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Regarding the development of distribution systems in the recent decades, fuel consumption of trucks has increased noticeably, which has a huge impact on greenhouse gas emissions. For this reason, the reduction of fuel consumption has been one of the most important research areas in the last decades. The aim of this paper is to propose a robust mathematical model for a variant of a vehicle routing problem (VRP) to optimize sales of distributers, in which the time of distributor service to customers is uncertain. To solve the model precisely, the improved differential evolution (IDE) algorithm is used and obtained results were compared with the result of a particle swarm optimization (PSO) algorithm. The results indicate that the IDE algorithm is able to obtain better solutions in solving large-sized problems; however, the computational time is worse than PSO.

A Green Competitive Vehicle Routing Problem under Uncertainty Solved by an Improved Differential Evolution Algorithm