Discrete many-objective optimization problems: The case of the pickup and delivery problem

Abstract

The pickup and delivery problem (PDP) deals with 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. PDP consists of finding a set of routes with minimum cost, such that all transportation requests are serviced by a fleet of vehicles. Usually, only two objectives have been considered to evaluate the cost of a solution. However, in many applications, some other objectives emerge, for example, the minimization of the workload imbalance, and the minimization of the uncollected profit. If we consider all these objectives equally important, PDP can be tackled as a many-objective problem. Although some studies have analyzed the scalability of continuous optimization problems, there are just a few studies using discrete optimization problems. Thus, in this paper we study the following elements: (i) the properties of the many-objective PDP regarding scalability, i.e., conflict between each pair of objectives and the proportion of non-dominated solutions as we vary the number of objectives, and finally (ii) the change of PDP's difficulty when the number of objectives is increased. Results show that most of the objectives pairs are actually in conflict, and that the problem is more difficult to solve as more objectives are considered, thus making it complicated to differentiate between equally good solutions.