A New Algorithm for Box-Constrained Global Optimization

An important class of deterministic methods for global optimization is based on the theory of terminal attractors and repellers. Unfortunately, the utilization of scalar repellers is unsuitable, when the dimension n of the problem assumes values of operational interest. In previous papers the author et al. showed that BFSG-type methods, approximating the Hessian of twice continuously differentiable functions with a structured matrix, are very efficient to compute local minima, particularly in the secant case. On the other hand, the algorithms founded on the classical αBB technique are often ineffective for computational reasons. In order to increase the power of repellers in the tunneling phases, the utilization of repeller matrices with a proper structure is certainly promising and deserves investigation. In this work, it is shown that a BFGS-type method of low complexity, implemented in the local optimizations, can be effectively matched with proper repeller matrices in the tunneling phases. The novel algorithm FBαBB, which can be applied in the frame of the αBB computational scheme, is very efficient in terms of Number of Functions Generations (NFG), Success Rates (SR) in the evaluation of the global minimum and Number of Local Searches (NLS).