Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918121817767936 |
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| author | Alghouass, Yasser Doerr, Benjamin Krejca, Martin S. Lagmah, Mohammed |
| author_facet | Alghouass, Yasser Doerr, Benjamin Krejca, Martin S. Lagmah, Mohammed |
| contents | 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 $σ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II Alghouass, Yasser Doerr, Benjamin Krejca, Martin S. Lagmah, Mohammed Neural and Evolutionary Computing 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 $σ$-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. |
| title | Proven Approximation Guarantees in Multi-Objective Optimization: SPEA2 Beats NSGA-II |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2505.01323 |