Node selection strategies in interval Branch and Bound algorithms

Bertrand Neveu (1, 2, 3) , Gilles Trombettoni (4) , Ignacio Araya (5)

1 ENPC - École des Ponts ParisTech
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 imagine [Marne-la-Vallée]
4 COCONUT - Agents, Apprentissage, Contraintes
5 PUCV - Pontificia Universidad Católica de Valparaíso

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.

Keywords: global optimization; branch and bound

Domains: Operations Research [cs.RO]

Bertrand Neveu, Gilles Trombettoni, Ignacio Araya. Node selection strategies in interval Branch and Bound algorithms. Journal of Global Optimization, 2016, 64 (2), pp.289-304. ⟨10.1007/s10898-015-0375-3⟩. ⟨hal-01230893⟩