What Weights Work for You? Adapting Weights for Any Pareto Front Shape in Decomposition-based Evolutionary Multi-Objective Optimisation

TL;DR

This paper introduces AdaW, an adaptive weight adjustment method for decomposition-based multi-objective optimization that effectively handles diverse Pareto front shapes without prior knowledge.

Contribution

The paper proposes a novel weight adaptation approach, AdaW, which dynamically adjusts weights during evolution to better fit various Pareto front geometries.

Findings

AdaW effectively handles diverse Pareto front shapes.

Improves solution distribution without prior front shape knowledge.

Demonstrates robustness across high-dimensional problems.

Abstract

The quality of solution sets generated by decomposition-based evolutionary multiobjective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often lead to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this paper, we propose an approach to adapt the weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating five parts in the weight adaptation --- weight generation, weight addition, weight deletion, archive maintenance, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerated, 6) the badly-scaled, and 7) the high-dimensional.