Improved ant colony algorithm for multi-depot bus scheduling problem with route time constraints

Vehicle or bus scheduling problem (VSP), involving in a given set of time-tabled trips to be assigned to vehicles to minimize capital and operating costs, is one of the most critical issues faced by transit agencies. This paper addresses a multi-depot multi-vehicle-type VSP with route time constraints as well as capacity of depot restrictions, and presents a model with multiple objectives to minimize the number of vehicles, deadhead and waiting time for VSP to meet all constraints. Solutions are obtained by an improved ant colony optimization (ACO) which initially incorporates ant colony system, MAX-MIN ant system and BEST-WORST ant system, and its relative performance is compared to other ACO algorithms. Numerical computations show that the proposed ACO can find good solutions effectively and efficiently.