An Ε-constraint column generation-and-enumeration algorithm for Bi-Objective Vehicle Routing Problems

A way to solve bi-objective problems is to use an effective single objective algorithm embedded inside an Ε-constraint approach. In this paper, we are interested in any Bi-Objective Vehicle Routing Problem such that if one objective is constrained, the resulting single objective optimization problem can be solved by a state-of-the-art column generation-based method. We propose mechanisms and techniques to significantly speed up the resulting algorithm. Computational experiments are conducted on two problems: the Bi-Objective Vehicle Routing Problem With Time Windows and the Bi-Objective Team Orienteering Problem with Time Windows. To the best of our knowledge, this paper presents the first exact method proposed for the first problem and the second exact method proposed for the second problem. On the first problem we demonstrate the effectiveness of the proposed mechanisms. On the second problem, our algorithm is competitive with algorithms from the literature. © 2021 Elsevier Ltd