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 |
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| Sprache: | Englisch |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 85 |
| Author | Pham, Hoang Giang Ta, Thuy Anh Mai, Tien |
| Author_xml | – sequence: 1 givenname: Hoang Giang surname: Pham fullname: Pham, Hoang Giang organization: Singapore Management University – sequence: 2 givenname: Thuy Anh orcidid: 0000-0002-4849-6143 surname: Ta fullname: Ta, Thuy Anh email: anh.tathuy@phenikaa-uni.edu.vn organization: OrLab, Phenikaa University – sequence: 3 givenname: Tien surname: Mai fullname: Mai, Tien organization: Singapore Management University |
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| Cites_doi | 10.1287/opre.49.3.334.11210 10.1177/10591478241263857 10.1287/msom.1050.0088 10.1111/poms.12191 10.1287/opre.1080.0567 10.1287/mnsc.45.11.1496 10.1016/j.orl.2019.09.009 10.1609/aaai.v37i5.25720 10.1007/s10898-022-01131-5 10.1007/978-94-009-0035-6 10.1016/j.ejor.2017.09.023 10.2139/ssrn.2543309 10.1016/j.ejor.2020.01.020 10.1007/BF01580665 10.1111/j.1937-5956.2012.01423.x 10.1287/opre.1100.0866 10.1287/opre.2021.2142 10.1111/poms.12365 10.1287/msom.3.3.191.9891 10.1287/opre.1120.1063 10.1016/S0377-2217(02)00775-0 10.1561/0100000088 10.1016/j.ejor.2021.09.006 10.1007/BF02592064 10.1023/A:1008316327038 10.1002/1099-1255(200009/10)15:5<447::AID-JAE570>3.0.CO;2-1 10.1287/opre.2017.1703 10.1287/ijoc.2019.0910 10.1016/j.dam.2012.03.003 10.1109/TSP.2018.2812733 |
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| Keywords | Cutting-plane Exponential cone Piece-wise linear approximation Fractional program |
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| SubjectTerms | 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 |
| Title | An exponential cone integer programming and piece-wise linear approximation approach for 0-1 fractional programming |
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