An Improved Discrete Bat Algorithm for Symmetric and Asymmetric Traveling Salesman Problems

TL;DR

This paper introduces an improved discrete bat algorithm tailored for symmetric and asymmetric traveling salesman problems, demonstrating superior performance over several existing metaheuristics through extensive statistical testing.

Contribution

The paper presents a novel improved discrete bat algorithm specifically designed for TSP, with comprehensive comparative analysis against multiple algorithms.

Findings

Outperforms five other algorithms in most instances

Shows faster convergence compared to simulated annealing and firefly algorithms

Statistically significant improvements demonstrated

Abstract

Bat algorithm is a population metaheuristic proposed in 2010 which is based on the echolocation or bio-sonar characteristics of microbats. Since its first implementation, the bat algorithm has been used in a wide range of fields. In this paper, we present a discrete version of the bat algorithm to solve the well-known symmetric and asymmetric traveling salesman problems. In addition, we propose an improvement in the basic structure of the classic bat algorithm. To prove that our proposal is a promising approximation method, we have compared its performance in 37 instances with the results obtained by five different techniques: evolutionary simulated annealing, genetic algorithm, an island based distributed genetic algorithm, a discrete firefly algorithm and an imperialist competitive algorithm. In order to obtain fair and rigorous comparisons, we have conducted three different statistical tests along the paper: the Student's $t$-test, the Holm's test, and the Friedman test. We have also compared the convergence behaviour shown by our proposal with the ones shown by the evolutionary simulated annealing, and the discrete firefly algorithm. The experimentation carried out in this study has shown that the presented improved bat algorithm outperforms significantly all the other alternatives in most of the cases.