为解决现有模型没有考虑公交线网及发车频率进行同步优化,以及求解的算法效率不高的问题,本文构建了以乘客出行时间最小化为目标的公交线网及发车频率同步优化的混合整数规划模型,并设计了相应的改进遗传算法求解该模型.为了提高算法执行效率,本文首先设计了客流换乘比例下界值对公交线网结构作出初步评价,对于客流换乘比例高于设定的下界值的线网不进行后续发车频率设计及目标函数计算,以减少由不可行解带来的后续计算.通过一案例测试分析表明该方法能够同时求解出公交线网的布局方案以及各线路相应的发车频率.最后,对下界值取值与计算时间及最终优化结果的关系进行了数值分析.结果表明:在下界值取值由1逐渐减小至0.4的阶段,目标函数值保持不变,但计算时间逐渐减小,节约时间最多达到40％以上.但当下界值取值小于0.4时,虽然计算时间仍在减小,但目标函数值逐渐变大已不是最优解.说明应用该模型及算法设计公交线网规划时,合理的下界值取值能够保证解的质量的同时极大提高算法执行效率.%Considering that the existing model doesn′t take into account the transit network and frequency synchronous optimization and that optimization algorithm is inefficient, a mixed integer programming model is designed to optimize transit network and corresponding frequency with the aim of minimizing travel time. To increase the efficiency of the algorithm, the structure of public transportation network is evaluated based on setting the lower bound of transfer. If the transfer ratio is greater than the set lower bound, the frequency and objective function will not be calculated, which can reduce the computation caused by unfeasible solutions. A case is tested by the proposed model and algorithm, showing that the method can obtain the transit network and frequency simultaneously. Finally, the influence on computation time and optimization results are analyzed by different values of lower bound. The results show that the optimization results are the same and more than 40％ of the computation time can be saved at most with the lower bound ranging from 1 to 0.4. However, when the lower bound is less than 0.4, the optimized solution by this algorithm is not optimal, which suggests that setting reasonable values for lower bound for the proposed method can save the computation time significantly with reliable solution, when the model and algorithm are applied to design transit network.
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