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

2025-02-23

AI Summary

Fixed-weight MOEA/D suffers from degraded performance on irregular Pareto fronts, while existing adaptive-weight strategies compromise convergence accuracy on regular fronts. Method: This paper proposes a stagnation-aware conditional weight adaptation mechanism that jointly integrates evolutionary stagnation detection and archive-driven Pareto front shape identification; weight adaptation is triggered only upon detecting front irregularity, otherwise fixed weights are retained to preserve optimization precision on regular fronts. Contribution/Results: Experimental results demonstrate that the proposed method significantly outperforms seven state-of-the-art adaptive-weight approaches on irregular fronts, while achieving performance comparable to standard MOEA/D on regular fronts. By reconciling generality and accuracy, this work establishes a new robust paradigm for MOEA/D, enhancing its applicability across diverse Pareto front geometries.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Mixture of Experts (MoE)
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Improving weight adaptation in MOEAs
• Distinguishing regular vs. irregular Pareto fronts
• Enhancing optimization for irregular Pareto fronts

Innovation

• Weight adaptation trigger mechanism
• Archive for Pareto front approximation
• Stagnation detection for weight adaptation