Where to Split and When to Charge: Optimal Route Construction from Customer Permutations in Electric Vehicle Routing

2026-05-26

AI Summary

This work addresses the challenge of optimally partitioning a fixed customer sequence and inserting charging stations in the electric vehicle routing problem, formalizing it as the Fixed-Sequence Splitting and Charging Problem. The study proposes the first exact joint decoding framework, which integrates dynamic programming with dominance pruning and a forward-labeling algorithm to efficiently generate minimum-distance feasible routes that satisfy both payload and battery constraints. The approach elucidates the coupling between route segmentation and charging decisions and incorporates multi-level simplification strategies to balance solution quality and computational efficiency. Experimental results demonstrate strong scalability on real-world instances: the most streamlined variant operates at near-heuristic speed while substantially improving solution quality and feasibility, whereas the full joint decoder provides a reliable benchmark for optimality.

Abstract

Permutation-based metaheuristics are widely used for electric vehicle routing, where candidate solutions are represented as ordered sequences of customers. Such sequences, however, do not directly define feasible vehicle routes: they must be decoded by choosing where to split the permutation into routes and where to insert charging-station visits, subject to cargo capacity and battery constraints. These decisions are inherently interdependent, since each return to the depot both separates consecutive routes and restores the vehicle battery. This paper formalizes the task as the Fixed-Permutation Splitting and Charging Problem and proposes an exact forward labeling algorithm that constructs a minimum-distance feasible decoding of a fixed customer permutation using dynamic programming with dominance pruning. We further derive restricted variants representing increasingly simplified decoding strategies: first separating route splitting from charging-station insertion, and then additionally limiting each inter-customer segment to at most one charging-station visit. Computational experiments on benchmark and randomly generated instances, including comparisons with heuristic decoders from the literature, confirm that the exact decoder remains tractable in practice and reveal a clear hierarchy among decoding strategies. The most restrictive variant achieves runtimes close to those of heuristic decoders while delivering substantially higher decoding success rates and better solution quality. Less restrictive variants further improve quality and robustness at the cost of additional runtime. The exact joint decoder provides the optimal reference for each fixed permutation, clarifying the trade-offs introduced by common decoding simplifications.

Problem

• Electric Vehicle Routing
• Permutation Decoding
• Charging Station Insertion
• Route Splitting
• Battery Constraints

Innovation

• electric vehicle routing
• permutation decoding
• dynamic programming
• charging station insertion
• route splitting