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本文介绍将GiIl数值稳定二次规划方法应用于铁路纵断面优化设计。提出了优化设计的数学模型。利用一次样条函数的结点参数作为设计变量,建立了以工程费为目标函数的二次函数解析表达式.并对Gill算法应用于分段连续函数的可行性作了分析,同时对目前使用的“梯度投影法”、“Goldfarb二次规划算法”以及“Gill数值稳定二次规划算法”进行了分析与比较。最后根据所编制的GRPOD电算程序,对实际铁路纵断面线进行计算,取得了预期的、满意结果。
In this paper, the quadratic programming method of GiIl numerical stability is applied to the optimization design of railway longitudinal section. Put forward the mathematical model of optimal design. Using the parameter of a spline function as a design variable, a quadratic function analytical expression with the engineering cost as the objective function is established, and the feasibility of applying the Gill algorithm to the piecewise continuous function is analyzed. At the same time, Gradient projection method, Goldfarb quadratic programming algorithm and Gill numerical stability quadratic programming algorithm were analyzed and compared. Finally, according to the compiled GRPOD computer program, the actual railway longitudinal section line is calculated, and the expected and satisfactory results are obtained.