考虑满载率均衡的城市轨道交通直通运营开行方案优化

为了优化城市轨道交通直通运营的开行方案，分析了城市轨道交通直通运营的运营组织方法，划分了直通运营条件下乘客OD类型，提出了直通运营条件下的列车满载率不均衡系数的计算方法；加入了对列车多编组以及满载率不均衡性的考虑，以直通运营区间范围、不同列车发车频率、不同列车编组为决策变量，以最小化乘客出行成本、企业运营成本以及满载率不均衡系数为目标，构建了直通运营条件下城市轨道交通列车开行方案优化模型，设计了混合编码的遗传算法进行求解；以北京地铁房山线与9号线为例，研究了高峰时段和平峰时段最优的城市轨道交通直通运营开行方案，对比分析了直通运营与独立运营模式下的区间满载率等运营指标，探究了不同目标权重对最优解及优化结果的影响。结果表明：在高峰时段，与独立运营模式相比，直通运营模式在不改变列车编组的条件下，优化效果达到了12.85%;在平峰时段，开行多编组的列车可以有效地提高全线的满载率均衡性；最后通过权重分析发现随着乘客服务水平权重下降、运营企业成本权重上升，直通列车的发车频率下降，直通运营区段逐渐变小，开通直通运营列车的效果逐渐变差。

Train planning optimization for through operation of urban rail transit considering load balance

To optimize the train planning for through operation of urban rail transit, the operation organization method of through operation was analyzed, the passenger flows under through operation mode were classified, and a method of calculating the imbalance coefficient of the maximum load was proposed. A train planning optimization model for the through operation of urban rail transit was established by considering multi-group train operations and the imbalance of the load factor. The objective of this model was to minimize the travel cost of passengers, the operation cost of enterprises, and the imbalance coefficient of the load factor. Three decision variables, the location of turn-back stations, the frequency of different routing trains, and the formation of train groups, were solved by a hybrid coding genetic algorithm. Taking the Beijing Metro Fangshan Line and Line 9 as an example, the train planning optimizations for peak and off-peak hours were studied. The operational indicators such as load factors under through operation mode and independent operation mode were compared and analyzed. The effects of different objective weights on the optimal solution and optimization results were investigated. Results showed that during peak hours, compared with the independent operation mode, the optimization effect of the through operation mode was improved by 12.85% without changing the train formation plan. During off-peak hours, the multi-group train operation significantly improved the balance of the load factor. Through weight analysis, it was found that with the decrease in passenger service level weight and the increase in operating enterprise cost weight, the frequency of through trains decreased, the section of through operation gradually declined, and the effect of through operation steadily deteriorated.