Abstract
•The multiple depots and closed paths MTSP with a minimum city number restriction is investigated.•Two PGAs and four new mutation operations are proposed. PSO algorithm is adopted by designing new PSO formulas.•Comparative experiments demonstrate the quality of the algorithms.•IWO algorithm, a state-of-art method from literature, is implemented as a comparison.•In MTSP, how to choose a rational number of salesmen is worth considering.
Multiple traveling salesman problem (MTSP) is a generalization of the classic traveling salesman problem (TSP). Compared to TSP, MTSP is more common in real-life applications. In this paper, in order to solve the minsum MTSP with multiple depots, closed path, and the requirement of minimum number of cities each salesman should visit, we propose two partheno genetic algorithms (PGA). One is a PGA with roulette selection and elitist selection in which four new kinds of mutation operation are proposed. The other one, named IPGA, binds the selection and mutation together. A new selection operator and a more comprehensive mutation operator are used. The new mutation operator is based on the four kinds of mutation operation in PGA, which eliminates the mutation probability. For comparative analysis, we also adopt particle swarm optimization algorithm (PSO) and one state of the art method (invasive weed optimization algorithm from literature) to solve MTSP. The algorithms are validated with publicly available TSPLIB benchmarks. The performance is discussed and evaluated through a series of comparative experiments. IPGA is demonstrated to be superior in solving MTSP.