Fixed-Parameter Tractability of the (1+1) Evolutionary Algorithm on Random Planted Vertex Covers

We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every \(O(n \log n)\) steps will find a cover at least as small as the planted cover in...

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Vydané v:	arXiv.org
Hlavní autori:	Kearney, Jack, Neumann, Frank, Sutton, Andrew M
Médium:	Paper
Jazyk:	English
Vydavateľské údaje:	Ithaca Cornell University Library, arXiv.org 16.09.2024
Predmet:	Evolutionary algorithms Parameters Polynomials
ISSN:	2331-8422
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Popis
Shrnutí:	We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every \(O(n \log n)\) steps will find a cover at least as small as the planted cover in polynomial time for sufficiently dense random graphs \(p > 0.71\). For superlogarithmic planted covers, we prove that the (1+1) EA finds a solution in fixed-parameter tractable time in expectation. We complement these theoretical investigations with a number of computational experiments that highlight the interplay between planted cover size, graph density and runtime.
Bibliografia:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2409.10144