Abstract
The Traveling Salesman Problem (TSP) is an integer programming problem that falls into the category of NP-Hard problems. As the problem become larger, there is no guarantee that optimal tours will be found within reasonable computation time. Heuristics techniques, like genetic algorithm and simulating annealing, can solve TSP instances with different levels of accuracy. Choosing which algorithm to use in order to get a best solution is still considered as a hard choice. This paper suggests domain reduction as a tool to be combined with any meta-heuristic so that the obtained results will be almost the same. The hybrid approach of combining domain reduction with any meta-heuristic encountered the challenge of choosing an algorithm that matches the TSP instance in order to get the best results.
Highlights
The traveling salesman problem (TSP) is a problem of “finding the shortest possible route given a list of cities and the distances between each pair of cities, such that the route visits each city exactly once and returns to the origin” [1]
For medium to large sized problems the solution obtained by applying genetic algorithm is very close for the solution obtained by applying simulating annealing
Using either genetic or simulating annealing provides similar results once domain reduction is combined with the selected algorithm
Summary
The traveling salesman problem (TSP) is a problem of “finding the shortest possible route given a list of cities and the distances between each pair of cities, such that the route visits each city exactly once and returns to the origin” [1]. This paper considers a symmetric TSP, where a number of cities (or customers) is given as well as the distances between each pair of these cities, and the problem is to find the shortest possible routes that visits each city exactly once and return to the origin. This problem was raised, with trial for a mathematical formulation, in the early 19th century in the UK [2]. The objective is to minimize the domain of the problem in order to minimize the search iterations for the algorithms and getting close (if not similar) results
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