lsmear: A Variable Selection Strategy for Interval Branch and Bound Solvers

Ignacio Araya (1) , Bertrand Neveu (2, 3, 4)

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

Smear-based variable selection strategies are well-known and commonly used by branch-and-prune interval-based solvers. They estimates the impact of the variables on each constraint of the system by using the partial derivatives and the sizes of the variable domains. Then they aggregate these values, in some way, to estimate the impact of each variable on the whole system. The variable with the greatest impact is then selected. A problem of these strategies is that they, generally, consider all constraints equally important. In this work, we propose a new variable selection strategy which first weights the constraints by using the optimal Lagrangian multipliers of a linearization of the original problem. Then, the impact of the variables is computed with a typical smear-based function but taking into account the weights of the constraints. The strategy is tested on classical benchmark instances outperforming significantly the classical ones.

Mots clés: global optimization; branch and bound; variable selection; Lagrangian multipliers; smear function

Domaines: Recherche opérationnelle [math.OC]

Ignacio Araya, Bertrand Neveu. lsmear: A Variable Selection Strategy for Interval Branch and Bound Solvers. GOW'16 XIII Global Optimization Workshop, Sep 2016, Braga, Portugal. ⟨hal-01376611⟩