September 20, 2025

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

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Mathematical proof demonstrates SPEA2's superior approximation guarantees in multi-objective optimization, suggesting it outperforms NSGA-II.

A steady-state SPEA2 can compute optimal approximations of the Pareto front efficiently, outperforming NSGA-II.
This work provides the first mathematical proof of the advantages of SPEA2's complex distance system over NSGA-II.
SPEA2 achieves optimal approximations in polynomial time, while NSGA-II offers lesser guarantees with approximation ratios of roughly two.
Both experimental and analytical results indicate that optimal solutions are rarely efficiently found with NSGA-II.

Alghouass et al. (2025) studied this question.

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Mathematical proof demonstrates SPEA2's superior approximation guarantees in multi-objective optimization, suggesting it outperforms NSGA-II.