The generalized independent set problem: Polyhedral analysis and solution approaches
•The Generalized Independent Set Problem is studied.•The polyhedron of an integer linear programming formulation is investigated.•Linear programming based heuristics are designed, implemented, and tested.•GRASP-tabu search using a 0–1 quadratic programming formulation is most effective. In the Gener...
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| Published in: | European journal of operational research Vol. 260; no. 1; pp. 41 - 55 |
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| Format: | Journal Article |
| Language: | English |
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01.07.2017
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •The Generalized Independent Set Problem is studied.•The polyhedron of an integer linear programming formulation is investigated.•Linear programming based heuristics are designed, implemented, and tested.•GRASP-tabu search using a 0–1 quadratic programming formulation is most effective.
In the Generalized Independent Set Problem, we are given a graph, a revenue for each vertex, and a set of removable edges with associated removal costs, and we seek to find an independent set that maximizes the net benefit, i.e., the difference between the revenues collected for the vertices in the independent set and the costs incurred for any removal of edges with both endpoints in the independent set. We study the polyhedron associated with a 0–1 linear programming formulation of the Generalized Independent Set Problem, deriving a number of facet-inducing inequalities, and we develop linear programming based heuristics to obtain high-quality solutions in a short amount of time. We also develop a heuristic method based on an unconstrained 0–1 quadratic programming formulation of the Generalized Independent Set Problem. In an extensive computational study, we assess the performance of these heuristics in terms of quality and efficiency. The best heuristic is then used to produce an initial solution for a branch-and-cut algorithm which uses some of the proposed facet-inducing inequalities. |
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| AbstractList | •The Generalized Independent Set Problem is studied.•The polyhedron of an integer linear programming formulation is investigated.•Linear programming based heuristics are designed, implemented, and tested.•GRASP-tabu search using a 0–1 quadratic programming formulation is most effective.
In the Generalized Independent Set Problem, we are given a graph, a revenue for each vertex, and a set of removable edges with associated removal costs, and we seek to find an independent set that maximizes the net benefit, i.e., the difference between the revenues collected for the vertices in the independent set and the costs incurred for any removal of edges with both endpoints in the independent set. We study the polyhedron associated with a 0–1 linear programming formulation of the Generalized Independent Set Problem, deriving a number of facet-inducing inequalities, and we develop linear programming based heuristics to obtain high-quality solutions in a short amount of time. We also develop a heuristic method based on an unconstrained 0–1 quadratic programming formulation of the Generalized Independent Set Problem. In an extensive computational study, we assess the performance of these heuristics in terms of quality and efficiency. The best heuristic is then used to produce an initial solution for a branch-and-cut algorithm which uses some of the proposed facet-inducing inequalities. |
| Author | Mansini, Renata Colombi, Marco Savelsbergh, Martin |
| Author_xml | – sequence: 1 givenname: Marco surname: Colombi fullname: Colombi, Marco email: m.colombi006@unibs.it organization: Department of Information Engineering, University of Brescia, Via Branze 38 - 25123 Brescia, Italy – sequence: 2 givenname: Renata surname: Mansini fullname: Mansini, Renata email: renata.mansini@unibs.it organization: Department of Information Engineering, University of Brescia, Via Branze 38 - 25123 Brescia, Italy – sequence: 3 givenname: Martin surname: Savelsbergh fullname: Savelsbergh, Martin email: martin.savelsbergh@isye.gatech.edu organization: H Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive, NW, Atlanta, GA 30332, USA |
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| Cites_doi | 10.1002/net.20088 10.1007/s10107-002-0356-4 10.1090/dimacs/026 10.1093/forestscience/43.4.544 10.1016/j.disopt.2005.03.004 10.1016/j.cor.2011.12.006 10.1287/mnsc.1040.0242 10.1007/s11590-006-0007-4 10.1007/s00291-003-0153-3 10.1287/opre.42.5.860 10.1007/BF01299447 10.1007/BF01580121 10.1007/s10107-005-0651-y 10.1007/BF01580222 10.1186/1748-7188-1-9 |
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| Keywords | Generalized independent set Facets Combinatorial optimization 0–1 quadratic programming GRASP tabu search |
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| References | Xiao, Nagamochi (bib0020) 2013 Warrier, Wilhelm, Warren, Hicks (bib0019) 2005; 46 Pelillo (bib0016) 2009 Hochbaum (bib0006) 2004; 50 Wang, Lü, Glover, Hao (bib0018) 2013; 40 Kochenberger, Alidaee, Glover, Wang (bib0009) 2007; 1 Rebennack (bib0017) 2009 Bonomo, Durán, Lin, Szwarcfiter (bib0001) 2006; 105 Hochbaum, Pathria (bib0007) 1997; 43 Johnson, Trick (bib0008) 1996 Nemhauser, Trotter Jr. (bib0014) 1974; 6 Padberg (bib0015) 1973; 5 Mannino, Sassano (bib0012) 1994; 3 Cogis, Thierry (bib0003) 2005; 2 Kochenberger, Glover, Alidaee, Rego (bib0010) 2004; 26 Marchiori (bib0013) 2002 Lehmann, Kaufmann, Steigele, Nieselt (bib0011) 2006; 1 Burer, Monteiro, Zhang (bib0002) 2002; 94 Colombi, Mansini, Savelsbergh (bib0004) 2016 Feo, Resende, Smith (bib0005) 1994; 42 Hochbaum (10.1016/j.ejor.2016.11.050_bib0006) 2004; 50 Kochenberger (10.1016/j.ejor.2016.11.050_bib0010) 2004; 26 Warrier (10.1016/j.ejor.2016.11.050_bib0019) 2005; 46 Padberg (10.1016/j.ejor.2016.11.050_bib0015) 1973; 5 Xiao (10.1016/j.ejor.2016.11.050_bib0020) 2013 Nemhauser (10.1016/j.ejor.2016.11.050_bib0014) 1974; 6 Pelillo (10.1016/j.ejor.2016.11.050_bib0016) 2009 Wang (10.1016/j.ejor.2016.11.050_bib0018) 2013; 40 Kochenberger (10.1016/j.ejor.2016.11.050_bib0009) 2007; 1 Feo (10.1016/j.ejor.2016.11.050_bib0005) 1994; 42 Bonomo (10.1016/j.ejor.2016.11.050_bib0001) 2006; 105 Johnson (10.1016/j.ejor.2016.11.050_bib0008) 1996 Cogis (10.1016/j.ejor.2016.11.050_bib0003) 2005; 2 Rebennack (10.1016/j.ejor.2016.11.050_bib0017) 2009 Marchiori (10.1016/j.ejor.2016.11.050_bib0013) 2002 Hochbaum (10.1016/j.ejor.2016.11.050_bib0007) 1997; 43 Lehmann (10.1016/j.ejor.2016.11.050_bib0011) 2006; 1 Mannino (10.1016/j.ejor.2016.11.050_bib0012) 1994; 3 Burer (10.1016/j.ejor.2016.11.050_bib0002) 2002; 94 Colombi (10.1016/j.ejor.2016.11.050_bib0004) 2016 |
| References_xml | – volume: 105 start-page: 233 year: 2006 end-page: 250 ident: bib0001 article-title: On balanced graphs publication-title: Mathematical programming – start-page: 3676 year: 2009 end-page: 3688 ident: bib0017 article-title: Stable set problem: branch & cut algorithms stable set problem: branch & cut algorithms publication-title: Encyclopedia of optimization – volume: 50 start-page: 709 year: 2004 end-page: 723 ident: bib0006 article-title: 50th anniversary article: selection, provisioning, shared fixed costs, maximum closure, and implications on algorithmic methods today publication-title: Management Science – volume: 43 start-page: 544 year: 1997 end-page: 554 ident: bib0007 article-title: Forest harvesting and minimum cuts: a new approach to handling spatial constraints publication-title: Forest Science – volume: 1 start-page: 111 year: 2007 end-page: 117 ident: bib0009 article-title: An effective modeling and solution approach for the generalized independent set problem publication-title: Optimization Letters – volume: 3 start-page: 243 year: 1994 end-page: 258 ident: bib0012 article-title: An exact algorithm for the maximum stable set problem publication-title: Computational Optimization and Applications – volume: 6 start-page: 48 year: 1974 end-page: 61 ident: bib0014 article-title: Properties of vertex packing and independence system polyhedra publication-title: Mathematical Programming – volume: 42 start-page: 860 year: 1994 end-page: 878 ident: bib0005 article-title: A greedy randomized adaptive search procedure for maximum independent set publication-title: Operations Research – year: 1996 ident: bib0008 article-title: Cliques, coloring, and satisfiability: second DIMACS implementation challenge, October 11–13, 1993 publication-title: Center for Discrete Mathematics and Theoretical Computer Science New Brunswick, NJ: DIMACS series in discrete mathematics and theoretical computer science – volume: 26 start-page: 237 year: 2004 end-page: 250 ident: bib0010 article-title: A unified modeling and solution framework for combinatorial optimization problems publication-title: OR Spectrum – start-page: 112 year: 2002 end-page: 121 ident: bib0013 article-title: Genetic, iterated and multistart local search for the maximum clique problem publication-title: Applications of evolutionary computing – volume: 5 start-page: 199 year: 1973 end-page: 215 ident: bib0015 article-title: On the facial structure of set packing polyhedra publication-title: Mathematical Programming – volume: 40 start-page: 3100 year: 2013 end-page: 3107 ident: bib0018 article-title: Probabilistic GRASP-tabu search algorithms for the ubqp problem publication-title: Computers & Operations Research – volume: 94 start-page: 137 year: 2002 end-page: 166 ident: bib0002 article-title: Maximum stable set formulations and heuristics based on continuous optimization publication-title: Mathematical Programming – volume: 1 start-page: 9 year: 2006 ident: bib0011 article-title: On the maximal cliques in c-max-tolerance graphs and their application in clustering molecular sequences publication-title: Algorithms for Molecular Biology – year: 2016 ident: bib0004 article-title: The generalized independent set problem: polyhedral analysis and LP-based heuristics publication-title: Technical Report, 1 – volume: 46 start-page: 198 year: 2005 end-page: 209 ident: bib0019 article-title: A branch-and-price approach for the maximum weight independent set problem publication-title: Networks – start-page: 1508 year: 2009 end-page: 1520 ident: bib0016 article-title: Heuristics for maximum clique and independent set publication-title: Encyclopedia of optimization – start-page: 328 year: 2013 end-page: 338 ident: bib0020 article-title: Exact algorithms for maximum independent set publication-title: Algorithms and computation – volume: 2 start-page: 185 year: 2005 end-page: 188 ident: bib0003 article-title: Computing maximum stable sets for distance-hereditary graphs publication-title: Discrete Optimization – year: 2016 ident: 10.1016/j.ejor.2016.11.050_bib0004 article-title: The generalized independent set problem: polyhedral analysis and LP-based heuristics – volume: 46 start-page: 198 issue: 4 year: 2005 ident: 10.1016/j.ejor.2016.11.050_bib0019 article-title: A branch-and-price approach for the maximum weight independent set problem publication-title: Networks doi: 10.1002/net.20088 – start-page: 328 year: 2013 ident: 10.1016/j.ejor.2016.11.050_bib0020 article-title: Exact algorithms for maximum independent set – volume: 94 start-page: 137 issue: 1 year: 2002 ident: 10.1016/j.ejor.2016.11.050_bib0002 article-title: Maximum stable set formulations and heuristics based on continuous optimization publication-title: Mathematical Programming doi: 10.1007/s10107-002-0356-4 – year: 1996 ident: 10.1016/j.ejor.2016.11.050_bib0008 article-title: Cliques, coloring, and satisfiability: second DIMACS implementation challenge, October 11–13, 1993 doi: 10.1090/dimacs/026 – volume: 43 start-page: 544 issue: 4 year: 1997 ident: 10.1016/j.ejor.2016.11.050_bib0007 article-title: Forest harvesting and minimum cuts: a new approach to handling spatial constraints publication-title: Forest Science doi: 10.1093/forestscience/43.4.544 – volume: 2 start-page: 185 issue: 2 year: 2005 ident: 10.1016/j.ejor.2016.11.050_bib0003 article-title: Computing maximum stable sets for distance-hereditary graphs publication-title: Discrete Optimization doi: 10.1016/j.disopt.2005.03.004 – volume: 40 start-page: 3100 issue: 12 year: 2013 ident: 10.1016/j.ejor.2016.11.050_bib0018 article-title: Probabilistic GRASP-tabu search algorithms for the ubqp problem publication-title: Computers & Operations Research doi: 10.1016/j.cor.2011.12.006 – volume: 50 start-page: 709 issue: 6 year: 2004 ident: 10.1016/j.ejor.2016.11.050_bib0006 article-title: 50th anniversary article: selection, provisioning, shared fixed costs, maximum closure, and implications on algorithmic methods today publication-title: Management Science doi: 10.1287/mnsc.1040.0242 – volume: 1 start-page: 111 issue: 1 year: 2007 ident: 10.1016/j.ejor.2016.11.050_bib0009 article-title: An effective modeling and solution approach for the generalized independent set problem publication-title: Optimization Letters doi: 10.1007/s11590-006-0007-4 – volume: 26 start-page: 237 issue: 2 year: 2004 ident: 10.1016/j.ejor.2016.11.050_bib0010 article-title: A unified modeling and solution framework for combinatorial optimization problems publication-title: OR Spectrum doi: 10.1007/s00291-003-0153-3 – start-page: 1508 year: 2009 ident: 10.1016/j.ejor.2016.11.050_bib0016 article-title: Heuristics for maximum clique and independent set – start-page: 3676 year: 2009 ident: 10.1016/j.ejor.2016.11.050_bib0017 article-title: Stable set problem: branch & cut algorithms stable set problem: branch & cut algorithms – volume: 42 start-page: 860 issue: 5 year: 1994 ident: 10.1016/j.ejor.2016.11.050_bib0005 article-title: A greedy randomized adaptive search procedure for maximum independent set publication-title: Operations Research doi: 10.1287/opre.42.5.860 – volume: 3 start-page: 243 issue: 3 year: 1994 ident: 10.1016/j.ejor.2016.11.050_bib0012 article-title: An exact algorithm for the maximum stable set problem publication-title: Computational Optimization and Applications doi: 10.1007/BF01299447 – volume: 5 start-page: 199 issue: 1 year: 1973 ident: 10.1016/j.ejor.2016.11.050_bib0015 article-title: On the facial structure of set packing polyhedra publication-title: Mathematical Programming doi: 10.1007/BF01580121 – start-page: 112 year: 2002 ident: 10.1016/j.ejor.2016.11.050_bib0013 article-title: Genetic, iterated and multistart local search for the maximum clique problem – volume: 105 start-page: 233 issue: 2–3 year: 2006 ident: 10.1016/j.ejor.2016.11.050_bib0001 article-title: On balanced graphs publication-title: Mathematical programming doi: 10.1007/s10107-005-0651-y – volume: 6 start-page: 48 issue: 1 year: 1974 ident: 10.1016/j.ejor.2016.11.050_bib0014 article-title: Properties of vertex packing and independence system polyhedra publication-title: Mathematical Programming doi: 10.1007/BF01580222 – volume: 1 start-page: 9 issue: 1 year: 2006 ident: 10.1016/j.ejor.2016.11.050_bib0011 article-title: On the maximal cliques in c-max-tolerance graphs and their application in clustering molecular sequences publication-title: Algorithms for Molecular Biology doi: 10.1186/1748-7188-1-9 |
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| SubjectTerms | 0–1 quadratic programming Combinatorial optimization Facets Generalized independent set GRASP tabu search |
| Title | The generalized independent set problem: Polyhedral analysis and solution approaches |
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