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

TL;DR

This paper provides a theoretical runtime analysis of the multi-valued compact genetic algorithm (cGA) on the generalized LeadingOnes problem, extending previous work to multi-valued variables and binary cases.

Contribution

It offers the first runtime analysis of the multi-valued cGA on r-LeadingOnes, including the binary case, with a derived runtime bound.

Findings

Runtime of r-cGA on r-LeadingOnes is O(n^2 r^2 log^3 n log^2 r) with high probability.

Extends analysis of EDAs to multi-valued decision variables and generalized functions.

Fills a gap in understanding the behavior of cGA on LeadingOnes for binary and multi-valued cases.

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.