基于均匀设计与Powell算法的全局最优化算法及并行实现

Global Optimization Algorithm Based on Uniform Design and Powell Method and Parallel Implementation

复杂函数的全局最优化问题是在求解各种复杂工程与科学计算问题中提炼出来的亟待解决的计算问题,均匀设计具有让试验点在高维空间内均匀分散的特点,而Powell算法具有很好的求解局部最优解的能力,将两种方法进行有效改进后使之相结合,设计出并行全局最优化算法。通过经典的全局最优化函数对算法进行了比较测试,发现该算法具有比以前的算法更好的寻优能力,并对算法时间、空间复杂度以及并行性进行分析和测试。基于均匀设计与Powell算法的全局最优化并行算法具有寻优能力强,时间开销与问题因素个数的平方和布点数成线性复杂度,空间开销与因素个数和布点数成线性复杂度,并行效率好的特点。

The matters of global optimization of complex function were in dire need of computation, which were depurated from complex scientific and engineering calculation. Powell algorithm had very strong ability to find the locally optimal solution, while and uniform design made the test points distribute evenly in higher space. Tow methods after some efficient improvement were combined, and a parallel global optimization algorithm, of which the time complexity and the parallel efficiency was test, using some classical global optimization functions. The algorithm designed has the characters such as strong ability in find global optimal solution, low time complexity that was directly proportional to square of the number of independent variables of goal function and the number of start points for computation, low space complexity that was in direct proportional to the number of independent variables of goal function and the number of start points for computation, and good parallel efficiency.