Branching and bounds tighteningtechniques for non-convex MINLP

Many industrial problems can be naturally formulated using Mixed Integer Nonlinear Programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for realworld MINLP problems, we have developed an sBB software package named couenne (Convex Overand Under-ENvelopes for Nonlinear Estimation) and used it for extensive tests on several combinations of bounds tightening and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver.