Interval Branch and Bound with Local Sampling for Constrained Global Optimization

In this article, we introduce a global optimization algorithm that integrates the basic idea of interval branch and bound, and new local sampling strategies along with an efficient data structure. Also included in the algorithm are procedures that handle constraints. The algorithm is shown to be abl...

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Bibliographic Details
Published inJournal of global optimization Vol. 33; no. 1; pp. 61 - 82
Main Authors Sun, M., Johnson, A.W.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.09.2005
Subjects
Algorithms
Interval arithmetic
Methods
Operations research
Optimization
Optimization algorithms
Optimization techniques
Ordinary differential equations
Partial differential equations
Sample variance
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Summary:In this article, we introduce a global optimization algorithm that integrates the basic idea of interval branch and bound, and new local sampling strategies along with an efficient data structure. Also included in the algorithm are procedures that handle constraints. The algorithm is shown to be able to find all the global optimal solutions under mild conditions. It can be used to solve various optimization problems. The local sampling (even if done stochastically) is used only to speed up the convergence and does not affect the fact that a complete search is done. Results on several examples of various dimensions ranging from 1 to 100 are also presented to illustrate numerical performance of the algorithm along with comparison with another interval method without the new local sampling and several noninterval methods. The new algorithm is seen as the best performer among those tested for solving multi-dimensional problems. [PUBLICATION ABSTRACT]
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-004-6097-6