We propose the general Filter-based Stochastic Algorithm (FbSA) for the global optimization of nonconvex and nonsmooth constrained problems. Under certain conditions on the probability distributions that generate the sample points, almost sure convergence is proved. In order to optimize problems with computationally expensive black-box objective functions, we develop the FbSA-RBF algorithm based on the general FbSA and assisted by Radial Basis Function (RBF) surrogate models to approximate the objective function. At each iteration, the resulting algorithm constructs/updates a surrogate model of the objective function and generates trial points using a dynamic coordinate search strategy similar to the one used in the Dynamically Dimensioned Search method. To identify a promising best trial point, a non-dominance concept based on the values of the surrogate model and the constraint violation at the trial points is used. Theoretical results concerning the sufficient conditions for the almost surely convergence of the algorithm are presented. Preliminary numerical experiments show that the FbSA-RBF is competitive when compared with other known methods in the literature.

针对非凸和非光滑约束问题的全局优化，我们提出了基于一般滤波器的随机算法（FbSA）。在生成样本点的概率分布的特定条件下，几乎可以证明收敛。为了优化具有计算量大的黑盒目标函数的问题，我们在常规FbSA的基础上开发了FbSA-RBF算法，并借助径向基函数（RBF）替代模型来近似目标函数。在每次迭代中，生成的算法都会构造/更新目标函数的替代模型，并使用类似于“动态尺寸搜索”方法中使用的动态坐标搜索策略来生成试验点。为了确定有希望的最佳试验点，使用基于代理模型的值和试验点处的约束违规的非主导概念。给出了关于算法几乎可以收敛的充分条件的理论结果。初步的数值实验表明，与文献中其他已知方法相比，FbSA-RBF具有竞争力。