Conference Paper

A Probing Algorithm for MINLP with Failure Prediction by SVM.

DOI: 10.1007/978-3-642-21311-3_15 Conference: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems - 8th International Conference, CPAIOR 2011, Berlin, Germany, May 23-27, 2011. Proceedings
Source: DBLP

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.

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    ABSTRACT: In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness in the limit case. Some numerical results will be presented to illustrate the behavior of the methods under NLP subproblem inexactness.
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