On the many-objective pickup and delivery problem: Analysis of the performance of three evolutionary algorithms

Abstract

Many-objective optimization focuses on solving optimization problems with four or more objectives. Effort has been made mainly on studying continuous problems, with interesting results and for which several optimizers have been proposed. Nevertheless, combinatorial problems have not received as much attention, making this an open research area. An important result on continuous problems states that the problem does not necessarily becomes more difficult while more objectives are considered, but, does this result hold for combinatorial problems? This investigation takes this subject on by studying a many-objective combinatorial problem, particularly, the pickup and delivery problem (PDP), which is an important combinatorial optimization problem in the transportation industry and consists in finding a collection of routes with minimum cost. Traditionally, cost has been associated with the number of routes and the total travel distance, however, some other objectives emerge in many applications, for example, travel time, workload imbalance, and uncollected profit. If we consider all these objectives equally important, PDP can be tackled as a many-objective problem. This study is concerned with the study of the performance of three multi-objective evolutionary algorithms on the PDP varying the number of objectives, in order to analyze the change of PDP’s difficulty when the number of objectives is increased. Results show that the problem becomes more difficult to solve while more objectives are considered.