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

TL;DR

This paper introduces an aging-based non-elitist selection mechanism for multi-objective evolutionary algorithms, demonstrating significant, objective-independent speed-ups in computing Pareto fronts, outperforming previous stochastic methods.

Contribution

It proposes a novel aging-based selection strategy that achieves faster convergence in SMS-EMOA, overcoming limitations of stochastic selection and providing objective-independent speed-ups.

Findings

Proves a speed-up factor of ((k)^{k-1}) regardless of objectives.

Demonstrates positive polynomial runtime speed-up for constant number of objectives.

Shows aging-based mechanisms outperform stochastic selection in efficiency.

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 $k \ge 4\log_2(n)$, 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.