Outer approximation for integer nonlinear programs via decision diagrams

Outer approximation for integer nonlinear programs via decision diagrams

As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems exploiting their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand...

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Bibliographic Details
Published in:Mathematical programming 2021-05, Vol.187 (1-2), p.111-150
Main Authors: Davarnia, Danial, van Hoeve, Willem-Jan
Format: Article
Language:eng
Subjects:
Approximation
Calculus of Variations and Optimal Control
Optimization
Combinatorial analysis
Combinatorics
Computational geometry
Convexity
Cutting
Dynamic programming
Full Length Paper
Integer programming
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Solvers
Theoretical
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Summary:As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems exploiting their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by introducing IP techniques that can be derived from DDs and used in conjunction with IP to enhance the overall performance. This perspective allows for studying problems with more general structure than those typically modeled via recursive formulations. In particular, we develop linear programming and subgradient-type methods to generate valid inequalities for the convex hull of the feasible region described by DDs. For convex IPs, these cutting planes dominate the so-called linearized cuts used in the outer approximation framework. These cutting planes can also be derived for nonconvex IPs, which leads to a generalization of the outer approximation framework. Computational experiments show significant optimality gap improvement for integer nonlinear programs over the traditional cutting plane methods employed in the state-of-the-art solvers.
ISSN:0025-5610
1436-4646