An optimal algorithm for variable knockout problems

citation_journal_title=Math Program Comput; citation_title=SCIP: Solving constraint integer programs; citation_author=T Achterberg; citation_volume=1; citation_issue=1; citation_publication_date=2009; citation_pages=1-41; citation_doi=10.1007/s12532-008-0001-1; citation_id=CR1 citation_journal_title=Networks; citation_title=Shortest path network interdiction with asymmetric information; citation_author=H Bayrak, MD Bailey; citation_volume=52; citation_issue=3; citation_publication_date=2008; citation_pages=133-140; citation_doi=10.1002/net.20236; citation_id=CR2 citation_journal_title=Eur J Oper Res; citation_title=An algorithm for set covering problem; citation_author=JE Beasley; citation_volume=31; citation_issue=1; citation_publication_date=1987; citation_pages=85-93; citation_doi=10.1016/0377-2217(87)90141-X; citation_id=CR3 citation_journal_title=J Oper Res Soc; citation_title=OR-Library: distributing test problems by electronic mail; citation_author=JE Beasley; citation_volume=41; citation_issue=11; citation_publication_date=1990; citation_pages=1069-1072; citation_doi=10.1057/jors.1990.166; citation_id=CR4 citation_journal_title=Networks; citation_title=An algorithm for the resource constrained shortest path problem; citation_author=JE Beasley, N Christofides; citation_volume=19; citation_issue=4; citation_publication_date=1989; citation_pages=379-394; citation_doi=10.1002/net.3230190402; citation_id=CR5 citation_journal_title=Eur J Oper Res; citation_title=A genetic algorithm for the set covering problem; citation_author=JE Beasley, PC Chu; citation_volume=94; citation_issue=2; citation_publication_date=1996; citation_pages=392-404; citation_doi=10.1016/0377-2217(95)00159-X; citation_id=CR6 citation_journal_title=Eur J Oper Res; citation_title=Enhancing an algorithm for set covering problems; citation_author=JE Beasley, K Jornsten; citation_volume=58; citation_issue=2; citation_publication_date=1992; citation_pages=293-300; citation_doi=10.1016/0377-2217(92)90215-U; citation_id=CR7 citation_journal_title=Bioinformatics; citation_title=Recovering metabolic pathways via optimization; citation_author=JE Beasley, FJ Planes; citation_volume=23; citation_issue=1; citation_publication_date=2007; citation_pages=92-98; citation_doi=10.1093/bioinformatics/btl554; citation_id=CR8 citation_journal_title=Eur J Oper Res; citation_title=A survey on bilevel optimization under uncertainty; citation_author=Y Beck, I Ljubi, M Schmidt; citation_volume=311; citation_issue=2; citation_publication_date=2023; citation_pages=401-426; citation_doi=10.1016/j.ejor.2023.01.008; citation_id=CR9 citation_journal_title=Oper Res; citation_title=A heuristic method for the set covering problem; citation_author=A Caprara, M Fischetti, P Toth; citation_volume=47; citation_issue=5; citation_publication_date=1999; citation_pages=730-743; citation_doi=10.1287/opre.47.5.730; citation_id=CR10 citation_journal_title=Ann Oper Res; citation_title=Algorithms for the set covering problem; citation_author=A Caprara, P Toth, M Fischetti; citation_volume=98; citation_publication_date=2000; citation_pages=353-371; citation_doi=10.1023/A:1019225027893; citation_id=CR11 citation_journal_title=Ann Oper Res; citation_title=An overview of bilevel optimization; citation_author=B Colson, P Marcotte, G Savard; citation_volume=153; citation_issue=1; citation_publication_date=2007; citation_pages=235-256; citation_doi=10.1007/s10479-007-0176-2; citation_id=CR12 citation_journal_title=Optimization; citation_title=Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints; citation_author=S Dempe; citation_volume=52; citation_issue=3; citation_publication_date=2003; citation_pages=333-359; citation_doi=10.1080/0233193031000149894; citation_id=CR13 DeNegre ST, Ralphs TK (2009) A branch-and-cut algorithm for integer bilevel linear programs. In: Chinneck JW, Kristjansson B, Saltzman MJ (eds) Operations research and cyber-infrastructure. Operations Research/Computer Science Interfaces, vol 47. Springer, Boston citation_journal_title=Networks; citation_title=Shortest-path network interdiction; citation_author=E Israeli, RK Wood; citation_volume=40; citation_issue=2; citation_publication_date=2002; citation_pages=97-111; citation_doi=10.1002/net.10039; citation_id=CR15 citation_journal_title=Math Probl Eng; citation_title=Bilevel programming and applications; citation_author=VV Kalashnikov, S Dempe, GA Perez-Valdes, NI Kalashnykova, JF Camacho-Vallejo; citation_publication_date=2023; citation_doi=10.1155/2015/310301; citation_id=CR16 citation_journal_title=EURO J Comput Optim; citation_title=A survey on mixed-integer programming techniques in bilevel optimization; citation_author=T Kleinert, M Labbe, I Ljubic, M Schmidt; citation_volume=9; citation_publication_date=2021; citation_doi=10.1016/j.ejco.2021.100007; citation_id=CR17 citation_journal_title=Eur J Oper Res; citation_title=An effective and simple heuristic for the set covering problem; citation_author=GH Lan, GW DePuy, GE Whitehouse; citation_volume=176; citation_issue=3; citation_publication_date=2007; citation_pages=1387-1403; citation_doi=10.1016/j.ejor.2005.09.028; citation_id=CR18 citation_journal_title=Eur J Oper Res; citation_title=An exact method for binary fortification games; citation_author=M Leitner, I Ljubic, M Monaci, M Sinnl, K Tantnmts; citation_volume=307; citation_issue=3; citation_publication_date=2023; citation_pages=1026-1039; citation_doi=10.1016/j.ejor.2022.10.038; citation_id=CR19 citation_journal_title=INFORMS J Comput; citation_title=A backward sampling framework for interdiction problems with fortification; citation_author=L Lozano, JC Smith; citation_volume=29; citation_issue=1; citation_publication_date=2017; citation_pages=123-139; citation_doi=10.1287/ijoc.2016.0721; citation_id=CR20 citation_journal_title=IEEE Trans Syst Man Cybern Syst; citation_title=Multiobjective bilevel optimization: a survey of the state-of-the-art; citation_author=J-A Mejia-de-Dios, A Rodriguez-Molina, E Mezura-Montes; citation_volume=53; citation_issue=9; citation_publication_date=2023; citation_pages=5478-5490; citation_doi=10.1109/TSMC.2023.3271125; citation_id=CR21 citation_journal_title=Eur J Oper Res; citation_title=An electromagnetism metaheuristic for the unicost set covering problem; citation_author=Z Naji-Azimi, P Toth, L Galli; citation_volume=205; citation_issue=2; citation_publication_date=2010; citation_pages=290-300; citation_doi=10.1016/j.ejor.2010.01.035; citation_id=CR22 citation_journal_title=Bioinformatics; citation_title=An optimization model for metabolic pathways; citation_author=FJ Planes, JE Beasley; citation_volume=25; citation_issue=20; citation_publication_date=2009; citation_pages=2723-2729; citation_doi=10.1093/bioinformatics/btp441; citation_id=CR23 citation_journal_title=Discret Appl Math; citation_title=Path finding approaches and metabolic pathways; citation_author=FJ Planes, JE Beasley; citation_volume=157; citation_issue=10; citation_publication_date=2009; citation_pages=2244-2256; citation_doi=10.1016/j.dam.2008.06.035; citation_id=CR24 citation_journal_title=Oper Res Int J; citation_title=A GRASP-based scheme for the set covering problem; citation_author=V Reyes, I Araya; citation_volume=21; citation_issue=4; citation_publication_date=2021; citation_pages=2391-2408; citation_doi=10.1007/s12351-019-00514-z; citation_id=CR25 citation_journal_title=Brief Bioinform; citation_title=Advances in network-based metabolic pathway analysis and gene expression data integration; citation_author=A Rezola, J Pey, L Tobalina, A Rubio, JE Beasley, FJ Planes; citation_volume=16; citation_issue=2; citation_publication_date=2015; citation_pages=265-279; citation_doi=10.1093/bib/bbu009; citation_id=CR26 citation_journal_title=Comput Ind Eng; citation_title=A bi-objective approach for shortest-path network interdiction; citation_author=CM Rocco, JE Ramirez-Marquez; citation_volume=59; citation_issue=2; citation_publication_date=2010; citation_pages=232-240; citation_doi=10.1016/j.cie.2010.04.004; citation_id=CR27 Schmidt M, Beck Y (2023) A gentle and incomplete introduction to bilevel optimization. https://optimization-online.org/wp-content/uploads/2021/06/bilevel-optimization.pdf . Accessed August 23 SCIP (2023) Solving constraint integer programs. https://www.scipopt.org/ . Accessed 21 February 2023 citation_journal_title=IEEE Trans Evol Comput; citation_title=A review on bilevel optimization: from classical to evolutionary approaches and applications; citation_author=A Sinha, P Malo, K Deb; citation_volume=22; citation_issue=2; citation_publication_date=2018; citation_pages=276-295; citation_doi=10.1109/TEVC.2017.2712906; citation_id=CR30 citation_journal_title=Eur J Oper Res; citation_title=A survey of network interdiction models and algorithms; citation_author=JC Smith, Y Song; citation_volume=283; citation_issue=3; citation_publication_date=2020; citation_pages=797-811; citation_doi=10.1016/j.ejor.2019.06.024; citation_id=CR31 citation_journal_title=J Glob Optim; citation_title=Bilevel and multilevel programming: a bibliography review; citation_author=LN Vicente, PH Calamai; citation_volume=5; citation_issue=3; citation_publication_date=1994; citation_pages=291-306; citation_doi=10.1007/BF01096458; citation_id=CR32 citation_journal_title=Eur J Oper Res; citation_title=Integer programming methods for solving binary interdiction games; citation_author=N Wei, JL Walteros; citation_volume=202; citation_issue=2; citation_publication_date=2022; citation_pages=456-469; citation_doi=10.1016/j.ejor.2022.01.009; citation_id=CR33