TY - CONF
A1 - Gleixner, Ambros
A1 - Weltge, Stefan
T1 - Learning and Propagating Lagrangian Variable Bounds for Mixed-Integer Nonlinear Programming
T2 - Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 10th International Conference, CPAIOR 2013, Yorktown Heights, NY, USA, May 18-22, 2013
N2 - Optimization-based bound tightening (OBBT) is a domain reduction technique commonly used in nonconvex mixed-integer nonlinear programming that solves a sequence of auxiliary linear programs. Each variable is minimized and maximized to obtain the tightest bounds valid for a global linear relaxation. This paper shows how the dual solutions of the auxiliary linear programs can be used to learn what we call Lagrangian variable bound constraints. These are linear inequalities that explain OBBT's domain reductions in terms of the bounds on other variables and the objective value of the incumbent solution. Within a spatial branch-and-bound algorithm, they can be learnt a priori (during OBBT at the root node) and propagated within the search tree at very low computational cost. Experiments with an implementation inside the MINLP solver SCIP show that this reduces the number of branch-and-bound nodes and speeds up solution times.
Y1 - 2013
UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/4819
VL - 7874
SP - 355
EP - 361
ER -