高效高精度全局优化算法及其气动应用研究

Study of the Efficient Global Optimization with High Accuracy and Its Applications in Aerodynamic

经典的高效全局优化(efficient global optimization,EGO)算法搜寻得到的最优解,受代理模型精度及过早收敛等问题的制约,其精度仍存在进一步改善的空间。围绕最优解精度进一步改善的问题,研究了面向精确最优解的EGO算法。该算法基于Kriging代理模型,涉及的最优加点策略采用考虑Kriging信任的改善期望函数法,使得优化迭代后期更偏向于局部寻优。此外,文中还考虑了与成熟的拟牛顿法和Powell法等局部优化方法协同的算法,以提高最优解的搜寻精度。选用了若干典型的检验函数,对优化算法的具体实施过程进行了模拟与分析,发现改进后的优化算法能以相对较少的额外函数评估次数得到比经典的EGO算法更精确的全局最优解,从而验证了算法的有效性和准确性。最后,把发展的算法应用到具体的跨音速翼型优化问题,算例表明,改进后的EGO算法翼型阻力较原EGO算法减小了1.11%,显示了其工程实用性。

Subjected to the accuracy of surrogate model and premature convergence sometimes occurs,the solution of classical efficient global optimization(EGO)usually can be improved.Regarding this point,this paper presents a thorough study of the EGO with high accuracy optimal solution.The algorithm is based on the Kriging surrogate model,in which the Kriging believe strategy based Expected Improvement(EI)function is adopted,it can help to lead the optimal solution to local optimum in the late period of iteration.Besides,in order to improving the accuracy,cooperating with quasi-Newton method and Powell method are also incorporated.Several representative numerical examples are selected to test the algorithms above,the result shows that the algorithms in this paper can reach more accurate global optimal solution than classical EGO,with less additional cost.At last,an aerodynamic optimization problem is developed,it shows that the drag coefficient decreased 1.11%further than the former EGO,shows its practicability in an engineering environment.