Abstract: Under the subsidy schemes of intercity transportation platforms for less-than-truck-load cargo, we established a vehicle routing optimization model considering goods-vehicles matching and three-dimensional loading constraints. The model minimized the sum of platform subsidy cost, vehicle operation cost, and fuel cost. To solve this model, we designed a hybrid quantum particle swarm optimization algorithm to determine the optimal cargo matching, vehicle path, cargo loading and unloading, and platform subsidy. The experimental results show that the gap between the solution obtained by the hybrid quantum particle swarm optimization algorithm and the optimal solution obtained by CPLEX software is 3.31% on average in small-scale cases. By introducing the fitness function value as the weight in solving the optimal middle position, the solution in the large-scale examples is 0.91% higher than the traditional quantum particle swarm optimization algorithm. By analyzing the characteristics of the optimal solution, the improved hybrid quantum particle swarm optimization algorithm is combined with a heuristic algorithm, and the solution quality is improved by 4.05% . Through the comparative experiments of subsidy modes, it is found that in a reasonable planning cycle, the increase of cargo owner time subsidy and no-load subsidy can effectively improve the platform profit and vehicle utilization while maintaining the total cost basically unchanged.

Key words: highway transportation, freight platform, quantum particle swarm optimization, intercity less-thantruckload cargo transportation, three-dimensional loading, vehicle routing

摘要： 在考虑城际零担货运平台现有各种不同补贴方案的基础上，以平台补贴成本、车辆使用成本及燃油成本之和最小为目标函数，建立考虑车-货匹配、车辆三维装载等约束条件的车辆路径优化模型。设计一种混合量子粒子群优化算法，计算货物匹配方案、车辆路径、货物装卸顺序、货物装载位置以及平台补贴最优决策方案。实验结果表明：改进的量子粒子群算法得到的小规模算例优化解与CPLEX优化软件得到的最优解偏差为3.31%；改进的量子粒子群算法通过在求解最佳中间位置时引入适应度函数值作为权重，求解的大规模算例结果比传统量子粒子群算法提高了0.91%；通过分析最优解的特点，将改进的量子粒子群算法与启发式算法相结合，算法的求解 质量提高了4.05%；通过补贴模式对比实验发现，在合理规划周期内，货主时长补贴和空载补贴的增长在维持总成本基本不变的情况下，可有效提升平台利润，提高车辆利用率。

关键词: 公路运输, 货运平台, 量子粒子群算法, 城际零担运输, 三维装载, 车辆路径