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arXiv · 2505.01323

Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II

Yasser Alghouass·Benjamin Doerr·Martin S. Krejca·Mohammed Lagmah
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Abstract

Together with the NSGA-II and SMS-EMOA, the strength Pareto evolutionary algorithm 2 (SPEA2) is one of the most prominent dominance-based multi-objective evolutionary algorithms (MOEAs). Different from the NSGA-II, it does not employ the crowding distance (essentially the distance to neighboring solutions) to compare pairwise non-dominating solutions but a complex system of $\sigma$-distances that builds on the distances to all other solutions. In this work, we give a first mathematical proof showing that this more complex system of distances can be superior. More specifically, we prove that a simple steady-state SPEA2 can compute optimal approximations of the Pareto front of the OneMinMax benchmark in polynomial time. The best proven guarantee for a comparable variant of the NSGA-II only assures approximation ratios of roughly a factor of two, and both mathematical analyses and experiments indicate that optimal approximations are not found efficiently.

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Yasser Alghouass, Benjamin Doerr, Martin S. Krejca, Mohammed Lagmah. 2025-05-02. Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II. https://arxiv.org/abs/2505.01323

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