An application of the self-organizing map in the non-Euclidean Traveling Salesman Problem

Authors:
Jan Faigl;Miroslav Kulich;Vojtch Vonásek;Libor Přeučil
Affiliations:
Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic;Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic;Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic;Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 166 27 Prague 6, Czech Republic
Venue:
Neurocomputing
Year:
2011

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Abstract

An application of the self-organizing map (SOM) to the Traveling Salesman Problem (TSP) has been reported by many researchers, however these approaches are mainly focused on the Euclidean TSP variant. We consider the TSP as a problem formulation for the multi-goal path planning problem in which paths among obstacles have to be found. We apply a simple approximation of the shortest path that seems to be suitable for the SOM adaptation procedure. The approximation is based on a geometrical interpretation of SOM, where weights of neurons represent nodes that are placed in the polygonal domain. The approximation is verified in a set of real problems and experimental results show feasibility of the proposed approach for the SOM based solution of the non-Euclidean TSP.