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.

翻译：基于排列的元启发式算法广泛用于电动车辆路径问题，其中候选解以顾客的有序序列表示。然而，这类序列并未直接定义可行的车辆路径：必须在满足载重约束和电池容量约束的前提下，通过选择序列的分割点以及插入充电站访问点来解码生成可行路径。由于每次返回仓库既分隔相邻路线又恢复车辆电池，这些决策具有内在的相互依赖性。本文将该任务形式化为固定排列分割与充电问题，并提出一种基于动态规划与支配剪枝的前向标号算法，可构建固定顾客排列的最小距离可行解码方案。我们进一步推导出三种简化解码策略的受限变体：首先分离路径分割与充电站插入决策，其次限制每段顾客间路径最多访问一个充电站。基于基准实例和随机生成实例的计算实验（包括与文献中启发式解码器的对比）证实：精确解码器在实践中仍具可计算性，且揭示了不同解码策略间的清晰层级关系。最严格的受限变体在保持接近启发式解码器运行时间的同时，实现了显著更高的解码成功率与更优的解质量。约束较弱的变体虽增加计算开销，但可进一步改善解的质量与鲁棒性。精确联合解码器为每个固定排列提供最优参考基准，明确了常见解码简化策略带来的性能权衡。