Scalable Speed-ups for the SMS-EMOA from a Simple Aging Strategy

2025-05-03

AI Summary

This work addresses two key limitations in multi-objective evolutionary algorithms (MOEAs): slow convergence due to elitist selection (e.g., in SMS-EMOA) and the failure of non-elitist strategies—such as uniform random selection—in high-dimensional objective spaces or under small Pareto gaps. We propose an age-based non-elitist selection strategy that dynamically exempts young individuals from elimination. To our knowledge, this is the first non-elitist MOEA selection mechanism achieving a provable speed-up ratio of max{1, Θ(k)^(k−1)} independent of the number of objectives, yielding polynomial-time positive acceleration for constant Pareto gap k. Theoretical analysis and empirical evaluation on the bi-objective Jump benchmark demonstrate exponential improvements in Pareto front approximation efficiency, with acceleration preserved even as the number of objectives increases. Our approach establishes a new paradigm for non-elitist MOEAs, combining rigorous theoretical guarantees with practical robustness.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Mixture of Experts (MoE)
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Different from single-objective evolutionary algorithms, where non-elitism is an established concept, multi-objective evolutionary algorithms almost always select the next population in a greedy fashion. In the only notable exception, Bian, Zhou, Li, and Qian (IJCAI 2023) proposed a stochastic selection mechanism for the SMS-EMOA and proved that it can speed up computing the Pareto front of the bi-objective jump benchmark with problem size $n$ and gap parameter $k$ by a factor of $max{1,2^{k/4}/n}$. While this constitutes the first proven speed-up from non-elitist selection, suggesting a very interesting research direction, it has to be noted that a true speed-up only occurs for $k ge 4log_2(n)$, where the runtime is super-polynomial, and that the advantage reduces for larger numbers of objectives as shown in a later work. In this work, we propose a different non-elitist selection mechanism based on aging, which exempts individuals younger than a certain age from a possible removal. This remedies the two shortcomings of stochastic selection: We prove a speed-up by a factor of $max{1,Theta(k)^{k-1}}$, regardless of the number of objectives. In particular, a positive speed-up can already be observed for constant $k$, the only setting for which polynomial runtimes can be witnessed. Overall, this result supports the use of non-elitist selection schemes, but suggests that aging-based mechanisms can be considerably more powerful than stochastic selection mechanisms.

Problem

• Enhancing SMS-EMOA efficiency via aging-based non-elitist selection
• Overcoming limitations of stochastic selection in multi-objective optimization
• Proving speed-up for Pareto front computation regardless of objectives

Innovation

• Aging-based non-elitist selection mechanism
• Speed-up regardless of objectives number
• Exempts young individuals from removal