A hybrid artificial bee colony algorithm with high robustness for the multiple traveling salesman problem with multiple depots

A hybrid artificial bee colony algorithm (AC-ABC) with high robustness is proposed to solve the multiple traveling salesman problem (MTSP) with multiple depots. It initially conducts small-scale local searches to generate a high-quality population. Subsequently, a probabilistic model is established to balance global and local searches in the process of updating this population and exploring the optimal solution for the MTSP based on pheromone concentration and city visibility. In the process of population representation and updating, we introduce a novel tensor representation, which not only offers more opportunities for crossover between populations, but also adaptively provides more route choices to meet the personalized needs of salesmen. Besides artificial bee colony (ABC), AC-ABC takes at least 23% less execution time than other algorithms to solve the MTSP on multiple TSPLIB instances, especially takes about 32%–93% less execution time than the ant colony-partheno genetic algorithm (AC-PGA). The travel cost of the optimal route obtained by AC-ABC is significantly better than that of ABC, partheno genetic algorithm (PGA), improved PGA (IPGA), and two-part wolf pack search (TWPS). AC-ABC always obtains less travel cost than AC-PGA when the number of cities $n\le 150$. AC-ABC only obtains about 0.5%–7.4% more travel cost than AC-PGA when the number of cities $n>150$.