Solving the Traveling Salesman Problem Based on The Genetic Reactive Bone Route Algorithm whit Ant Colony System

Abstract

Abstract:The TSP is considered one of the most well-known combinatorial optimization tasks and researchers have paid so much attention to the TSP for many years. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The objective is to minimize the total distance traveled by the salesman. Because this problem is a non-deterministic polynomial (NP-hard) problem in nature, a hybrid meta-heuristic algorithm called REACSGA is used for solving the TSP. In REACSGA, a reactive bone route algorithm that uses the ant colony system (ACS) for generating initial diversified solutions and the genetic algorithm (GA) as an improved procedure are applied. Since the performance of the Metaheuristic algorithms is significantly influenced by their parameters, Taguchi Method is used to set the parameters of the proposed algorithm. The proposed algorithm is tested on several standard instances involving 24 to 318 nodes from the literature. The computational result shows that the results of the proposed algorithm are competitive with other metaheuristic algorithms for solving the TSP in terms of better quality of solution and computational time respectively. In addition, the proposed REACSGA is significantly efficient and finds closely the best known solutions for most of the instances in which thirteen best known solutions are also found.

Annealing Ant Colony Optimization with Mutation Operator for Solving TSP

“…As can be seen in Table 4, the values of columns best and PD_Best show that there was no significant difference between the proposed algorithm and Yousefikhoshbakht et al [32] on the small instances with cities less than or equal to 100. For the larger instances, the proposed algorithm gained much better results than Yousefikhoshbakht et al [32].…”

“…As can be seen in Table 4, the values of columns best and PD_Best show that there was no significant difference between the proposed algorithm and Yousefikhoshbakht et al [32] on the small instances with cities less than or equal to 100. For the larger instances, the proposed algorithm gained much better results than Yousefikhoshbakht et al [32]. Comparing with Mahi et al [31], the proposed algorithm achieved better results in all the 8 instances with respect to best found solution, average solution, PD_Best, and PD_Avg.…”

“…In the second experiment, the proposed algorithm was compared with four state-of-the-art metaheuristic algorithms: Chen and Chien [27], Wang et al [41], Yousefikhoshbakht et al [32], and Mahi et al [31]. The authors of these algorithms proved that their algorithms outperformed the other algorithms in the literature.…”

“…In Table 4, the proposed algorithm was compared with Yousefikhoshbakht et al [32] and Mahi et al [31] on 15 and 8 benchmark instances, respectively, with cities from 51 to 200 as reported in their studies. As can be seen in Table 4, the values of columns best and PD_Best show that there was no significant difference between the proposed algorithm and Yousefikhoshbakht et al [32] on the small instances with cities less than or equal to 100.…”

“…The PSO was used to determine the optimum values of the two main parameters of ACO which affected algorithm performance and the 3-Opt was used to escape from the local optima found by ACO algorithm. Furthermore, Yousefikhoshbakht et al [32] proposed REACSGA for solving small TSP instances which employed the modified ACS for generating initial diversified solutions and GA for intensification mechanisms.…”