A probabilistic analysis of neighborhoods for combinatorial optimization problems and its application

Taichi Kaji ()
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Taichi Kaji: Otaru University of Commerce

Journal of Heuristics, 2021, vol. 27, issue 6, No 4, 1057-1079

Abstract: Abstract Metaheuristics are a class of approximate methods, which are designed to attack hard combinatorial optimization problems. In metaheuristics, a neighborhood is defined by the specified move operation for a solution. The neighborhood plays an essential role in the performance of its algorithms. It is important to capture the statistical properties of neighborhoods. In this paper, we present a theoretical analysis of neighborhoods for a wide class of combinatorial optimization problems, instead of just for restricted instances. First, we give a probabilistic model which allows us to compute statistics for various types of neighborhoods. Here we introduce an approach in which the solution space (the landscape) for a wide class of combinatorial optimization problems can be approximated to AR(1), which can be used to capture the statistics of the solution space. The theoretical results obtained from our proposed model closely match empirically observed behavior. Second, we present an application in which we use our probabilistic model of neighborhoods.

Keywords: Neighborhood; Metaheuristics; Combinatorial optimization; Probabilistic analysis; First-order autoregressive process (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10732-021-09484-y

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