The Pickup and Delivery Problem: a Many-objective Analysis

The pickup and delivery problem (PDP) considers a set of transportation requests, which specify the quantity of product that has to be picked up from an origin and delivered to a destination. 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, cost has been associated with the number of routes and the total travel distance. However, in many applications, some other objectives emerge, for example, the minimization of travel time and the maximization of the collected profit. If we consider all these four objectives equally important, PDP can be tackled as a many-objective problem. In this paper we are interested in analyzing this many-objective problem in order to study some of its properties, specifically, (i) the change of difficulty when the number of objectives is increased, and (ii) the conflict degree between each pair of objectives. In order to analyze these topics, we compare the performance of a recently proposed multi-objective evolutionary algorithm against that of the well-known -MOEA, which has shown good results in many-objective problems.