Subdivision direction selection in interval methods for global optimization

The role of the interval subdivision-selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allows convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required CPU time, the number of function and derivative evaluations, and space complexity, and two rules can provide substantial improvements in efficiency.