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Criticality and parallelism in combinatorial optimization.

W G Macready·A G Siapas·S A Kauffman
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Abstract

Local search methods constitute one of the most successful approaches to solving large-scale combinatorial optimization problems. As these methods are increasingly parallelized, optimization performance initially improves but then abruptly degrades to no better than that of random search beyond a certain point. The existence of this transition is demonstrated for a family of generalized spin-glass models and the traveling salesman problem. Finite-size scaling is used to characterize size-dependent effects near the transition, and analytical insight is obtained through a mean-field approximation.

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AlgorithmsModels, StatisticalTemperatureThermodynamicsJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.

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W G Macready, A G Siapas, S A Kauffman. 1996-01-05. Criticality and parallelism in combinatorial optimization.. https://doi.org/10.1126/science.271.5245.56

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