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Abstract
One of the most important extensions of the vehicle routing problem is the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) in which the objective is to minimize the distance traveled by using a fleet of vehicles for servicing a set of customers. Because the VRPSPD is an NP-hard problem, practical large-scale instances of this problem cannot be solved by exact solution methodologies within acceptable computational time, and most of the researchers have focused on metaheuristic solution approaches. For this reason, a combined modified tabu search and elite ant system (MTSEAS) is proposed for solving the VRPSPD in this paper. The proposed algorithm is tested on 54 standard instances available from the literature. The computational result shows that the MTSEAS obtains 39 best known solutions of the benchmark problem, and it is competitive with other metaheuristic algorithms for solving VRPSPD.