A Hybrid Cellular Genetic Algorithm for the Traveling Salesman Problem

Yanlan Deng,Qiuhong Wang,Juxia Xiong,Ali Asghar Rahmani Hosseinabadi

doi:10.1155/2021/6697598

Yanlan Deng, Qiuhong Wang + Show 2 more

Open Access

https://doi.org/10.1155/2021/6697598

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Abstract

The traveling salesman problem (TSP), a typical non-deterministic polynomial (NP) hard problem, has been used in many engineering applications. Genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. However, it has some issues for solving TSP, including quickly falling into the local optimum and an insufficient optimization precision. To address TSP effectively, this paper proposes a hybrid Cellular Genetic Algorithm with Simulated Annealing (SA) Algorithm (SCGA). Firstly, SCGA is an improved Genetic Algorithm (GA) based on the Cellular Automata (CA). The selection operation in SCGA is performed according to the state of the cell. Secondly, SCGA, combined with SA, introduces an elitist strategy to improve the speed of the convergence. Finally, the proposed algorithm is tested against 13 standard benchmark instances from the TSPLIB to confirm the performance of the three cellular automata rules. The experimental results show that, in most instances, the results obtained by SCGA using rule 2 are better and more stable than the results of using rule 1 and rule 3. At the same time, we compared the experimental results with GA, SA, and Cellular Genetic Algorithm (CGA) to verify the performance of SCGA. The comparison results show that the distance obtained by the proposed algorithm is shortened by a mean of 7% compared with the other three algorithms, which is closer to the theoretical optimal value and has good robustness.

Highlights

Traveling salesman problem (TSP) is one of the most common combinatorial optimization problems, and it has been widely used in this field
Algorithm 8 shows the pseudocode of the proposed hybrid Cellular Genetic Algorithm with Simulated Annealing (SA) (SCGA) and its required steps for the TSP solution
In order to solve the TSP effectively, a hybrid Cellular Genetic Algorithm with SA (SCGA) is proposed. e algorithm combines the principles of GA, Cellular Automata (CA), and SA to improve the optimization GA’s performance

Summary

Introduction

Traveling salesman problem (TSP) is one of the most common combinatorial optimization problems, and it has been widely used in this field. Many problems in the field of combinatorial optimization can be formulated as special TSP instances [1]. Resource optimization in the shortest path and shop scheduling problems are the most frequent TSP applications [2,3,4]. In Word Sense Disambiguation (WSD), problems can be solved by describing WSD as a TSP variant [5]. If the exact algorithm is used to solve TSP, it will take a long time, so the feasibility of using the exact algorithm to solve TSP is very low. Using an approximate solution to solve TSP problems cannot guarantee an optimal solution, it can reach a satisfactory solution in a very short time [8]. Using an approximate solution to solve TSP problems cannot guarantee an optimal solution, it can reach a satisfactory solution in a very short time [8]. us, with the development of heuristic algorithms [9,10,11,12,13,14], many experts and scholars have begun to apply heuristic algorithms to solve TSP, which provides new ideas for solving TSP [15,16,17,18,19,20,21]

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