A probing algorithm for MINLP with failure prediction by SVM

Authors:
Giacomo Nannicini;Pietro Belotti;Jon Lee;Jeff Linderoth;François Margot;Andreas Wächter
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Dept. of Mathematical Sciences, Clemson University, Clemson, SC;IBM T. J. Watson Research Center, Yorktown Heights, NY;Industrial and Systems Eng., University of Wisconsin-Madison, Madison, WI;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;IBM T. J. Watson Research Center, Yorktown Heights, NY
Venue:
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Year:
2011

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Abstract

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.