The rapid deployment of electric vehicles (EVs) in public parking facilities and fleet operations raises challenging intra-day charging scheduling problems under tight charger capacity and limited dwell times. We model this problem as a variant of the Partition Coloring Problem (PCP), where each vehicle defines a partition, its candidate charging intervals are vertices, and temporal and resource conflicts are represented as edges in a conflict graph. On this basis, we design a branch-and-price algorithm in which the restricted master problem selects feasible combinations of intervals, and the pricing subproblem is a maximum independent set problem. The latter is reformulated as a quadratic unconstrained binary optimization (QUBO) model and solved by quantum-annealing-inspired algorithms (QAIA) implemented in the MindQuantum framework, specifically the ballistic simulated branching (BSB) and simulated coherent Ising machine (SimCIM) methods, while the master problem is solved by Gurobi. Computational experiments on a family of synthetic EV charging instances show that the QAIA-enhanced algorithms match the pure Gurobi-based branch-and-price baseline on small and medium instances, and clearly outperform it on large and hard instances. In several cases where the baseline reaches the time limit with non-zero optimality gaps, the QAIA-based variants close the gap and prove optimality within the same time budget. These results indicate that integrating QAIA into classical decomposition schemes are a promising direction for large-scale EV charging scheduling and related PCP applications.

翻译：电动汽车在公共停车设施和车队运营中的快速部署，使得在充电桩容量紧张和停留时间有限的约束下，产生了具有挑战性的日内充电调度问题。我们将该问题建模为划分着色问题（PCP）的一个变体：每辆电动汽车定义为一个划分，其候选充电时段对应顶点，时间与资源冲突在冲突图中表示为边。基于此框架，我们设计了一种分支定价算法，其中受限主问题选择可行的充电时段组合，而定价子问题为最大独立集问题。后者被重构为二次无约束二元优化（QUBO）模型，采用基于量子退火启发的算法（QAIA）在MindQuantum框架中求解，具体实现了弹道模拟分支（BSB）与模拟相干伊辛机（SimCIM）两种方法，主问题则通过Gurobi求解。在合成电动汽车充电实例数据集上的计算实验表明：针对中小规模实例，QAIA增强型算法的性能与纯Gurobi分支定价基线持平；而在大规模困难实例上，该算法显著优于基线。在多个基线算法因达到时间限制而存在非零最优性间隙的场景中，基于QAIA的算法在相同时间预算内消除了间隙并证明了最优性。这些结果表明，将QAIA融入经典分解框架是大规模电动汽车充电调度及相关PCP应用领域具有前景的研究方向。