On a linearization technique for solving the quadratic set covering problem and variations
In this paper we identify various inaccuracies in the paper by Saxena and Arora (Optimization 39:33–42, 1997 ). In particular, we observe that their algorithm does not guarantee optimality, contrary to what is claimed. Experimental analysis has been carried out to assess the value of this algorithm...
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| Published in | Optimization letters Vol. 11; no. 7; pp. 1357 - 1370 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1862-4472 1862-4480 |
| DOI | 10.1007/s11590-016-1081-x |
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| Abstract | In this paper we identify various inaccuracies in the paper by Saxena and Arora (Optimization 39:33–42,
1997
). In particular, we observe that their algorithm does not guarantee optimality, contrary to what is claimed. Experimental analysis has been carried out to assess the value of this algorithm as a heuristic. The results disclose that for some classes of problems the Saxena–Arora algorithm is effective in achieving good quality solutions while for some other classes of problems, its performance is poor. We also discuss similar inaccuracies in another related paper. |
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| AbstractList | In this paper we identify various inaccuracies in the paper by Saxena and Arora (Optimization 39:33–42,
1997
). In particular, we observe that their algorithm does not guarantee optimality, contrary to what is claimed. Experimental analysis has been carried out to assess the value of this algorithm as a heuristic. The results disclose that for some classes of problems the Saxena–Arora algorithm is effective in achieving good quality solutions while for some other classes of problems, its performance is poor. We also discuss similar inaccuracies in another related paper. |
| Author | Pandey, Pooja Punnen, Abraham P. |
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| Cites_doi | 10.1287/opre.19.4.998 10.1016/S0377-2217(96)00161-0 10.1287/moor.1110.0509 10.1287/mnsc.32.10.1274 10.1016/j.disopt.2013.02.003 10.1080/02331939708844269 10.1287/opre.23.1.150 10.1002/1520-6750(199002)37:1<151::AID-NAV3220370110>3.0.CO;2-2 10.1016/j.disopt.2007.10.001 10.1007/s10288-006-0015-3 |
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| Keywords | Agorithms Set covering problem Quadratic programming 0-1 programming Heuristic |
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| References | Bazaraa, Goode (CR3) 1975; 23 Grossman, Wool (CR9) 1997; 101 Adams, Sherali (CR1) 1986; 32 Balas, Ho (CR2) 1980; 12 Gupta, Saxena (CR11) 2014; 4 CR6 Kabadi, Punnen (CR12) 2011; 36 CR5 CR18 Beasley (CR4) 1990; 37 CR15 Garfinkel, Nemhauser (CR8) 1972 Lemke, Salkin, Spielberg (CR13) 1971; 19 CR14 Gupta, Saxena (CR10) 2014; 4 Escoffier, Hammer (CR7) 2007; 4 Punnen, Kabadi (CR16) 2013; 10 Saxena, Arora (CR17) 1997; 39 B Escoffier (1081_CR7) 2007; 4 CE Lemke (1081_CR13) 1971; 19 T Grossman (1081_CR9) 1997; 101 AP Punnen (1081_CR16) 2013; 10 SN Kabadi (1081_CR12) 2011; 36 E Balas (1081_CR2) 1980; 12 R Gupta (1081_CR11) 2014; 4 JE Beasley (1081_CR4) 1990; 37 1081_CR5 RR Saxena (1081_CR17) 1997; 39 1081_CR6 MS Bazaraa (1081_CR3) 1975; 23 WP Adams (1081_CR1) 1986; 32 1081_CR18 R Gupta (1081_CR10) 2014; 4 1081_CR15 RS Garfinkel (1081_CR8) 1972 1081_CR14 |
| References_xml | – volume: 19 start-page: 998 year: 1971 end-page: 1022 ident: CR13 article-title: Set covering by single branch enumeration with linear programming sub-problem publication-title: Oper. Res. doi: 10.1287/opre.19.4.998 – volume: 101 start-page: 81 year: 1997 end-page: 92 ident: CR9 article-title: Computational experience with approximation algorithms for the set covering problem publication-title: Eur. J. Oper. Res. doi: 10.1016/S0377-2217(96)00161-0 – ident: CR18 – volume: 4 start-page: 9 year: 2014 end-page: 18 ident: CR11 article-title: Set packing problem with linear fractional objective function publication-title: Int. J. Math. Comput. Appl. Res. – volume: 36 start-page: 754 year: 2011 end-page: 761 ident: CR12 article-title: An algorithm for the QAP linearization problem publication-title: Math. Oper. Res. doi: 10.1287/moor.1110.0509 – volume: 32 start-page: 1274 year: 1986 end-page: 1290 ident: CR1 article-title: A tight linearization and an algorithm for zero-one quadratic programming problems publication-title: Manag. Sci. doi: 10.1287/mnsc.32.10.1274 – ident: CR14 – ident: CR15 – ident: CR6 – volume: 10 start-page: 200 year: 2013 end-page: 209 ident: CR16 article-title: A linear time algorithm for the Koopmans-Beckman QAP linearization and related problems publication-title: Discrete Optim. doi: 10.1016/j.disopt.2013.02.003 – volume: 39 start-page: 33 year: 1997 end-page: 42 ident: CR17 article-title: A linearization technique for solving the quadratic set covering problem publication-title: Optimization doi: 10.1080/02331939708844269 – ident: CR5 – volume: 23 start-page: 150 year: 1975 end-page: 158 ident: CR3 article-title: A cutting-plane algorithm for the quadratic set-covering problem publication-title: Oper. Res. doi: 10.1287/opre.23.1.150 – volume: 37 start-page: 151 year: 1990 end-page: 164 ident: CR4 article-title: A lagrangian heuristic for set-covering problems publication-title: Naval Res. Logist. doi: 10.1002/1520-6750(199002)37:1<151::AID-NAV3220370110>3.0.CO;2-2 – volume: 12 start-page: 37 year: 1980 end-page: 60 ident: CR2 article-title: Set covering algorithms using cutting planes, heuristics, and sub-gradient optimization: a computational study publication-title: Math. Progr. – year: 1972 ident: CR8 publication-title: Integer Programming – volume: 4 start-page: 9 year: 2014 end-page: 20 ident: CR10 article-title: Linearization technique for solving quadratic set packing and partitioning problems publication-title: Int. J. Math. Comput. Appl. Res. – volume: 4 start-page: 378 year: 2007 end-page: 386 ident: CR7 article-title: Approximation of the quadratic set covering problem publication-title: Discrete Optim. doi: 10.1016/j.disopt.2007.10.001 – ident: 1081_CR15 – volume: 23 start-page: 150 year: 1975 ident: 1081_CR3 publication-title: Oper. Res. doi: 10.1287/opre.23.1.150 – ident: 1081_CR6 – volume: 4 start-page: 9 year: 2014 ident: 1081_CR11 publication-title: Int. J. Math. Comput. Appl. Res. – volume: 10 start-page: 200 year: 2013 ident: 1081_CR16 publication-title: Discrete Optim. doi: 10.1016/j.disopt.2013.02.003 – volume: 39 start-page: 33 year: 1997 ident: 1081_CR17 publication-title: Optimization doi: 10.1080/02331939708844269 – ident: 1081_CR18 – ident: 1081_CR5 – volume: 37 start-page: 151 year: 1990 ident: 1081_CR4 publication-title: Naval Res. Logist. doi: 10.1002/1520-6750(199002)37:1<151::AID-NAV3220370110>3.0.CO;2-2 – ident: 1081_CR14 doi: 10.1007/s10288-006-0015-3 – volume: 101 start-page: 81 year: 1997 ident: 1081_CR9 publication-title: Eur. J. Oper. Res. doi: 10.1016/S0377-2217(96)00161-0 – volume: 36 start-page: 754 year: 2011 ident: 1081_CR12 publication-title: Math. Oper. Res. doi: 10.1287/moor.1110.0509 – volume-title: Integer Programming year: 1972 ident: 1081_CR8 – volume: 4 start-page: 9 year: 2014 ident: 1081_CR10 publication-title: Int. J. Math. Comput. Appl. Res. – volume: 32 start-page: 1274 year: 1986 ident: 1081_CR1 publication-title: Manag. Sci. doi: 10.1287/mnsc.32.10.1274 – volume: 19 start-page: 998 year: 1971 ident: 1081_CR13 publication-title: Oper. Res. doi: 10.1287/opre.19.4.998 – volume: 4 start-page: 378 year: 2007 ident: 1081_CR7 publication-title: Discrete Optim. doi: 10.1016/j.disopt.2007.10.001 – volume: 12 start-page: 37 year: 1980 ident: 1081_CR2 publication-title: Math. Progr. |
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1997
). In particular, we observe that their algorithm... |
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| Title | On a linearization technique for solving the quadratic set covering problem and variations |
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