Hot off the Press: Proven Approximation Superiority of SPEA2 over NSGA-II
TL;DR
This paper provides the first proof that the more complex σ-distance mechanism of the SPEA2 yields a provably superior approximation ability, and shows the first result showing a provable qualitative gap between the approximation abilities of these two algorithms.
Abstract
The SPEA2 and the NSGA-II are two of the most widely used dominance-based multi-objective evolutionary algorithms (MOEAs). While prior theoretical work established similar runtime guarantees for both, the differences in their selection mechanisms were not well understood from an approximation perspective. We provide the first proof that the more complex σ-distance mechanism of the SPEA2 yields a provably superior approximation ability. Specifically, the steady-state SPEA2 computes an optimal spread of the OneMinMax Pareto front in O(μ2n log(μ;) log(n)) expected function evaluations. In contrast, the steady-state NSGA-II, when started near an optimal spread with just two sub-optimal gaps, fails to achieve optimality within polynomial time with overwhelming probability. This is the first result showing a provable qualitative gap between the approximation abilities of these two algorithms. This paper summarizes the work Yasser Alghouass, Benjamin Doerr, Martin S. Krejca, and Mohammed Lagmah: Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II. International Joint Conference on Artificial Intelligence, IJCAI 2025. [1].