Split cuts from sparse disjunctions
| Autor: | Ricardo Fukasawa, Laurent Poirrier, Shenghao Yang |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
021103 operations research Exploit Computer science 0211 other engineering and technologies Structure (category theory) DISJUNCTION 010103 numerical & computational mathematics 02 engineering and technology CUTS CUTTING PLANES SPARSE SPLIT CUTS DISJUNCTION INTEGER PROGRAMMING OPTIMIZATION 01 natural sciences Theoretical Computer Science INTEGER PROGRAMMING Simplex algorithm SPLIT SPARSE Theory of computation Decomposition (computer science) CUTTING PLANES 0101 mathematics OPTIMIZATION Integer programming Algorithm Software |
| Zdroj: | Mathematical Programming Computation. 12:295-335 |
| ISSN: | 1867-2957 1867-2949 |
| DOI: | 10.1007/s12532-020-00180-9 |
| Popis: | Split cuts are arguably the most effective class of cutting planes within a branch-and-cut framework for solving general Mixed-Integer Programs (MIP). Sparsity, on the other hand, is a common characteristic of MIP problems, and it is an important part of why the simplex method works so well inside branch-and-cut. In this work, we evaluate the strength of split cuts that exploit sparsity. In particular, we show that restricting ourselves to sparse disjunctions—and furthermore, ones that have small disjunctive coefficients—still leads to a significant portion of the total gap closed with arbitrary split cuts. We also show how to exploit sparsity structure that is implicit in the MIP formulation to produce splits that are sparse yet still effective. Our results indicate that one possibility to produce good split cuts is to try and exploit such structure. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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