On the selection of subdivision directions in interval branch-and-bound methods for global optimization

Abstract

Abstract. This paper investigates the in uence of the interval subdivision selection rule on the convergenceof interval branch-and-bound algorithmsfor global optimization. F or the class of rules that allows convergence, we study the e ects of the rules on a model algorithm with special list ordering. Four di erent rules are investigated in theory and in practice. A wide spectrum of test problems is used for numerical tests indicating that there are substantial di erences between the rules with respect to the required CPU time, the number of function and derivative e v aluations, and the necessary storage space. Two rules can provide considerable improvements in e ciency for our model algorithm.

New results on verified global optimization

“…For some problems a huge amount of time can be gained by use of a different strategy than the traditional one of bisecting a box orthogonal to the direction with greatest diameter. This confirms results of Csendes and Ratz [5,18]. It is also shown that it is better to bisect a box always twice than only once in one step, which was the standard case in literature until now.…”

Global Optimization for Imprecise Problems

“…In the case of the computation of global minimizers our algorithm can be more accelerated by parallel techniques [5] and/or using several special tests such as cut-off test, concavity test, local search procedures, as well as special subdivision direction rules [7,39].…”

Efficient interval partitioning for constrained global optimization

“…The presented interval subdivision direction selection rule is an alternative of earlier rules as those published in [CR97], [RC95], and [CGC00]. This pair of variables is identified for each constraint and the objective function, and placed in the pool of variables whose domains will be possibly partitioned in the next iteration.…”