基于坐标的既有铁路曲线整正约束优化算法研究

Existing Railway Curve Realignment Constrained Optimization Algorithm Research Based on Coordinates

既有铁路曲线整正是既有线改建设计中的重要部分,且结果直接影响最终设计质量和运营安全.基于最优化思想直接利用既有线上测点坐标进行曲线整正.构建了体现曲线整正成果优劣的目标函数,考虑了规范约束和控制点约束,建立了曲线整正约束最优化计算模型.基于罚函数的思想将曲线整正的非线性约束最优化问题转换为无约束最优化问题.根据目标函数的特点,采用N elder-M ead单纯形法迭代求解最优值.该算法逻辑简单,应用方便.应用结果表明算法可优化出拨距小,且满足约束条件的曲线整正成果,具有较强的实用性.

Existing railway curve realignment is an important part of existing railway reconstruction design, and the result directly affects the design quality, project cost and operation safety. This paper makes curve realignment by using surveying point coordinates in the existing railway, base of optimization theory. An objective function, which quantifies the curve realignment result, is built. Design code and control point constraints are all considered. At last, curve realignment constraint optimization model is proposed. Base of penalty function theory it converts this constrained optimization problem to unconstrained optimization problem. Considering the objective function＇ Characteristics, Nelder-Mead simplex method is choose to solve this unconstrained optimization problem. This algorithm has simple logic, and convenient application. Application results show this algorithm can generate satisfactory result that has little adjusting distance and satisfies the constraint condition. So it has good practicality.