Benchmark for Multiple Traveling Salesmen Problem with Visiting Constraints

Multiple Traveling Salesmen Problem with Visiting Constraints (VCMTSP) is a universal variant of Multiple Traveling Salesmen Problem (MTSP) by modeling the accessibility of salesmen to cities with a general accessibility matrix. Such a problem widely exists in practice and has attracted attentions from researchers. However, as far as we know, there is no common benchmark set in VCMTSP for researchers to evaluate the optimization effectiveness of their optimization methods. To fill this gap, this paper builds a common VCMTSP benchmark set based on the popular TSPLIB set. In particular, this benchmark set consists of VCMTSP instances with a variety of numbers of salesmen and cities along with three different types of visiting constraints, namely tight visiting constraints, moderate visiting constraints, and loose visiting constraints. To assess the validity of this benchmark set, this paper further adapts two classical evolutionary algorithms, namely Ant Colony Optimization (ACO) and Genetic Algorithm (GA), to tackle the established VCMTSP instances. Experimental results show that GA and ACO are capable of addressing VCMTSP, yet their performance still needs improvement. With this study, it is expected that the established VCMTSP instances could provide a benchmark set for researchers to comprehensively validate their optimization methods by fairly comparing with others in this direction. In particular, the benchmark set can be accessed by https://gitee.com/absinthhh/vcmtsp.