Abstract
This paper presents a variant of the vehicle routing problem (VRP) that combines several constraints. This variant addresses the pickup and delivery problem (PDP), the use of multiple vehicles (m), the multi-depots (MD) and the time constraint (TW): m-MDPDPTW. In the m-MDPDPTW, one should build a route made up of several pairs (customer / supplier), which starts and ends at the same depot and respects the precedence and capacity constraints. For solving this problem, two approaches based on particle swarms are proposed with a view to minimizing the total distance travelled by all vehicles. The results yielded by these two algorithms, the continuous PSO and the discrete PSO, are then compared by making use of the benchmarks generated by Li and Lim.