MOEA/D with poorly defined vectors. Thus, our adaptive mechanism mitigates problems related to the choice of the number of weight vectors in MOEA/D, increasing the final performance of MOEA/D by filling empty areas of the objective space while avoiding premature stagnation of the search progress.