一种求解函数全局优化问题的正交方向法

Orthogonal direction algorithm for global function optimization

提出了一种求解函数全局优化问题的正交方向法.该方法通过前三轮大范围的正交设计寻找全局最优解的大体位置,然后通过若干轮小范围的正交设计进行最优解的精确逼近.每一轮正交设计中,探索设计空间的试验点依据正交表围绕一个中心点产生,设计变量的取值范围逐渐减小.而在每一轮正交设计后,采用一维搜索提高搜索精度.一维搜索的方向由每轮正交设计的中心点和最好(或最坏)点决定.该算法计算量较小且易于编程.采用两个数学优化问题和一个火箭动力、水平发射的单级入轨飞行器的弹道优化问题对算法进行了测试.这些算例表明,当目标函数的极值数少于正交表提供的试验方案数时,正交方向法常常能以较小的计算量获得全局最优解.

A global optimization algorithm for function optimization named orthogonal direction algorithm was raised. This algorithm uses 3 times of large ranged orthogonal design to find the approximate location of the global optimization solution and then uses several times of small ranged orthogonal design to make precise approach. In each times of orthogonal design, the experimental points which detect the design space are generated according to the orthogonal table around a central point and the range of the design variables decrease gradually. After each times of orthogonal design, one-dimension search is also employed to improve search precision, the search direction is determined by the central point and the best (or worst) design points. This algorithm need less times of objective function calculation and is easy to make program. Two numerical optimization problem and a trajectory optimization problem of a rocket-powered horizontal-launched single-stage-to-orbit vehicle were solved to test this algorithm. These examples show when the peak of the objection function is less than the number of experimental points provided by the orthogonal table, orthogonal direction algorithm can often find the global optimization solution with small calculation.