A Probing Algorithm for MINLP with Failure Prediction by SVM

Bound tightening is an important component of algorithms for solving nonconvex Mixed Integer Nonlinear Programs. A probing algorithm is a bound-tightening procedure that explores the consequences of restricting a variable to a subinterval with the goal of tightening its bounds.We propose a variant of probing where exploration is based on iteratively applying a truncated Branch-and-Bound algorithm. As this approach is computationally expensive, we use a Support-Vector-Machine classifier to infer whether or not the probing algorithm should be used. Computational experiments demonstrate that the use of this classifier saves a substantial amount of CPU time at the cost of a marginally weaker bound tightening.

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