Subpath-Based Column Generation for Electric Vehicle Routing Problems

TL;DR

This paper introduces a novel subpath-based column generation approach for solving complex electric vehicle routing problems with time windows and nonlinear charging, significantly improving solution quality and scalability.

Contribution

It develops a new algorithm that decomposes the routing problem into subpaths and optimizes charging, enabling exact solutions for various EV routing scenarios.

Findings

Outperforms path-based benchmarks in computational time and solution quality.

Effective for large instances with up to 100 customers.

Handles multiple EVRP variants with nonlinear charging and time windows.

Abstract

Motivated by widespread electrification targets, this paper studies an Electric Vehicle Routing Problem with Time Windows and Nonlinear Charging (EVRPTWNL) that jointly optimizes routing-scheduling decisions and charging decisions given vehicle capacities, time windows and battery capacities. We develop a column generation scheme with a subpath-based label-setting algorithm that decomposes the pricing problem into two phases: (i) generating subpaths between charging stations, and (ii) combining subpaths into paths while optimizing charging decisions in between. We formalize a domination framework to establish the convergence and exactness of the algorithm, and prove that the methodology can solve a range of EVRP variants (e.g., with vehicle capacities, time windows, and nonlinear charging) and relaxation-tightening strategies (e.g., ng-relaxations and subset-row cuts). Computational results show improvements over path-based benchmarks in both computational time and solution quality, especially when time windows become wider, when vehicles can perform multiple tasks on a single charge and when vehicles still need to recharge several times across the planning horizon. Ultimately, the methodology can scale to otherwise intractable instances with up to 100 customers, thereby enhancing fleet management capabilities across electrified logistics areas.