Multi-ant colonies algorithms for the VRPSPDTW

Abstract

The vehicle routing problem with simultaneous pickups and deliveries and time windows (VRP-SPDTW) is the problem of optimally integrating forward (good distribution) and reverse logistics (returning materials) for cost saving and environmental protection. We constructed a general mixed integer programming model of VRP-SPDTW. We present an Improved Ant Colony System (ACS) for the VRPSPDTW (Vehicle Routing Problem with Simultaneous Pick-up and Delivery with Time Windows). We submit adaptations and additions to the different solutions for VRPSPDTW. The real treated problem is to minimize the number of bus fleet that have to serve several schools (stations) for pick-up and delivery of different groups of students at different time windows. In detail, this problem is particularly complex. The significant improvement is to take into account the individual time windows, the time of service in each station and the preference function related to operation type at each served station.