An exponential cone integer programming and piece-wise linear approximation approach for 0-1 fractional programming

We study a class of binary fractional programs commonly encountered in important application domains such as assortment optimization and facility location. These problems are known to be NP-hard to approximate within any constant factor, and existing solution approaches typically rely on mixed-integ...

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Veröffentlicht in:Journal of combinatorial optimization Jg. 49; H. 5; S. 85
Hauptverfasser: Pham, Hoang Giang, Ta, Thuy Anh, Mai, Tien
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2025
Springer Nature B.V
Schlagworte:
Approximation
Combinatorics
Convex and Discrete Geometry
Integer programming
Linear programming
Mathematical Modeling and Industrial Mathematics
Mathematical programming
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research/Decision Theory
Optimization
Ratios
Theory of Computation
Cutting-plane
Exponential cone
Piece-wise linear approximation
Fractional program
ISSN:1382-6905, 1573-2886
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Zusammenfassung:We study a class of binary fractional programs commonly encountered in important application domains such as assortment optimization and facility location. These problems are known to be NP-hard to approximate within any constant factor, and existing solution approaches typically rely on mixed-integer linear programming or second-order cone programming reformulations. These methods often utilize linearization techniques (e.g., big-M or McCormick inequalities), which can result in weak continuous relaxations. In this work, we propose a novel approach based on an exponential cone reformulation combined with piecewise linear approximation. This allows the problem to be solved efficiently using standard cutting-plane or branch-and-cut procedures. We further provide a theoretical analysis of the approximation quality yielded by our reformulation and discuss strategies for optimizing the problem size of the exponential cone formulation. Experiments on instances of various sizes demonstrate that our approach delivers competitive performance on small and medium instances while offering superior performance on large instances compared to state-of-the-art baselines.
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-025-01318-y