Nested Simulated Annealing Algorithm to Solve Large-Scale TSP Problem

Abstract

AbstractTraveling Salesman Problem is one of the most valuable combination optimization NP-hard in mathematics and computer science. Simulated Annealing Algorithm is one of the better algorithms to solve the TSP problem. However, with the increasing scale of the TSP problem, this algorithm also shows some limitations. That is, the solution performance is poor, and the efficiency is low. This paper proposes a new Nested Simulated Annealing Algorithm (NSA), which divides the megacity group into small and medium-sized urban groups through recursive diffusion and setting the threshold method. In this way, the large-scale TSP problem can be transformed into small and medium-sized TSP problem at first. And then optimize the small and medium-sized TSP problem by using the Simulated Annealing Algorithm. Finally, synthesize a whole to achieve the final optimization effect. In this paper, we use three large-scale TSP problems in the TSPLIB database to test the proposed algorithm and compare it with the traditional Simulated Annealing Algorithm. The results show that the Nested Simulated Annealing Algorithm proposed in this paper has better efficiency and effect than the original algorithm in solving large-scale TSP problems.KeywordsLarge-scale TSP ProblemNested Simulated Annealing AlgorithmRecursive diffusionK-means