A neural network algorithm in matrix form and a heuristic greedy method for traveling salesperson problem

Authors:
Nicolae Popoviciu;Mioara Boncuţ
Affiliations:
Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania;Lucian Blaga University of Sibiu, Department of Mathematics, Sibiu, Romania
Venue:
ACMOS'07 Proceedings of the 9th WSEAS international conference on Automatic control, modelling and simulation
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. The section 2 gives a heuristic greedy method and a numerical example, with the mention that this method doesn't assure the optimal route. By using [4] as a main reference, we formulate an algorithm in a matrix form to solve the problem for optimal route. 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 computational program. The work has seven sections. The section 6 describes the algorithm to solve the traveling salesperson problem and the section 7 contains another numerical example.