A coevolutionary algorithm for the flexible delivery and pickup problem with time windows

This paper addresses a flexible delivery and pickup problem with time windows (FDPPTW) and formulates the problem into a mixed binary integer programming model in order to minimize the number of vehicles and to minimize the total traveling distance. This problem is shown to be NP-hard. In this study, therefore, a coevolutionary algorithm incorporated with a variant of the cheapest insertion method is developed to speed up the solution procedure. The FDPPTW scheme overcomes the shortcomings of the existing schemes for the delivery and pickup problems. By testing with some revised Solomon's benchmark problems, the computational results have shown the efficiency and the effectiveness of the developed algorithm.