Abstract
We present an algorithm for finding a feasible solution to a convex mixed integer nonlinear program. This algorithm, called Feasibility Pump, alternates between solving nonlinear programs and mixed integer linear programs. We also discuss how the algorithm can be iterated so as to improve the first solution it finds, as well as its integration within an outer approximation scheme. We report computational results.
Highlights
Finding a good feasible solution to a Mixed Integer Linear Program (MILP) can be difficult, and sometimes just finding a feasible solution is an issue
Note that in the case where the region g x y b is nonconvex, the method can still be applied, but the outer approximation constraints (3) are not always valid. This may result in the problem FP OA i being infeasible and the method failing while there exists some integer feasible solution to MINLP
In addition, the region g x y " b is convex, the enhanced FP is an exact algorithm: either it finds a feasible solution of MINLP if one exists, or it proves that none exists
Summary
(Part of this research was carried out when Andrea Lodi was Herman Goldstine Fellow of the IBM T. LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. Report for early dissemination of its contents. Requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). Copies may be requested from IBM T.
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