A discrete gravitational search algorithm for solving combinatorial optimization problems

Metaheuristics are general search strategies that, at the exploitation stage, intensively exploit areas of the solution space with high quality solutions and, at the exploration stage, move to unexplored areas of the solution space when necessary. The Gravitational Search Algorithm (GSA) is a stochastic population-based metaheuristic that was originally designed for solving continuous optimization problems. It has a flexible and well-balanced mechanism for enhancing exploration and exploitation abilities. In this paper, a Discrete Gravitational Search Algorithm (DGSA) is proposed to solve combinatorial optimization problems. The proposed DGSA uses a Path Re-linking (PR) strategy instead of the classic way in which the agents of GSA usually move from their current position to the position of other agents. The proposed algorithm was tested on a set of 54 Euclidean benchmark instances of TSP with sizes ranging from 51 to 2392 nodes. The results were satisfactory and in the majority of the instances, the results were equal to the best known solution. The proposed algorithm ranked ninth when compared with 54 different algorithms with regard to quality of the solution.