Theoretical challenges towards cutting-plane selection

Theoretical challenges towards cutting-plane selection Math. Program., Ser. B https://doi.org/10.1007/s10107-018-1302-4 FULL LENGTH PAPER 1 2 Santanu S. Dey · Marco Molinaro Received: 1 February 2018 / Accepted: 16 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018 Abstract While many classes of cutting-planes are at the disposal of integer pro- gramming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and dis- cuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection. Mathematics Subject Classification 90C11 · 90C57 1 Introduction Mixed-integer linear programming (MILP) has become a mature area of research both in theory and practice, with powerful commercial and non-commercial solvers available, like CPLEX, GUROBI, XPRESS, and SCIP, to name a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

Theoretical challenges towards cutting-plane selection

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
D.O.I.
10.1007/s10107-018-1302-4
Publisher site
See Article on Publisher Site

Abstract

Math. Program., Ser. B https://doi.org/10.1007/s10107-018-1302-4 FULL LENGTH PAPER 1 2 Santanu S. Dey · Marco Molinaro Received: 1 February 2018 / Accepted: 16 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018 Abstract While many classes of cutting-planes are at the disposal of integer pro- gramming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and dis- cuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection. Mathematics Subject Classification 90C11 · 90C57 1 Introduction Mixed-integer linear programming (MILP) has become a mature area of research both in theory and practice, with powerful commercial and non-commercial solvers available, like CPLEX, GUROBI, XPRESS, and SCIP, to name a

Journal

Mathematical ProgrammingSpringer Journals

Published: May 29, 2018

References

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