A mathematical method for solving multi-depot vehicle routing problem.

Because logistics companies usually have multiple depots to serve their many dispersed customers, multi-depot vehicle routing problem (MDVRP) has gained significant research attention. To solve an MDVRP model, this paper develops a hybrid ant colony optimization based on a polygonal circumcenter (BPC-HACO). Furthermore, because ACO has been found to fall easily into the local optimum, simulated annealing and three local optimization operations are introduced to encourage the ACO to improve the algorithm's optimization ability. Finally, MDVRP benchmarks and data sets of other papers are employed to verify the effectiveness of the BPC-HACO in solving MDVRP (In 23 instances, BPC-HACO finds 14 BSKs, and 3 results are better than the BSKs), MDVRP with distance constraints (Compared to other papers, the route length is reduced by an average of 17.94%) and dynamic MDVRP (In 10 instances, BPC-HACO finds 3 BSKs, and 2 results are better than the BSKs). Finally, fitness landscape analysis has been applied to analyze the structural features of MDVRP to choose the most appropriate algorithm for MDVRP. [ABSTRACT FROM AUTHOR]