基于线路能力约束下的铁路空车调配迭代算法

以空车总走行里程最小为目标,以空车供需平衡和车流量不超过线路通过能力为约束条件,建立空车调配数学模型,并设计分步优化迭代算法进行求解。该算法的基本思路是：先放弃模型中能力约束条件,将问题转化为标准运输问题求解;再检验解是否满足能力约束条件,若满足,则得到最优解;否则,记忆有效解,调整OD供需量、路段通过容量和路网路段,形成新的能力约束条件下的空车调配子模型,再求解。如此反复迭代,直到全部空车车流配置殆尽为止;累计各步迭代的结果,得到空车调配方案。在应用实例中,分别采用直接求解算法和分步优化迭代算法求解,分步优化迭代算法得到的空车调配方案比直接求解法可减少空车走行里程6000km,且路网配流相对均衡。结果验证了空车调配数学模型及其分步优化迭代算法的正确性及可行性。

Iterative Algorithm of Railway Network Empty Cars Distribution Based on Restriction of Route Capacity

Combined with the restrictive conditions of empty cars supply-demand equilibrium and flow less than route capacity, the linear programming model for distribution of empty cars is established in order to realize empty cars running distance minimum, which is solved by multi-step-optimization iterative algorithm. The basic thoughtway of this algorithm is as follows. Firstly the restrictive condition of route capacity is abandoned to transform this problem into a normal transportation problem to solve. Then the primary results are checked up to see whether satisfy the restrictive condition. If so, the optimal solution is obtained. Otherwise, the following measures should be adopted in turn, as memorizing effectual solution, modulating OD supply and demand quantity, the capacity of route sections and railway network, so as to establish a new submodel for the distribution of empty cars and again get the optimal solution. Calculations are thus iteratively conducted until all the empty cars are distributed completely. Then the total effectual solutions are accumulated to obtain the distribution scheme of empty cars. The direct algorithm and iteratire algorithm are used respectively in example to get two schemes. Empty cars running distance of the latter algorithm is 6 000 km less than that of the former, and empty cars flow is distributed more balanced correspondingly. Applied result has testified the feasibility and validity of railway network empty ears distribution model and multi-step-optimization iterative algorithm.