Globally-biased BIRECT algorithm with local accelerators for expensive global optimization

In this paper, black-box global optimization problem with expensive function evaluations is considered. This problem is challenging for numerical methods due to the practical limits on computational budget often required by intelligent systems. For its efficient solution, a new DIRECT-type hybrid technique is proposed. The new algorithm incorporates a novel sampling on diagonals and bisection strategy (instead of a trisection which is commonly used in the existing DIRECT-type algorithms), embedded into the globally-biased framework, and enriched with three different local minimization strategies. The numerical results on a test set of almost 900 problems from the literature and on a real-life application regarding nonlinear regression show that the new approach effectively addresses well-known DIRECT weaknesses, has beneficial effects on the overall performance, and on average, gives significantly better results compared to several DIRECT-type methods widely used in decision-making expert systems.