A hybrid electromagnetism algorithm for multi-depot periodic vehicle routing problem

Electromagnetism algorithm is a meta-heuristic proposed to derive approximate solutions for computationally hard problems. In the literature, several successful applications have been reported for graph-based optimization problems, such as scheduling problems. This paper presents a novel hybrid electromagnetism algorithm called SA_EM to solve the multi-depot periodic vehicle routing problem (MDPVRP). The main feature of the hybrid algorithm is to hybridize the solution construction mechanism of the electromagnetism (EM) with simulated annealing (SA). Moreover, during implementing the hybrid algorithm, cyclic transfers, an effective class of neighborhood search is applied. The objective consists of two terms as follows: total traveled distance at each depot and total waiting time of all customers to take service. Distances are assumed Euclidean or straight line. These conditions are exactly consistent with the real-world situation and have little attention in the literature. Finally, the experimental results have shown that the proposed hybrid method is competitive to solve the vehicle routing problem compared with the best existing methods in terms of solution quality.