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

• URL: http://arxiv.org/abs/2210.03618v1
• Date: Fri, 7 Oct 2022 15:18:32 GMT
• Title: The $(1+(\lambda,\lambda))$ Global SEMO Algorithm
• Authors: Benjamin Doerr, Omar El Hadri, Adrien Pinard
• Abstract summary: We show that the $(lambda,lambda))$ genetic computation can be transported to multi-objective evolutionary computation. We define the $(lambda,lambda))$ global SEMO algorithm, a variant of the classic global SEMO algorithm, and prove that it optimize the OneMinMax algorithm benchmarkally faster than the global SEMO.
• Score: 8.34061303235504
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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