Traveling salesperson problem and neural networks: a complete algorithm in matrix form

Authors:
Nicolae Popoviciu;Mioara Boncut
Affiliations:
Faculty of Mathematics-Informatics, Department of Mathematics, Hyperion University of Bucharest, Bucharest, Romania;Faculty of Sciences, Department of Mathematics, Lucian Blaga University of Sibiu, Sibiu, Romania
Venue:
ICCOMP'07 Proceedings of the 11th WSEAS International Conference on Computers
Year:
2007

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Abstract

The work describes all the necessary steps to solve the traveling salesperson problem. This optimization problem is very easy to formulate -and a lot of works do it-, but it is rather difficult to solve it. By using [1] as a main reference, we formulate an algorithm in a matrix form to solve the problem. The mathematical approach is based on Hopfield neural networks and uses the energy function with the descent gradient method. The algorithm in matrix form is easier to use or to write a computation program. The work has six sections. The section 5 describes the algorithm to solve the traveling salesperson problem and the section 6 contain an numerical example.