A Weight Adaptation Trigger Mechanism in Decomposition-based Evolutionary Multi-Objective Optimisation

TL;DR

Decomposition-based MOEAs rely on fixed, uniformly distributed weights that align with regular Pareto fronts, but struggle with irregular fronts. The authors propose ATM-MOEA/D, an archive-guided trigger mechanism that detects stagnation and assesses consistency between the population and an archive to decide when weight adaptation is needed, applying an AdaW-inspired add-delete scheme only for irregular fronts. Experimental results across 36 problems show that ATM-MOEA/D outperforms state-of-the-art weight-adaptation methods on irregular fronts and matches fixed-weight MOEA/D on regular fronts in both IGD and HV, while reducing unnecessary weight changes and improving convergence. The approach offers a practical path to robust performance for decomposition-based MOEAs across diverse front geometries, with archive fidelity and parameter settings identified as key future considerations.

Abstract

Decomposition-based multi-objective evolutionary algorithms (MOEAs) are widely used for solving multi-objective optimisation problems. However, their effectiveness depends on the consistency between the problems Pareto front shape and the weight distribution. Decomposition-based MOEAs, with uniformly distributed weights (in a simplex), perform well on problems with a regular (simplex-like) Pareto front, but not on those with an irregular Pareto front. Previous studies have focused on adapting the weights to approximate the irregular Pareto front during the evolutionary process. However, these adaptations can actually harm the performance on the regular Pareto front via changing the weights during the search process that are eventually the best fit for the Pareto front. In this paper, we propose an algorithm called the weight adaptation trigger mechanism for decomposition-based MOEAs (ATM-MOEA/D) to tackle this issue. ATM-MOEA/D uses an archive to gradually approximate the shape of the Pareto front during the search. When the algorithm detects evolution stagnation (meaning the population no longer improves significantly), it compares the distribution of the population with that of the archive to distinguish between regular and irregular Pareto fronts. Only when an irregular Pareto front is identified, the weights are adapted. Our experimental results show that the proposed algorithm not only performs generally better than seven state-of-the-art weight-adapting methods on irregular Pareto fronts but also is able to achieve the same results as fixed-weight methods like MOEA/D on regular Pareto fronts.

Figures (14)

• Figure 1: Comparison of the performance of a weight-fixing algorithm, RVEA Cheng2016, and a weight-adaptive algorithm, RVEAi-GNG Liu2020, on two tri-objective optimisation problems: DTLZ1 Deb2005a with a regular Pareto front and IDTLZ1 Deb2014 with an irregular Pareto front.
• Figure 2: An illustration that the distribution of the stagnant population (i.e., the population close to the intersections between the weight directions and the Pareto front) is similar to that of the archive, so a regular Pareto front may be derived.
• Figure 3: An illustration that the distribution of the stagnant population is not very similar to that of the archive (as the population is distributed not very uniformly), so an irregular Pareto front may be derived.
• Figure 4: The overall flowchart of ATM-MOEA/D.
• Figure 5: The final solution set of the five algorithms on the 2-objective DTLZ1.