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：随着电动汽车在公共停车设施和车队运营中的快速部署，在紧张的充电容量和有限的停留时间约束下，具有挑战性的日内充电调度问题日益凸显。我们将该问题建模为划分着色问题的一种变体：每辆电动车定义一个划分，其候选充电区间对应顶点，时空冲突与资源冲突由冲突图中的边表示。在此基础上，设计了一个分支定价算法：受限主问题选择可行的区间组合，定价子问题则转化为最大独立集问题。后者被重构为二次无约束二进制优化模型，并通过MindQuantum框架中实现的量子退火启发式算法求解，具体包括弹道模拟分支和模拟相干伊辛机两种方法，而主问题由Gurobi求解器处理。基于合成电动汽车充电实例的计算实验表明：在中小规模实例上，量子退火启发式增强算法与纯Gurobi分支定价基线性能持平；在大规模困难实例上则显著超越基线。在多个基线达到时间限制且存在非零最优性间隙的案例中，基于量子退火启发式的变体能在相同时间预算内消除间隙并证明最优性。这些结果表明，将量子退火启发式算法整合至经典分解框架中，是大规模电动汽车充电调度及相关划分着色问题应用的有效方向。