Max-Min ant system for bus transit multi-depot vehicle scheduling problem with route time constraints

The bus transit vehicle scheduling problem (VSP), in which a given set of scheduled trips have to be assigned to vehicles stationed at different depots, minimizing the capital cost and the overall operational cost, has caused great concern to the bus transit companies. Considering the real world operational restrictions, this paper researches the bus transit multi-depot vehicle scheduling problem with route time constraints and depot capability restrictions, and puts forward a model with comprehensive objective to minimize the number of required vehicles, travel time along deadheading trips and the waiting time at the starting stations of service trips for VSP satisfying a set of constraints. This problem is NP-hard, and therefore its solution is obtained by a Max-Min ant system. This article describes steps of the whole algorithm in detail, especially construction of solutions and pheromone updating rule. Finally, an example was analyzed to demonstrate that the correctness of the application of the MMAS, and it prove to be more efficient and effective in solving this problem compared with the ACS.