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

TL;DR

This paper introduces a new multi-objective evolutionary algorithm inspired by a recent single-objective method, demonstrating faster optimization on benchmark problems through theoretical analysis and dynamic parameter tuning.

Contribution

It extends the $(1+(eta,eta))$ genetic algorithm to multi-objective optimization, creating the $(1+(eta,eta))$ global SEMO algorithm with proven faster asymptotic performance.

Findings

The new algorithm outperforms the classic global SEMO on OneMinMax.

Dynamic parameter setting further reduces runtime to $O(n^2)$.

The approach introduces a novel application of single-objective ideas to multi-objective optimization.

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 $O(n^2 \log n)$.