Branch-Price-and-Cut Accelerated with a Pricing for Integrality Heuristic for the Electrical Vehicle Routing Problem with Time Windows and Charging Time Slots

TL;DR

This paper introduces a new primal heuristic for vehicle routing problems that improves the efficiency of branch-price-and-cut methods, especially for electric vehicle routing with time windows and charging slots, by generating more promising columns.

Contribution

It proposes a pricing for integrality heuristic that enhances column generation, leading to better primal solutions in complex vehicle routing problems with scheduling constraints.

Findings

Heuristic closes 30-40% of the root gap on average.

Improves the quality of primal solutions in electric vehicle routing problems.

Enhances branch-price-and-cut efficiency for problems with time windows and charging slots.

Abstract

Branch-price-and-cut is the state-of-the-art exact method for solving many types of vehicle routing problems, and is particularly effective for vehicle routing problems with time windows. A well-known challenge in branch-price-and-cut is that the generation of columns is guided by information from the linear relaxation of the master problem, with no guarantee that they will be useful from an integer perspective. As a consequence, high-quality primal solutions are often found only after significant cutting and branching or the use of primal heuristics. In this work, based on the ideas of pricing for integrality, we propose a new primal heuristic for vehicle routing problems. The heuristic is designed to generate columns that are more likely to be part of high-quality integer solutions. It begins by constructing a partial integer solution from a given column pool and then iteratively searches for columns that complement this solution. The search is done by modifying the pricing problem with respect to the partial solution, linear program dual information as well as previously generated columns in the heuristic. Computational tests are performed on the electrical vehicle routing problem with time windows extended with charging time slots, a problem that has both scheduling and routing aspects, making it well-suited to evaluate the performance of the proposed heuristic. The results show that the proposed heuristic closes 30% - 40% of the root node gap on average in comparison to a restricted master heuristic.