几何约束问题求解的方向可选指数进制步长优化算法

A variable step-size revisable optimization algorithm to solve geometry constraint

针对参数化设计中的复杂几何约束求解问题,提出1种可选指数进制变步长数值求解优化算法。在给定的优化目标下,采用指数进制变步长,对每个设计参数变量进行"前进、后退、保持一步"的方向选择式试探判断,即算法每迭代循环1次,误差以指数方式进行递减,变量则逐渐逼近先前设定的参数目标。利用该优化算法,求解相切圆填充和正二十面体优化2个经典的几何优化问题。研究结果表明:该算法稳定性强,收敛速度快,求解精度高并对初始值不敏感;该算法能够求解多变量复杂参数化设计问题,并不受优化变量个数的影响;利用方向可选指数变进制变步长优化算法能有效解决二维和三维空间内的参数化几何约束优化问题。

To solve the problems of complex geometry constraint in parametric design, a variable step-size revisable optimization algorithm was presented. For the optimization objective, with the exponential notation variable step and the test strategy of＂forward, backward or maintain a step＂ to approach the optimization objective for each design parameter, the precision solution was gotten with iterative search. The filling problem for single circularity and iscsahedron problem were solved using this optimization approach. The results show that this algorithm is not sensitive to initial variable and has high convergence. And by solving the iscsahedron problem, this algorithm is not restricted by the number of parametric design variable and can solve the complex geometric constraint problem. The variable step-size revisable optimization algorithm can solve olanar and three-dimensional geometry constraint effectively.