. "6"^^ . "[B358D907ADFB]" . "genetic algorithm; travelling salesman probl\u00E9m; max-min algebra; max-plus algebra; Monge matrix"@en . . . "RIV/62690094:18450/12:50001880" . "Usage of the extremal algebra in solving the travelling salesman problem" . . . "Usage of the extremal algebra in solving the travelling salesman problem"@en . "2"^^ . "000316715900126" . . "2"^^ . "Usage of the extremal algebra in solving the travelling salesman problem" . "O" . "2012-01-11+01:00"^^ . "RIV/62690094:18450/12:50001880!RIV14-MSM-18450___" . . . . "Slezsk\u00E1 univerzita. Obchodn\u011B podnikatelsk\u00E1 fakulta" . . . "18450" . "Pozd\u00EDlkov\u00E1, Alena" . . . . "Usage of the extremal algebra in solving the travelling salesman problem"@en . . . "Cimler, Richard" . "Mathematical methods in economics : proceedings of 30th international conference" . "This article compares many ways of solving the traveling salesman problem. At first classical heuristic methods and methods using graph theory are mentioned. At the first part many universal methods are described, which can be also used in other transportation problems. The traveling salesman problem is solved by using genetic algorithm in the second part of this article. This algorithm generates at the beginning the first generation, chooses five thousand parents by the roulette method, crosses these pairs and determines the next generation. This process continues with next generations until stabilization. The algorithm is demonstrated on two examples. At the final part extremal algebras, max-plus algebra and max-min algebra, are defined and illustrated by examples. Monge matrices and some their properties are described in these algebras. The optimization of the traveling salesman problem, which leads to a reduction of the computation complexity, is described for these matrices. The optimization is solved at first for the classical case and then for the matrices that satisfy the strict Monge property. Matrices with the strict Monge property lead to the linear complexity of the problem." . "176289" . . "978-80-7248-779-0" . "This article compares many ways of solving the traveling salesman problem. At first classical heuristic methods and methods using graph theory are mentioned. At the first part many universal methods are described, which can be also used in other transportation problems. The traveling salesman problem is solved by using genetic algorithm in the second part of this article. This algorithm generates at the beginning the first generation, chooses five thousand parents by the roulette method, crosses these pairs and determines the next generation. This process continues with next generations until stabilization. The algorithm is demonstrated on two examples. At the final part extremal algebras, max-plus algebra and max-min algebra, are defined and illustrated by examples. Monge matrices and some their properties are described in these algebras. The optimization of the traveling salesman problem, which leads to a reduction of the computation complexity, is described for these matrices. The optimization is solved at first for the classical case and then for the matrices that satisfy the strict Monge property. Matrices with the strict Monge property lead to the linear complexity of the problem."@en . . "Karvin\u00E1" . . "Karvin\u00E1" .