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Bat algorithm is a population metaheuristic proposed in 2010 which is basedon the echolocation or bio-sonar characteristics of microbats. Since its firstimplementation, the bat algorithm has been used in a wide range of fields. Inthis paper, we present a discrete version of the bat algorithm to solve thewell-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 havecompared its performance in 37 instances with the results obtained by fivedifferent techniques: evolutionary simulated annealing, genetic algorithm, anisland based distributed genetic algorithm, a discrete firefly algorithm and animperialist competitive algorithm. In order to obtain fair and rigorouscomparisons, we have conducted three different statistical tests along thepaper: the Student's $t$-test, the Holm's test, and the Friedman test. We havealso compared the convergence behaviour shown by our proposal with the onesshown by the evolutionary simulated annealing, and the discrete fireflyalgorithm. The experimentation carried out in this study has shown that thepresented improved bat algorithm outperforms significantly all the otheralternatives in most of the cases.

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