Hot off the Press: Runtime Analysis of the Compact Genetic Algorithm on the LeadingOnes Benchmark

Marcel Chwialkowski, Benjamin Doerr, Martin S. Krejca

Abstract: The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA)—another simple EDA—, the cGA has been subject to extensive mathematical runtime analyses, often showcasing a similar or even superior performance to competing approaches. Surprisingly though, up to date and in contrast to the UMDA and many other heuristics, we lack a rigorous runtime analysis of the cGA on the LeadingOnes benchmark—one of the most studied theory benchmarks in the domain of evolutionary computation.We fill this gap in the literature by conducting a formal runtime analysis of the cGA on LeadingOnes of problem size n. For the cGA's single parameter μ = Ω(n log2 n), we prove that the cGA samples the optimum of LeadingOnes with high probability within O(μn log n) function evaluations. For the best choice of μ, our result matches, up to polylogarithmic factors, the typical O(n2) runtime that many randomized search heuristics exhibit on LeadingOnes.This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Marcel Chwiałkowski, Benjamin Doerr, and Martin S. Krejca: Runtime analysis of the compact genetic algorithm on the LeadingOnes benchmark. IEEE Transactions on Evolutionary Computation 2025. Early access. DOI: 10.1109/TEVC.2025.3549929 [3].

External IDs:dblp:conf/gecco/ChwialkowskiDK25