DIRECT算法及其实现

DIRECT algorithm and its Python implementation

为了有效地解决传统Lipschitz函数极值求解方法向高维推广时遇到的复杂度及计算量急剧增加的问题,DIRECT算法使用超矩形的中心点替代顶点,降低了算法的复杂度及运算量。在进行初始化后,迭代进行“查找潜在超矩形”和“细分超矩形”,直至运算结果满足要求。本文从实用角度出发,对该算法的原理及实现的细节进行了全面介绍,并对算法进行了实现,验证了算法的可行性。

In order to effectively solve the problem that the complexity and calculation increase sharply when the traditional Lipschitz function extremum solving method is extended to high dimension,DIRECT algorithm uses the center point of hyperrectangles to replace the vertices,which reduces the complexity and calculation of the algorithm.After initialization,iteratively"finding potentially optimal hyper-rectangles"and"subdividing the hyper-rectangles"until the calculation results meet the requirements.In this paper,from the practical point of view,the principle and implementation details of the algorithm are comprehensively introduced,and the algorithm is implemented to verify its feasibility.