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ISPRS Int. J. Geo-Inf. 2018, 7(3), 115; https://doi.org/10.3390/ijgi7030115

Spatial Transformation of Equality – Generalized Travelling Salesman Problem to Travelling Salesman Problem

1,2,†,* , 2,3,†
and
1,†
1
Geomatics Engineering Department, Istanbul Technical University, Maslak, Istanbul 34469, Turkey
2
National Innovation and Research Center for Geographical Information Technologies, Maslak, Istanbul 34469, Turkey
3
Department of Geology, Faculty of Mines, Istanbul Technical University, Maslak, Istanbul 34469, Turkey
Current address: Istanbul Technical University, Maslak, Istanbul 34469, Turkey.
*
Author to whom correspondence should be addressed.
Received: 9 February 2018 / Revised: 23 February 2018 / Accepted: 23 February 2018 / Published: 15 March 2018
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Abstract

The Equality-Generalized Travelling Salesman Problem (E-GTSP), which is an extension of the Travelling Salesman Problem (TSP), is stated as follows: given groups of points within a city, like banks, supermarkets, etc., find a minimum cost Hamiltonian cycle that visits each group exactly once. It can model many real-life combinatorial optimization scenarios more efficiently than TSP. This study presents five spatially driven search-algorithms for possible transformation of E-GTSP to TSP by considering the spatial spread of points in a given urban city. Presented algorithms are tested over 15 different cities, classified by their street-network’s fractal-dimension. Obtained results denote that the R-Search algorithm, which selects the points from each group based on their radial separation with respect to the start–end point, is the best search criterion for any E-GTSP to TSP conversion modelled for a city street network. An 8.8% length error has been reported for this algorithm. View Full-Text
Keywords: generalized travelling salesman problem; shortest route; combinatorial optimization; OpenStreetMap generalized travelling salesman problem; shortest route; combinatorial optimization; OpenStreetMap
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Zia, M.; Cakir, Z.; Seker, D.Z. Spatial Transformation of Equality – Generalized Travelling Salesman Problem to Travelling Salesman Problem. ISPRS Int. J. Geo-Inf. 2018, 7, 115.

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