scholarly journals Node selection strategies in interval Branch and Bound algorithms

2015 ◽  
Vol 64 (2) ◽  
pp. 289-304 ◽  
Author(s):  
Bertrand Neveu ◽  
Gilles Trombettoni ◽  
Ignacio Araya
Keyword(s):  
Branch And Bound ◽  
Node Selection ◽  
Branch And Bound Algorithms ◽  
Selection Strategies ◽  
Interval Branch And Bound

scholarly journals Interval Tests and Contractors Based on Optimality Conditions for Bound-Constrained Global Optimization

2020 ◽  
Vol 29 (03n04) ◽  
pp. 2060001
Author(s):  
Laurent Granvilliers
Keyword(s):  
Experimental Study ◽  
Optimality Conditions ◽  
Branch And Bound ◽  
Global Optimum ◽  
Constrained Global Optimization ◽  
First Order ◽  
Branch And Bound Algorithms ◽  
Complete Search ◽  
Monotonicity Test ◽  
Interval Branch And Bound

We study the problem of finding the global optimum of a nonlinear real function over an interval box by means of complete search techniques, namely interval branch-and-bound algorithms. Such an algorithm typically generates a tree of boxes from the initial box by alternating branching steps and contraction steps in order to remove non optimal sub-boxes. In this paper, we introduce a new contraction method that is designed to handle the boundary of the initial box where a minimizer may not be a stationary point. This method exploits the first-order optimality conditions and we show that it subsumes the classical monotonicity test based on interval arithmetic. A new branch-and-bound algorithm has been implemented in the interval solver Realpaver. An extensive experimental study based on a set of standard benchmarks is presented.

scholarly journals Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning

2016 ◽  
Vol 19 ◽  
pp. 79-102 ◽  
Author(s):  
David R. Morrison ◽  
Sheldon H. Jacobson ◽  
Jason J. Sauppe ◽  
Edward C. Sewell
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithms ◽  
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