Numerical Approach of Symmetric Traveling Salesman Problem Using Simulated Annealing

Abstract

The aim of this paper is to elaborate the performance of Simulated Annealing (SA) algorithm for solving traveling salesmen problems. In this paper, SA algorithm is modified by using the interaction between outer and inner loop of algorithm. This algorithm produces low standard deviation and fast computational time compared with benchmark algorithms from several research papers. Here SA uses a certain probability as indicator for finding the best and worse solution. Moreover, the strategy of SA as cooling to temperature ratio is still given. Thirteen benchmark cases and thirteen square grid symmetric TSP are used to see the performance of the SA algorithm. It is shown that the SA algorithm has promising results in finding the best solution of the benchmark cases and the squared grid TSP with relative error 0 - 7.06% and 0 – 3.31%, respectively. Further, the SA algorithm also has good performance compared with the well-known metaheuristic algorithms in references.

Simulated Annealing – 2 Opt Algorithm for Solving Traveling Salesman Problem

“…The use of the results from the inner loop as the outer loop input is proven to improve the performance of the SA algorithm in solving small-scale symmetric TSP problems with the number of cities from 9 -225. The use of these interactions gives good results compared to several other algorithms such as ACO (ant colony optimization), PSO (particle swarm optimization), SFLA (shuffled frog leaping algorithms), GA (genetic algorithm), BHA (black hole algorithm), STA (state transition algorithm) in completing the TSP symmetric benchmark test [4]. However, using interaction to get the optimal solution still requires much time, especially for many cities.…”

“…In this case, a numerical experiment was conducted to test the performance of the SA -2 Opt algorithm in solving symmetric TSP cases consisting of 16 -225 cities. Comparisons were made with the results of the SA algorithm presented in reference [4]. The results of this comparison are presented in Table 1.…”

“…In the article [4], there are two cases of symmetric TSPs, namely cases taken from the benchmark data available in reference [18] and the case of the square grid TSP. SG denotes this TSP square grid case in Table 1.…”

“…Various modifications were done to improve the performance of the SA algorithm. Several studies about the modification of the SA algorithm can be found in some references [4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…According to [4], the combination of outer and inner loops in the SA algorithm can simplify the algorithm in finding local solutions. Continuing the research, started in [4], by adding process loops at one temperature before the temperature reduction scheme is carried out and incorporating 2-opt local searches is the focus of this article.…”