保留可行性的量子约束运输路径搜索
Feasibility-Preserving Quantum Search for Constrained Transportation Routing
AI总结：
该研究针对TSP、VRP等运输路径问题，提出带可行性保留混频器的QAOA+框架，对比三种约束处理架构，发现其对可行路径采样等有显著影响，为量子路径规划提供新方法。
AI中文摘要：
旅行商问题（TSP）、车辆路径问题（VRP）等运输路径问题具有严格的可行性要求，涉及客户分配与访问规则、路径排序、返回 depot（配送中心）的逻辑，同时以成本最小化为目标。多数量子路径规划方案采用二次无约束二元优化（QUBO）编码，通过代价哈密顿量中的惩罚项间接纳入可行性要求。尽管该方法便于量子近似优化算法（QAOA）的标准实现，但QUBO编码会使量子搜索动力学为不可行路径配置分配大量概率。本研究开发了基于运输场景的感知约束量子交替算子ansatz（QAOA+）框架，将保留可行性的逻辑直接嵌入搜索算子。我们引入定制混频器，作为保留可行性的路径邻域的量子模拟，采用逐列交换操作，将演化限制在可行配置内，同时支持对有效路径的结构化探索。我们对比了三种约束处理架构：基于惩罚的QUBO QAOA、带有保留可行性混频器的无惩罚QAOA+、以及结合混频器可行性与惩罚引导的混合QAOA+。小型TSP和VRP实例的结果表明，约束处理架构对可行路径采样、收敛行为以及低成本可行路径上的概率集中度有显著影响。这些发现将感知约束的量子搜索定位为运输路径搜索方法的方法论扩展，其中可行性通过可允许的量子跃迁而非事后惩罚来实现。
英文摘要：
Transportation routing problems such as the Traveling Salesperson Problem (TSP) and the Vehicle Routing Problem (VRP) are characterized by strict feasibility requirements involving customer assignment and visit rules, route sequencing, and depot-return logic alongside cost minimization. Most quantum routing formulations adopt Quadratic Unconstrained Binary Optimization (QUBO) encodings, where feasibility is incorporated indirectly via penalty terms in the cost Hamiltonian. While convenient for standard implementations of the Quantum Approximate Optimization Algorithm (QAOA), QUBO encodings allow the quantum search dynamics to allocate substantial probability to infeasible route configurations. This study develops a transportation-grounded constraint-aware Quantum Alternating Operator Ansatz (QAOA+) framework that embeds feasibility-preserving logic directly into the search operator. We introduce a custom mixer that functions as a quantum analogue of feasibility-preserving routing neighborhoods, using column-wise swap moves, it restricts evolution to feasible configurations while enabling structured exploration of valid routes. We compare three constraint-handling architectures: penalty-based QUBO QAOA, penalty free QAOA+ with the feasibility-preserving mixer, and a Hybrid QAOA+ combining mixer based feasibility with and penalty guidance. Results on small TSP and VRP instances show that constraint-handling architecture strongly influences feasible-route sampling, convergence behavior, and probability concentration over low-cost feasible routes. These findings position constraint-aware quantum search as a methodological extension of transportation routing search approaches, where feasibility is enforced through admissible quantum transitions rather than post-hoc penalties.
