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A review of subdivision direction selection in interval methods for global optimization

This paper gives a short overview of the latest results on the role of the interval subdivision selection rule in branch-and-bound algorithms for global optimization. The class of rules that allow convergence for two slightly different model algorithms is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. An extensive 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. Two of the rules can provide substantial improvements in efficiency.