几何约束求解的BFGS-混沌混合算法

Combined BFGS-chaos method for solving geometric constraint

为了提高约束求解的效率和鲁棒性,提出了一个将混沌方法嵌入BFGS算法的约束求解混和算法.将约束求解问题转化为优化问题,并对多变量函数求全局极值,用混沌算法跳过局部搜索陷阱.算法分析确定几何元素的初始搜索范围,并利用BFGS方法的超线性收敛速度和混沌优化方法的内在特点进行求解.对Camel函数极值和正五边形约束求解的实验结果表明,该混合算法能够处理欠/过约束问题,有效克服BFGS算法容易陷入局部最优以及无法越过临界点的情况,可以高效鲁棒地进行约束求解.

To improve the efficiency and robustness of constraint solving algorithms, a hybrid algorithm to integrate chaos method into BFGS algorithm was proposed. By translating a geometric constraint problem into an optimization problem, the global optimum of a multi-variation function was sought for and the local traps were ignored by using chaos method in the algorithm. After the initial ranges of geometric elements were defined, the algorithm was solved by utilizing the characteristic of high convergence speed of the BFGS algorithm and the inherent virtue of the chaos optimization method. The experimental results on Camel function and 5-side polygon indicate that the algorithm can handle under-/over- constraint problem, can overcome the drawbacks that the BFGS algorithm easily fails in local optimum and cannot skip the critical point, and can solve constraint problems efficiently and robustly.