An evolutionary approach to the multi-objective pickup and delivery problem with time windows

The pickup and delivery problem (PDP) has many real-life applications. In this problem there is a customer set which is partitioned into two subsets: the customers requiring an amount of product (delivery) and the customers providing the product (pickup). There is also a set of transportation requests, which specify the quantity of product that has to be picked up from an origin customer and delivered to a destination customer. There exist a number of vehicles available to be used for completing these tasks. PDP consists of finding a collection of routes with minimum cost, such that all transportation request are serviced. Traditionally, the number of routes has been minimized first, and then the travel distance, however, if these objectives are considered to be equally important, the problem can be tackled as a bi-objective problem. Moreover, time is not always directly proportional to distance, thus travel time can also be considered an important criterion to be optimized and, consequently, PDP has to be regarded as a tri-objective problem. In this paper, we solve PDP as a problem with multiple objectives by means of an evolutionary algorithm and evaluate its performance with proper multi-objective performance tools.