Filter-based stochastic algorithm for global optimization

Abstract

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.

Continuation Newton methods with deflation techniques for global optimization problems

“…When problem (1) is nonconvex and large-scale, it may have many local minimizers and it is a challenge to find its global minimum. For problem (1), there are many popular global optimization methods, such as the multi-start methods [11,20,26,43,73,85], the branch-and-bound methods [10,17,76,83], the genetic evolution algorithms [32,46,59,63] and their memetic algorithms [35,60,78,84].…”

Continuation Newton methods with deflation techniques and quasi-genetic evolution for global optimization problems

“…When problem (1) is nonconvex and large-scale, it may have many local minimizers and it is challenge to find its global minimum. For problem (1), there are some popular global optimization methods, such as the multi-start methods [7,15,48,56], the genetic evolution algorithms [20,28,40,43] and their hybrid algorithms [22,41,51,55].…”