Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that the spatial coverage of a road network is increased while redundant overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode unique coverage rewards and pairwise overlap penalties. A single penalty parameter controls the coverage-overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with an exact mixed-integer solver (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to 10 000 vehicles reveal a clear coverage-overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve essentially identical objective values with only minor differences in runtime as problem size grows.

翻译：多智能体路径规划旨在选择车辆（每辆车关联一条预定义路径），以在限制冗余重叠的同时提高道路网络的空间覆盖率。本文给出了形式化问题定义，通过从加权集合覆盖问题归约证明了其NP难度，并推导出二次无约束二进制优化（QUBO）模型，其系数直接编码了唯一覆盖奖励与成对重叠惩罚。单个惩罚参数控制着覆盖率与重叠度的权衡关系。我们区分了两种机制：支持多目标探索的软惩罚机制，以及惩罚强度足以强制实现近似无重叠路径的硬惩罚机制。我们描述了生成城市实例、构建候选路径、建立QUBO矩阵，并采用精确混合整数求解器（Gurobi）、模拟退火算法及D-Wave混合量子退火求解的完整流程。在包含多达10,000辆车的巴塞罗那实例实验中，我们观察到明显的覆盖率-重叠度拐点，并发现帕累托最优解主要在硬惩罚机制下获得，而D-Wave混合求解器与Gurobi在目标函数值上基本一致，仅随问题规模增长在运行时间上存在微小差异。