Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations

This paper focuses on methods that improve the performance of solution approaches for multiple-ratio fractional 0–1 programs (FPs) in their general structure. In particular, we explore the links between equivalent mixed-integer linear programming and conic quadratic programming reformulations of FPs...

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Bibliographic Details
Published in:Journal of global optimization Vol. 75; no. 2; pp. 273 - 339
Main Authors: Mehmanchi, Erfan, Gómez, Andrés, Prokopyev, Oleg A.
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2019
Springer
Springer Nature B.V
Subjects:
Computer Science
Formulations
Integer programming
Integers
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Performance enhancement
Quadratic programming
Real Functions
Assortment optimization
Fractional 0–1 programming
Binary-expansion
Conic quadratic programming
Mixed-integer linear programming
Polymatroid cuts
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:This paper focuses on methods that improve the performance of solution approaches for multiple-ratio fractional 0–1 programs (FPs) in their general structure. In particular, we explore the links between equivalent mixed-integer linear programming and conic quadratic programming reformulations of FPs. Thereby, we show that integrating the ideas behind these two types of reformulations of FPs allows us to push further the limits of the current state-of-the-art results and tackle larger-size problems. We perform extensive computational experiments to compare the proposed approaches against the current reformulations from the literature.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-019-00817-7