Abstract
The imperialist competitive algorithm (ICA) is a new heuristic algorithm proposed for continuous optimization problems. The research about its application on solving the traveling salesman problem (TSP) is still very limited. Aiming to explore its ability on solving TSP, we present a discrete imperialist competitive algorithm in this paper. The proposed algorithm modifies the original rules of the assimilation and introduces the 2-opt algorithm into the revolution process. To examine its performance, we tested the proposed algorithm on 10 small-scale and 2 large-scale standard benchmark instances from the TSPLIB and compared the experimental results with that obtained by two other ICA-based algorithms and six other existing algorithms. The proposed algorithm shows excellent performance in the experiments and comparisons.
Highlights
Because of its widespread application and significant research value, the traveling salesman problem (TSP) has probably become the most classical, famous and extensively studied problem in the field of combinatorial optimization [1,2,3]
Mohammad Ahmadvand et al [36] proposed a hybrid algorithm based on imperialist competitive algorithm (ICA) and tabu search, using ICA to solve TSP at first and using a tabu search to improve the solution, the results obtained by the hybrid algorithm are not yet good enough
Here we define that this assignment is according to the formula (7), in where the N denotes the size of the initial population, the m denotes the number of imperialists, N and m can be set freely according to the size of the TSP to be solved, the kj denotes the number of colonies assigned to the jth imperialist and the fj denotes the cost of the jth imperialist
Summary
Because of its widespread application and significant research value, the traveling salesman problem (TSP) has probably become the most classical, famous and extensively studied problem in the field of combinatorial optimization [1,2,3]. Compared with the exact algorithms for solving TSP, the approximate algorithms are simpler. They cannot guarantee to find the optimal solution, often they can obtain a satisfactory solution. They are more suitable to be used to solve larger-scale TSP [5]. Mohammad Ahmadvand et al [36] proposed a hybrid algorithm based on ICA and tabu search, using ICA to solve TSP at first and using a tabu search to improve the solution, the results obtained by the hybrid algorithm are not yet good enough.
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