A multioperator genetic algorithm for the traveling salesman problem with job-times

This paper addresses the traveling salesman problem with job-times (TSPJ). TSPJ considers two sets of equal size, a set of tasks and a set of vertices, where a traveler must visit each vertex exactly once, return to the starting vertex, and perform a unique task at each vertex. Each task is assigned to only one vertex, and each task is completed with a job-time that depends on each vertex. Thus, the objective is to minimize the time of the last task performed. However, due to its NP-hardness, existing algorithms do not optimally solve the TSPJ larger instances. Therefore, we propose an approach based on a multioperator genetic algorithm (MGA) that utilizes various initial population procedures, crossover and mutation operators. MGA applies five initial population procedures to generate a diverse population, and employs three crossover operators and six mutation operators, with four mutations focused on diversification and two designed to aid intensification. Furthermore, to improve the quality of the best individual found, a local search is used in every generation, and generational replacement with elitism is considered when generating a new population. MGA is evaluated on four sets of instances ranging in size from 17 to 1200 vertices: tsplib, small, medium, and large. Our approach outperforms the state-of-the-art algorithms on the four instance sets. This performance is attributed to the synergistic effect of the multioperators of crossover and mutation, along with effective parameter tuning.