Fractional 0–1 programming and submodularity

In this note we study multiple-ratio fractional 0–1 programs, a broad class of NP -hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then w...

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Bibliographic Details
Published in:Journal of global optimization 2022-09, Vol.84 (1), p.77-93
Main Authors: Han, Shaoning, Gómez, Andrés, Prokopyev, Oleg A.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Combinatorial analysis
Computer Science
Greedy algorithms
Industrial locations
Integer programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
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Summary:In this note we study multiple-ratio fractional 0–1 programs, a broad class of NP -hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then we illustrate our theoretical results with the assortment optimization and facility location problems, and discuss practical situations that guarantee submodularity in the considered application settings. In such cases, near-optimal solutions for multiple-ratio fractional 0–1 programs can be found via simple greedy algorithms.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01131-5