A list-based simulated annealing algorithm with crossover operator for the traveling salesman problem

The traveling salesman problem (TSP) is one of the most popular combinatorial optimization problems today. It is a problem that is easy to identify but hard to solve. Therefore, it belongs to the class of NP-hard optimization problems, and it is a problem of high time complexity. The TSP can be used to solve various real-world problems. Therefore, researchers use it as a standard test bench for performance evaluation of new algorithms. In this study, a new simulated annealing algorithm with crossover operator was proposed, and it was called LBSA-CO. The LBSA-CO is a population-based metaheuristic method. In this method, a list-based temperature cooling schedule, which can adapt to the topology of the solution space of the problem, was used. The solutions in the population were improved with the inversion, insertion and 2-opt local search operators. The order crossover (OX1) and genetic edge recombination crossover (ER) operators were applied to the improved solutions to accelerate the convergence. In addition, the Taguchi method was used to tune the parameters of the LBSA-CO. The proposed method was tested on 65 well-known TSP instances. The results indicated that this method performs better than the state-of-the-art methods on many instances.