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A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem. (English) Zbl 1084.90014
Summary: A quantitative study is presented of the typical behavior of the simulated annealing algorithm based on a cooling schedule presented previously by the authors. The study is based on the analysis of numerical results obtained by systematically applying the algorithm to a 100-city traveling salesman problem. The expectation and the variance of the cost are analyzed as a function of the control parameter of the cooling schedule. A semiempirical average-case performance analysis is presented from which estimates are obtained on the expectation of the average final result obtained by the simulated annealing algorithm as a function of the distance parameter, which determines the decrement of the control parameter.

MSC:
90B10 Deterministic network models in operations research
82-08 Computational methods (statistical mechanics) (MSC2010)
82D99 Applications of statistical mechanics to specific types of physical systems
90C27 Combinatorial optimization
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