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Operations Research and Fuzziology 2026

容量约束电动汽车路径问题的Q-Learning超启发式优化模型与动态规划充电策略
A Q-Learning Hyper-Heuristic Optimization Model and Dynamic Programming Charging Strategy for the Capacitated Electric Vehicle Routing Problem

DOI: 10.12677/orf.2026.165030, PP. 8-21

杨洋, 刘志威, 李伍奕, 李志萤

Keywords: 容量约束电动汽车路径问题，0-1混合整数规划，组合优化，马尔可夫决策过程，Q-Learning超启发式
Capacitated Electric Vehicle Routing Problem, 0-1 Mixed-Integer Programming, Combinatorial Optimization, Markov Decision Process, Q-Learning Hyper-Heuristic

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Abstract:

本文研究容量约束电动汽车路径问题(CEVRP)，在车辆载重与电池电量双重约束下，建立以车队总行驶距离最小为目标的0-1混合整数规划模型。令客户集、充电站副本集和扩展节点集分别为 $C$ 、 $F^{'}$ 和 $V$ 。以 $x_{i j}$ 表示弧选择变量，以 $w_{i}$ 和 $b_{i}$ 表示载重与剩余电量状态，目标函数为 $m i n ？ Z = \sum_{(i, j) \in A} d_{i j} x_{i j}$ ，并以唯一服务、流守恒、载重递推和电量递推约束定义可行域。针对该NP难组合优化问题，将低层启发式算子选择建模为有限马尔可夫决策过程 $？ = ？ (S, A, P, R, γ)$ ，依据Bellman最优方程更新 $Q (s, a$

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容量约束电动汽车路径问题的Q-Learning超启发式优化模型与动态规划充电策略A Q-Learning Hyper-Heuristic Optimization Model and Dynamic Programming Charging Strategy for the Capacitated Electric Vehicle Routing Problem

容量约束电动汽车路径问题的Q-Learning超启发式优化模型与动态规划充电策略
A Q-Learning Hyper-Heuristic Optimization Model and Dynamic Programming Charging Strategy for the Capacitated Electric Vehicle Routing Problem