This paper tackles the Electric Capacitated Vehicle Routing Problem (E-CVRP) through a bilevel optimization framework that handles routing and charging decisions separately or jointly depending on the search stage. By analyzing their interaction, we introduce a surrogate objective at the upper level to guide the search and accelerate convergence. A bilevel Late Acceptance Hill Climbing algorithm (b-LAHC) is introduced that operates through three phases: greedy descent, neighborhood exploration, and final solution refinement. b-LAHC operates with fixed parameters, eliminating the need for complex adaptation while remaining lightweight and effective. Extensive experiments on the IEEE WCCI-2020 benchmark show that b-LAHC achieves superior or competitive performance against eight state-of-the-art algorithms. Under a fixed evaluation budget, it attains near-optimal solutions on small-scale instances and sets 9/10 new best-known results on large-scale benchmarks, improving existing records by an average of 1.07%. Moreover, the strong correlation (though not universal) observed between the surrogate objective and the complete cost justifies the use of the surrogate objective while still necessitating a joint solution of both levels, thereby validating the effectiveness of the proposed bilevel framework and highlighting its potential for efficiently solving large-scale routing problems with a hierarchical structure.

翻译：本文通过双层优化框架处理电动容量车辆路径问题（E-CVRP），该框架根据搜索阶段分别或联合处理路径规划与充电决策。通过分析二者交互关系，我们在上层引入替代目标以引导搜索并加速收敛。提出一种双层延迟接受爬山算法（b-LAHC），该算法通过三个阶段运行：贪婪下降、邻域探索及最终解精炼。b-LAHC采用固定参数运行，无需复杂自适应调节，同时保持轻量级特性与高效性。在IEEE WCCI-2020基准测试上的大量实验表明，b-LAHC在八种先进算法中展现出优越或具有竞争力的性能。在固定评估预算下，该算法在小规模实例上获得近最优解，并在大规模基准测试中创下9/10项最新最优记录，将现有纪录平均提升1.07%。此外，替代目标与完整成本之间观察到的高度相关性（虽非普遍存在）为替代目标的使用提供了合理性依据，同时仍需对两个层级进行联合求解，从而验证了所提双层框架的有效性，并凸显其在高效求解具有层次结构的大规模路径问题中的潜力。