Powell机械优化方法的改进

Improvements of Powell mechanical optimization

Powell优化方法是最经典最实用的,可称为基于寻优方向组的新方向取舍法。根据共轭方向的特点,主要进行了几点改进:沿最后一个基本方向寻优,并将其最优点作为第一轮寻优的初始点;必须沿新方向寻优并将其收入基本寻优方向组;与共轭性相关的寻优方向采用较小的终止条件值,其他方向只要更新当前点即可;根据与新方向的点乘积确定离开基本寻优方向组的旧方向。无论从计算量还是从存储量衡量,新算法都优于经典算法。文中给出了新算法的算法步骤和程序流程图,分析了算法特点,提供了C语言计算机程序,保证了研究结果的可重复性。二次二维目标函数和Rosenbrock目标函数的算例表明,新算法具有较好的寻优效果。对于多维优化问题,新算法更具优势。提出的算法可称为方向组不降维的构造共轭方向法。

Powell optimization,classic and practical,is a new method of direction choice based on the optimization-seeking direction group.In this article,several improvements are made according to the characteristics of conjugate direction.The optimization is carried out along the last basic direction;its optimal point is taken as the initial point of the first loop.It’s necessary to search along the new direction and integrate it into the basic direction group.For the direction of optimization associated with the conjugate,a small termination-condition value is adopted;for the other directions,the current point is updated.According to the multiplication result with the new direction,the old direction where the basic optimization-seeking direction group heads off is identified.The new algorithm is better than its classical counterpart in terms of computation or storage.Besides,its steps and program flow-chart are given;its characteristics are analyzed.The C-language computer program is provided to ensure the repeatability of the results obtained in this article.The numerical examples of the quadratic 2-dimension and Rosenbrock objective functions show that the new algorithm has better performance in optimization-seeking and it has more advantages with regard to the multi-dimensional optimization.It can be adopted to construct the conjugate direction without any dimension-reducing of direction group.