Discrete Teaching-learning-based optimization Algorithm for Traveling Salesman Problems

Abstract

Abstract. In this paper, a discrete variant of TLBO (DTLBO) is proposed for solving the traveling salesman problem (TSP). In the proposed method, an effective learner representation scheme is redefined based on the characteristics of TSP problem. Moreover, all learners are randomly divided into several sub-swarms with equal amounts of learners so as to increase the diversity of population and reduce the probability of being trapped in local optimum. In each subswarm, the new positions of learners in the teaching phase and the learning phase are generated by the crossover operation, the legality detection and mutation operation, and then the offspring learners are determined based on greedy selection. Finally, to verify the performance of the proposed algorithm, benchmark TSP problems are examined and the results indicate that DTLBO is effective compared with other algorithms used for TSP problems.

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“…For this reason, it is necessary to make a change in the original TLBO algorithm, so that discrete values taken from a set can be selected. This discrete version of the algorithm (DTLBO) is based on the research proposed in [35] and substantial changes have been made to adapt it to the TSP case study.…”

“…In [35], the whole population consists of 100 individuals. Although the paper does not mention it implicitly, it can be guessed that each subpopulation contains four individuals, so 25 subpopulations are supposed to be formed.…”

“…In Figure 2, it can be observed that locations 3 and 5 appear in the last positions they occupied in the original unfeasible vector, that is, positions 5 and 6, respectively. In contrast to the work proposed in [35], which uses four completely random subpopulations, in this version of the DTLBO one of the individuals is not generated randomly but is assigned initial values based on a greedy strategy. This is intended to accelerate the convergence of the algorithm and preserve its ability to avoid local minima by maintaining randomness in the subpopulations.…”

“…In this version of the algorithm, four different ways of creating new individuals from crossovers were introduced and are shown in Equation (5). In contrast to the work presented in [35], in which a fixed cross is assigned between individuals, this approach makes a random selection for each cross operation. This randomness avoids falling into local minima and increases the variability of populations.…”

“…Although the accuracy of the DTLBO presented in [35] is best when compared with well-known algorithms such as ACO, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA), and only in some specific cases it is slightly beaten by ACO and ABC. It is also the case that its performance is low when cities have a large number of places to visit.…”