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.
Highlights
The Travelling Salesman Problem (TSP) is one of the most well-known and extensively studied combinatorial optimization problems by far
In order to test the five proposed search algorithms above for efficient Equality-Generalized Travelling Salesman Problem (E-GTSP) to TSP transformation, 15 cities are selected based on their different level of street-network patterns and density, for which the data was obtained from the OSM API
Each colored circle represents the average fractional error in the E-GTSP route-length estimated with respect to the optimal route
Summary
The Travelling Salesman Problem (TSP) is one of the most well-known and extensively studied combinatorial optimization problems by far It has been used as a benchmark problem for new urban and navigation developments for decades. It is equivalent to finding the minimum-cost Hamiltonian cycle in G [1] It has many applications in ranging areas of geo-spatial sciences and GIS, like in vehicle routing, urban communication networking, public transport sequencing and scheduling, to name a few (please read [2]). It has always been a great source of attraction from various other disciplines too, especially during the last three decades [3]
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