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The purpose of this paper is to present a specific variant of vehicle routing problem with simultaneous full pickup and delivery problem (VRPSFPD) known as one-to-many-to-one (1-M-1) problem with several vehicles, where every customer can receive and send goods simultaneously, which has added the notion of the totality for the pickup goods. Currently, hybrid metaheuristics have become more popular because they offer the best solutions to several combinatorial optimization problems. Therefore, due to the complexity of 1-M-1 a hybrid genetic algorithm with variable neighborhood descent (HGAVND) local search is proposed. To improve the solution provided by the HGAVND the authors suggest applying a structure OR-Opt. To test the performance of the algorithm the authors have used a set of benchmarks from the literature and apply the HGAVND algorithm to solve the real case of distribution of soft drink in Tunisia. The experimental results indicate that the algorithm can outperform all other algorithms proposed in literature with regard to solution quality and processing time. Moreover, the authors improve the best known solution of the majority of benchmark instances taken from the literature.

Due to the complexity of 1-M-1 a HGAVND local search is proposed.

First, in the presence of full pickup constraints, the problem becomes more complex, this implies that the choice of a good metaheuristic can provide good results. Second, the best contribution consists in a specific variant of VRPSFPD problem as 1-M-1 which the paper present the first application of metaheuristics to solve the specific 1-M-1 and to apply it in real case of distribution of soft drink.