A Runtime Analysis of the Multi-Valued Compact Genetic Algorithm on Generalized LeadingOnes

• URL: http://arxiv.org/abs/2501.09514v2
• Date: Thu, 23 Jan 2025 10:37:42 GMT
• Title: A Runtime Analysis of the Multi-Valued Compact Genetic Algorithm on Generalized LeadingOnes
• Authors: Sumit Adak, Carsten Witt,
• Abstract summary: We analyze the runtime analysis of the multi-valued cGA on the r-valued LeadingOnes function. We show that the runtime of the r-cGA on r-LeadingOnes is O(n2r2 log3 n log2 r) with high probability.
• Score: 2.07180164747172
• License:
• Abstract: In the literature on runtime analyses of estimation of distribution algorithms (EDAs), researchers have recently explored univariate EDAs for multi-valued decision variables. Particularly, Jedidia et al. gave the first runtime analysis of the multi-valued UMDA on the r-valued LeadingOnes (r-LeadingOnes) functions and Adak et al. gave the first runtime analysis of the multi-valued cGA (r-cGA) on the r-valued OneMax function. We utilize their framework to conduct an analysis of the multi-valued cGA on the r-valued LeadingOnes function. Even for the binary case, a runtime analysis of the classical cGA on LeadingOnes was not yet available. In this work, we show that the runtime of the r-cGA on r-LeadingOnes is O(n^2r^2 log^3 n log^2 r) with high probability.

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