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

• URL: http://arxiv.org/abs/2503.21439v1
• Date: Thu, 27 Mar 2025 12:32:15 GMT
• Title: Improved Runtime Analysis of a Multi-Valued Compact Genetic Algorithm on Two Generalized OneMax Problems
• Authors: Sumit Adak, Carsten Witt,
• Abstract summary: We present the first theoretical analysis of the multi-valued cGA (r-cGA) on the G-OneMax function.<n>We demonstrate that the runtime is O(nr3 log2 n log r) with high probability.<n>We also refine the previously established runtime analysis of the r-cGA on r-OneMax.
• Score: 2.07180164747172
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent research in the runtime analysis of estimation of distribution algorithms (EDAs) has focused on univariate EDAs for multi-valued decision variables. In particular, the runtime of the multi-valued cGA (r-cGA) and UMDA on multi-valued functions has been a significant area of study. Adak and Witt (PPSN 2024) and Hamano et al. (ECJ 2024) independently performed a first runtime analysis of the r-cGA on the r-valued OneMax function (r-OneMax). Adak and Witt also introduced a different r-valued OneMax function called G-OneMax. However, for that function, only empirical results were provided so far due to the increased complexity of its runtime analysis, since r-OneMax involves categorical values of two types only, while G-OneMax encompasses all possible values. In this paper, we present the first theoretical runtime analysis of the r-cGA on the G-OneMax function. We demonstrate that the runtime is O(nr^3 log^2 n log r) with high probability. Additionally, we refine the previously established runtime analysis of the r-cGA on r-OneMax, improving the previous bound to O(nr log n log r), which improves the state of the art by an asymptotic factor of log n and is tight for the binary case. Moreover, we for the first time include the case of frequency borders.

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