Node selection strategies in interval Branch and Bound algorithms

Abstract : We present in this article new strategies for selecting nodes in interval Branch and Bound algorithms for constrained global optimization. For a minimization problem the standard best-first strategy selects a node with the smallest lower bound of the objective function estimate. We first propose new node selection policies where an upper bound of each node/box is also taken into account. The good accuracy of this upper bound achieved by several contracting operators leads to a good performance of the node selection rule based on this criterion. We propose another strategy that also makes a trade-off between diversification and intensification by greedily diving into potential feasible regions at each node of the best-first search. These new strategies obtain better experimental results than classical best-first search on difficult constrained global optimization instances.
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Journal of Global Optimization, Springer Verlag, 2016, 64 (2), pp.289-304. 〈http://link.springer.com/article/10.1007/s10898-015-0375-3〉. 〈10.1007/s10898-015-0375-3〉
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Bertrand Neveu, Gilles Trombettoni, Ignacio Araya. Node selection strategies in interval Branch and Bound algorithms. Journal of Global Optimization, Springer Verlag, 2016, 64 (2), pp.289-304. 〈http://link.springer.com/article/10.1007/s10898-015-0375-3〉. 〈10.1007/s10898-015-0375-3〉. 〈hal-01230893〉

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