Evolutionary Approach for Energy Minimizing Vehicle Routing Problem with Time Windows and Customers’ Priority

Abstract

A new model and solution for the energy minimizing vehicle routing problem with time windows (EVRPTW) and customers' priority is presented in this paper. In this paper unlike prior attempts to minimize cost by minimizing overall traveling distance, the model also incorporates energy minimizing which meets the latest requirements of green logistics. This paper includes the vehicles load as an additional indicator of the cost in addition to the distance traveled cost. Moreover, this paper tries to maximize the customers' satisfaction using their preference and considers the customers' priority for servicing. Every customer is assigned to a group (e.g., very important, important, casual and unimportant) and the customers' preference is represented as a convex fuzzy number with respect to the satisfaction for service time. The detailed mathematical formulation of proposed model is provided and it is interpreted as multi-objective optimization where, the energy consumed and the total number of vehicles are minimized and the total satisfaction rate of customers is maximized. In general, the relationship between these defined objectives is unknown until the problem is solved in a proper multi-objective manner. Thus, a multi-objective evolutionary algorithm is proposed and its performance on several completely random instances is compared with Non-dominated Sorting Genetic Algorithm II (NSGA II) and CPLEX Solver. The hypervolume indicator is used to evaluate the two Pareto set approximations found by NSGA-II and the proposed approach. The performance proposed evolutionary is further demonstrated through several computational experiments and the results indicate the good quality of the method.