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arXiv · 2210.03618

The $(1+(\lambda,\lambda))$ Global SEMO Algorithm

Benjamin Doerr·Omar El Hadri·Adrien Pinard
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Abstract

The $(1+(\lambda,\lambda))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties. We show that its main working principle, mutation with a high rate and crossover as repair mechanism, can be transported also to multi-objective evolutionary computation. We define the $(1+(\lambda,\lambda))$ global SEMO algorithm, a variant of the classic global SEMO algorithm, and prove that it optimizes the OneMinMax benchmark asymptotically faster than the global SEMO. Following the single-objective example, we design a one-fifth rule inspired dynamic parameter setting (to the best of our knowledge for the first time in discrete multi-objective optimization) and prove that it further improves the runtime to $O(n^2)$, whereas the best runtime guarantee for the global SEMO is only $O(n^2 \log n)$.

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Benjamin Doerr, Omar El Hadri, Adrien Pinard. 2022-10-07. The $(1+(\lambda,\lambda))$ Global SEMO Algorithm. https://doi.org/10.1145/3512290.3528868

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