A Differential Evolution & Genetic Algorithm for Vehicle Routing Problem with Simultaneous Delivery and Pick-up and Time Windows

Abstract

The vehicle routing problem with simultaneous delivery and pick-up and time windows (VRP-SDPTW) is presented from the point of strategic view that combines the logistics and reverse logistics (bidirectional logistics). A general mixed integer programming mathematic model of VRP-SDPTW is constructed, it can transform into other classical vehicle routing problems by setting different parameters. A hybrid optimization algorithm (HOA) is proposed, which is based principally on the combination of the differential evolution (DE) theory and genetic algorithm (GA). In operation process, we firstly adopted the novel decimal coding to construct the chromosome, and then the differential evolution operator is adopted as the main optimizing scheme, while such techniques of the genetic algorithm, as the novel crossover-operator mutation-operator are designed to improve the result. Therefore it is expected that advantages of both the differential evolution and the genetic algorithm are kept so that the hybrid optimum algorithm can optimize large scale highly nonlinear problems well and improve the efficiency of the optimization process, and can avoid effectively the common defects of early convergence and the diversity of population in traditional genetic algorithm. The computer simulations are used to compare the performance of the proposed method with GA and DE, and numerical results show that the performance of the proposed method is better than the other method.