Runtime Analysis of a Multi-Valued Compact Genetic Algorithm on Generalized OneMax

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Hauptverfasser: Adak, Sumit, Witt, Carsten
Format: Preprint
Veröffentlicht: 2024
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author Adak, Sumit
Witt, Carsten
author_facet Adak, Sumit
Witt, Carsten
contents A class of metaheuristic techniques called estimation-of-distribution algorithms (EDAs) are employed in optimization as more sophisticated substitutes for traditional strategies like evolutionary algorithms. EDAs generally drive the search for the optimum by creating explicit probabilistic models of potential candidate solutions through repeated sampling and selection from the underlying search space. Most theoretical research on EDAs has focused on pseudo-Boolean optimization. Jedidia et al. (GECCO 2023) proposed the first EDAs for optimizing problems involving multi-valued decision variables. By building a framework, they have analyzed the runtime of a multi-valued UMDA on the r-valued LeadingOnes function. Using their framework, here we focus on the multi-valued compact genetic algorithm (r-cGA) and provide a first runtime analysis of a generalized OneMax function. To prove our results, we investigate the effect of genetic drift and progress of the probabilistic model towards the optimum. After finding the right algorithm parameters, we prove that the r-cGA solves this r-valued OneMax problem efficiently. We show that with high probability, the runtime bound is O(r2 n log2 r log3 n). At the end of experiments, we state one conjecture related to the expected runtime of another variant of multi-valued OneMax function.
format Preprint
id arxiv_https___arxiv_org_abs_2404_11239
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Runtime Analysis of a Multi-Valued Compact Genetic Algorithm on Generalized OneMax
Adak, Sumit
Witt, Carsten
Neural and Evolutionary Computing
A class of metaheuristic techniques called estimation-of-distribution algorithms (EDAs) are employed in optimization as more sophisticated substitutes for traditional strategies like evolutionary algorithms. EDAs generally drive the search for the optimum by creating explicit probabilistic models of potential candidate solutions through repeated sampling and selection from the underlying search space. Most theoretical research on EDAs has focused on pseudo-Boolean optimization. Jedidia et al. (GECCO 2023) proposed the first EDAs for optimizing problems involving multi-valued decision variables. By building a framework, they have analyzed the runtime of a multi-valued UMDA on the r-valued LeadingOnes function. Using their framework, here we focus on the multi-valued compact genetic algorithm (r-cGA) and provide a first runtime analysis of a generalized OneMax function. To prove our results, we investigate the effect of genetic drift and progress of the probabilistic model towards the optimum. After finding the right algorithm parameters, we prove that the r-cGA solves this r-valued OneMax problem efficiently. We show that with high probability, the runtime bound is O(r2 n log2 r log3 n). At the end of experiments, we state one conjecture related to the expected runtime of another variant of multi-valued OneMax function.
title Runtime Analysis of a Multi-Valued Compact Genetic Algorithm on Generalized OneMax
topic Neural and Evolutionary Computing
url https://arxiv.org/abs/2404.11239