Heuristic and exact algorithms for vehicle routing problems

The pickup and delivery problem with time windows is the problem of serving a number of transportationrequests using a limited amount of vehicles. Each request involves moving a number of goods from apickup location to a delivery location. Our task is to construct routes that visit all locations such thatcorresponding pickups and deliveries are placed on the same route and such that a pickup is performedbefore the corresponding delivery. The routes must also satisfy time window and capacity constraints.This paper presents a heuristic for the problem based on an extension of the Large Neighborhood Searchheuristic previously suggested for solving the vehicle routing problem with time windows. The proposedheuristic is composed of a number of competing sub-heuristics which are used with a frequency correspond-ing to their historic performance. This general framework is denoted Adaptive Large Neighborhood Search.The heuristic is tested on more than 350 benchmark instances with up to 500 requests. It is able toimprove the best known solutions from the literature for more than 50% of the problems.The computational experiments indicate that it is advantageous to use several competing sub-heuristicsinstead of just one. We believe that the proposed heuristic is very robust and is able to adapt to variousinstance characteristics.