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

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.