考虑碳排放的混合轴辐式多式联运网络枢纽扩增选址-路径问题

针对现有多式联运网络枢纽饱和度高、枢纽到城市直达运输成本高且效率低等不足，提出采用混合轴辐式多式联运网络研究扩增枢纽选址，同时优化运输线路；基于允许枢纽间转运和需求城市间巡回运输的运输网络，考虑低碳因素构建了最小化总运输成本、二级枢纽开放建设成本、枢纽处转运成本和总碳排放成本的数学模型，将问题分解为选址-分配与路径优化2个阶段，并针对两阶段特点分别采用0-1编码和数字编码设计了两阶段遗传算法；针对现有实际案例采用设计的算法进行求解，并将求得的最优运输方案与现实方案进行对比。研究结果表明:采用提出的算法进行10次运行获得的最优解与其平均值的差值百分比仅为4.7%，且平均求解时间仅为90.6 s；优化后网络扩增了2个枢纽，弃用了1个不合理枢纽，网络转运能力提高了11.3%，枢纽的平均饱和度降低了15.7%，不同枢纽的饱和度比原网络更均衡，不仅缓解了饱和枢纽的压力，还提高了空闲枢纽的周转率，从而提高了转运效率；优化后运输方案对应的总成本、运输成本、中转成本和碳排放成本分别降低了68.41%、68.14%、56.55%和86.76%，且碳排放减少最为突出。由此可见，提出的模型和算法对扩张轴辐式网络选址和混合轴辐式多式联运网络运输方案的组合优化具有较好的性能。 

Expanding hub location-routing problem for hybrid hub-and-spoke multimodal transport network considering carbon emissions

In view of the high hub saturation, as well as the high cost and low efficiency of direct transportation from a hub to cities of the existing multimodal transport network, a hybrid hub-and-spoke multimodal transport network was proposed to expand the hub locations and optimize the transportation routes. On the basis of the transport network allowing transfer between hubs and tours between cities and considering the low-carbon factors, a mathematical model was built to minimize costs including the total transportation cost, the construction cost to open secondary hubs, the transfer cost at hubs, and the total carbon emission cost. In this way, the problem was decomposed into two stages: the location-allocation and route optimization, and according to the characteristics of the two stages, a two-stage genetic algorithm using the 0-1 coding and digital coding was designed, respectively. The designed algorithm was applied to solve an existing real case, and the optimal transportation scheme obtained by the algorithm was compared with the actual scheme. Research results show that the difference percentage between the optimal solution and its average value obtained by 10 runs of the proposed algorithm is only 4.7%, and the average solution time is only 90.6 s. In the optimized network, two hubs are added, and an unreasonable hub is abandoned. The transfer capacity of the network improves by 11.3%, and the average saturation of hubs reduces by 15.7%. The saturations of different hubs are more balanced than that in the original network. The pressures of saturated hubs are relieved, and the turnover rates of idle hubs are raised to improve the transfer efficiency. The total cost, transportation cost, transfer cost, and carbon emission cost corresponding to the optimized transportation scheme reduce by 68.41%, 68.14%, 56.55%, and 86.76%, respectively, with the most prominent reduction in carbon emissions. It can be seen that the proposed model and algorithm have good performance in expanding the hub-and-spoke network locations and comprehensively optimizing the transportation scheme for the hybrid hub-and-spoke multimodal transport network. 7 tabs, 12 figs, 31 refs.