基于单纯形法改进的混沌控制算法

Improved chaos control algorithm based on simplex method

混沌控制(chaos control,CC)算法在求解结构可靠度问题中具有优越的稳健性,但由于其对步长的严格限制,导致计算速度较慢。单纯形法是一种不将梯度方向作为寻优方向的算法,该算法初始计算速度较快,能够迅速逼近至极限状态面附近,此后计算速度明显下降,且计算结果误差较大。为此,提出一种基于单纯形法改进的混沌控制算法。首先,通过增广乘子法将可靠度计算中的非线性等式约束问题转化为非约束问题;然后,通过单纯形法进行初始迭代计算;最后,使用CC算法进行收敛计算。算例结果表明:本文算法能够有效解决高非线性功能函数可靠度求解问题,且兼具两种算法的优点,与混沌控制算法相比,提高了计算效率。

Chaos control(CC)algorithm has superior robustness in solving structural reliability problems,but the strict restriction for step size makes calculation speed low.Simplex method is an algorithm that does not take the gradient direction as the optimization direction.The initial calculation speed of the simplex method is fast.And it can approach to the limit state surface quickly at the beginning of calculation,after that,the calculation speed decreases obviously and the error of calculation results is large.In this paper,an improved chaos control algorithm based on simplex method is proposed.Firstly,the nonlinear equation constraint problem in reliability calculation is transformed into unconstrained problem by the augmented multiplier method.Then,the simplex method is used for initial iterative calculation.Finally,CC algorithm is used for convergence calculation.The numerical results show that the proposed algorithm can solve the reliability problem of high nonlinear function effectively and has the advantages of both algorithms.Compared with the chaos control algorithm,the proposed algorithm improves the calculation efficiency.