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...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	arXiv.org
Hlavní autoři:	Kearney, Jack, Neumann, Frank, Sutton, Andrew M
Médium:	Paper
Jazyk:	angličtina
Vydáno:	Ithaca Cornell University Library, arXiv.org 16.09.2024
Témata:	Evolutionary algorithms Parameters Polynomials
ISSN:	2331-8422
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

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.
Bibliografie:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2409.10144