Trust-region based adaptive radial basis function algorithm for global optimization of expensive constrained black-box problems

Abstract

It has been a very challenging task to develop efficient and robust techniques to solve real-world engineering optimization problems due to the unknown function properties, complex constraints and severely limited computational budget. To address this issue, TARBF algorithm (trust-region based adaptive radial basis function interpolation) for solving expensive constrained black-box optimization problems is proposed in this paper. The approach successfully decomposes the original optimization problem into a sequence of sub-problems approximated by radial basis functions in a series of trust regions. Then, the solution of each sub-problem becomes the starting point for the next iteration. According to the values of objective and constraint functions, an effective online normalization technique is further developed to adaptively improve the model accuracy in the trust region, where the surrogate is updated iteratively. Averagely, TARBF has the ability to robustly solve the 21 G-problems (CEC’2006) and 4 engineering problems within 535.69 and 234.44 function evaluations, respectively. The comparison results with other state-of-the-art metamodel-based algorithms prove that TARBF is a convergent, efficient and accurate paradigm. Moreover, the sophisticated trust region strategy developed in TARBF, which is a major contribution to the field of the efficient constrained optimization, has the capability to facilitate an effective balance of exploration and exploitation for solving constrained black-box optimization problems.