Branch-and-Bound for Biobjective Mixed-Integer Linear Programming

Published Online:https://doi.org/10.1287/ijoc.2021.1092

References

  • Achterberg T, Wunderling R (2013) Mixed integer programming: Analyzing 12 years of progress. Jünger M, Reinelt G, eds. Facets of Combinatorial Optimization (Springer, Berlin), 449–481.CrossrefGoogle Scholar
  • Achterberg T, Bixby RE, Gu Z, Rothberg E, Weninger D (2020) Presolve reductions in mixed integer programming. INFORMS J. Comput. 32(2):473–506.LinkGoogle Scholar
  • Adelgren N, Gupte A (2016) Branch-and-bound for biobjective mixed-integer linear programming. Preprint, first available at Optimization Online, http://www.optimization-online.org/DB_HTML/2016/10/5676.html.Google Scholar
  • Adelgren N, Belotti P, Gupte A (2018) Effecient storage of Pareto points in biobjective mixed integer programming. INFORMS J. Comput. 30(2):324–338.LinkGoogle Scholar
  • Bazgan C, Jamain F, Vanderpooten D (2013) On the number of non-dominated points of a multicriteria optimization problem. Discrete Appl. Math. 161(18):2841–2850.CrossrefGoogle Scholar
  • Bazgan C, Jamain F, Vanderpooten D (2015) Approximate Pareto sets of minimal size for multi-objective optimization problems. Oper. Res. Lett. 43(1):1–6.CrossrefGoogle Scholar
  • Bazgan C, Jamain F, Vanderpooten D (2017) Discrete representation of the non-dominated set for multi-objective optimization problems using kernels. Eur. J. Oper. Res. 260(3):814–827.CrossrefGoogle Scholar
  • Belotti P, Soylu B, Wiecek MM (2012) A branch-and-bound algorithm for biobjective mixed-integer programs. Preprint, December 2012 Optimization-Online, http://www.optimization-online.org/DB_HTML/2013/01/3719.html.Google Scholar
  • Belotti P, Soylu B, Wiecek MM (2016) Fathoming rules for biobjective mixed integer linear programs. Discrete Optim. 22:341–363.Google Scholar
  • Bérubé J-F, Gendreau M, Potvin J-Y (2009) An exact eps-constraint method for bi-objective combinatorial optimization problems: Application to the traveling salesman problem with profits. Eur. J. Oper. Res. 194(1):39–50.CrossrefGoogle Scholar
  • Blanco V, Puerto J (2012) A new complexity result on multiobjective linear integer programming using short rational generating functions. Optim. Lett. 6(3):537–543.CrossrefGoogle Scholar
  • Boland N, Charkhgard H, Savelsbergh M (2015) A criterion space search algorithm for biobjective integer programming. INFORMS J. Comput. 27(4):735–754.LinkGoogle Scholar
  • Boland N, Charkhgard H, Savelsbergh M (2016) The L-shape search method for triobjective integer programming. Math. Programming Comput. 8(2):217–251.CrossrefGoogle Scholar
  • Boland N, Charkhgard H, Savelsbergh M (2017) The Quadrant Shrinking method: A simple and efficient algorithm for solving tri-objective integer programs. Eur. J. Oper. Res. 260(3):873–885.CrossrefGoogle Scholar
  • Boland N, Charkhgard H, Savelsbergh M (2019) Preprocessing and cut generation techniques for multi-objective binary programming. Eur. J. Oper. Res. 274(3):858–875.CrossrefGoogle Scholar
  • Burachik RS, Kaya CY, Rizvi M (2017) A new scalarization technique and new algorithms to generate pareto fronts. SIAM J. Optim. 27(2):1010–1034.CrossrefGoogle Scholar
  • Cacchiani V, D’Ambrosio C (2017) A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs. Eur. J. Oper. Res. 260(3):920–933.CrossrefGoogle Scholar
  • Dächert K, Klamroth K (2015) A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems. J. Global Optim. 61(4):643–676.CrossrefGoogle Scholar
  • De Loera JA, Hemmecke R, Köppe M (2009) Pareto optima of multicriteria integer linear programs. INFORMS J. Comput. 21(1):39–48.LinkGoogle Scholar
  • De Santis M, Eichfelder G, Niebling J, Rocktäschel S (2020) Solving multiobjective mixed integer convex optimization problems. SIAM J. Optim. 30(4):3122–3145.CrossrefGoogle Scholar
  • Ehrgott M (2005) Multicriteria Optimization (Springer, Berlin).Google Scholar
  • Ehrgott M (2006) A discussion of scalarization techniques for multiple objective integer programming. Ann. Oper. Res. 147(1):343–360.CrossrefGoogle Scholar
  • Ehrgott M, Gandibleux X (2007) Bound sets for biobjective combinatorial optimization problems. Comput. Oper. Res. 34(9):2674–2694.CrossrefGoogle Scholar
  • Ehrgott M, Ruzika S (2008) Improved eps-constraint method for multiobjective programming. J. Optim. Theory Appl. 138(3):375–396.CrossrefGoogle Scholar
  • Fattahi A, Turkay M (2018) A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems. Eur. J. Oper. Res. 266(2):415–425.CrossrefGoogle Scholar
  • Forget N, Klamroth K, Gadegaard SL, Przybylski A, Nielsen LR (2020) Branch-and-bound and objective branching with three objectives. Preprint, December 2020 Optimization-Online, http://www.optimization-online.org/DB_HTML/2020/12/8158.html.Google Scholar
  • Gadegaard SL, Nielsen LR, Ehrgott M (2019) Bi-objective branch-and-cut algorithms based on lp relaxation and bound sets. INFORMS J. Comput. 31(4):790–804.LinkGoogle Scholar
  • Gamrath G, Koch T, Martin A, Miltenberger M, Weninger D (2015) Progress in presolving for mixed integer programming. Math. Programming Comput. 7(4):367–398.CrossrefGoogle Scholar
  • Gleixner A, Hendel G, Gamrath G, Achterberg T, Bastubbe M, Berthold T, Christophel PM, et al. (2021) MIPLIB 2017: Data-driven compilation of the 6th mixed-integer programming library. Math. Programming Comput. 13:443–490.Google Scholar
  • Grandoni F, Ravi R, Singh M, Zenklusen R (2014) New approaches to multi-objective optimization. Math. Programming 146(1–2):525–554.CrossrefGoogle Scholar
  • Hale JQ, Zhu H, Zhou E (2020) Domination measure: A new metric for solving multiobjective optimization. INFORMS J. Comput. 32(3):565–581.LinkGoogle Scholar
  • Herzel A, Ruzika S, Thielen C (2021) Approximation methods for multiobjective optimization problems. INFORMS J. Comput., ePub ahead of February 5, https://doi.org/10.1287/ijoc.2020.1028.LinkGoogle Scholar
  • Jozefowiez N, Laporte G, Semet F (2012) A generic branch-and-cut algorithm for multiobjective optimization problems: Application to the multilabel traveling salesman problem. INFORMS J. Comput. 24(4):554–564.LinkGoogle Scholar
  • Kirlik G, Sayin S (2014) A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems. Eur. J. Oper. Res. 232(3):479–488.CrossrefGoogle Scholar
  • Kiziltan G, Yucaoğlu E (1983) An algorithm for multiobjective zero-one linear programming. Management Sci. 29(12):1444–1453.LinkGoogle Scholar
  • Klein D, Hannan E (1982) An algorithm for the multiple objective integer linear programming problem. Eur. J. Oper. Res. 9(4):378–385.CrossrefGoogle Scholar
  • Lee J, Vygen J, eds. (2014) The triangle splitting method for biobjective mixed integer programming. Integer Programming Combinatorial Optim. (IPCO), Lecture Notes in Computer Science, vol. 8494 (Springer International Publishing, Berlin), 162–173.CrossrefGoogle Scholar
  • Leitner M, Ljubić I, Sinnl M (2014) A computational study of exact approaches for the bi-objective prize-collecting steiner tree problem. INFORMS J. Comput. 27(1):118–134.LinkGoogle Scholar
  • Leitner M, Ljubić I, Sinnl M, Werner A (2016) Ilp heuristics and a new exact method for bi-objective 0/1 ilps. Comput. Oper. Res. 72:128–146.CrossrefGoogle Scholar
  • Lokman B, Köksalan M (2013) Finding all nondominated points of multi-objective integer programs. J. Global Optim. 57:347–365.CrossrefGoogle Scholar
  • Mavrotas G, Florios K (2013) An improved version of the augmented ε-constraint method (AUG-MECON2) for finding the exact pareto set in multi-objective integer programming problems. Appl. Math. Comput. 219(18):9652–9669.CrossrefGoogle Scholar
  • Mittal S, Schulz AS (2013) A general framework for designing approximation schemes for combinatorial optimization problems with many objectives combined into one. Oper. Res. 61(2):386–397.LinkGoogle Scholar
  • Morrison DR, Jacobson SH, Sauppe JJ, Sewell EC (2016) Branch-and-bound algorithms: A survey of recent advances in searching, branching, and pruning. Discrete Optim. 19:79–102.CrossrefGoogle Scholar
  • Özpeynirci Ö, Köksalan M (2010) An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Management Sci. 56(12):2302–2315.LinkGoogle Scholar
  • Parragh SN, Tricoire F (2019) Branch-and-bound for bi-objective integer programming. INFORMS J. Comput. 31(4):805–822.LinkGoogle Scholar
  • Perini T, Boland N, Pecin D, Savelsbergh M (2020) A criterion space method for biobjective mixed integer programming: The boxed line method. INFORMS J. Comput. 32(1):16–39.LinkGoogle Scholar
  • Pettersson W, Ozlen M (2020) Multiobjective integer programming: Synergistic parallel approaches. INFORMS J. Comput. 32(2):461–472.AbstractGoogle Scholar
  • Przybylski A, Gandibleux X (2017) Multi-objective branch and bound. Eur. J. Oper. Res. 260(3):856–872.CrossrefGoogle Scholar
  • Przybylski A, Gandibleux X, Ehrgott M (2010) A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optim. 7(3):149–165.CrossrefGoogle Scholar
  • Ralphs TK, Saltzman MJ, Wiecek MM (2006) An improved algorithm for solving biobjective integer programs. Ann. Oper. Res. 147(1):43–70.CrossrefGoogle Scholar
  • Rasmi SAB, Türkay M (2019) GoNDEF: An exact method to generate all non-dominated points of multi-objective mixed-integer linear programs. Optim. Engrg. 20(1):89–117.CrossrefGoogle Scholar
  • Royset JO, Wood RK (2007) Solving the bi-objective maximum-flow network-interdiction problem. INFORMS J. Comput. 19(2):175–184.LinkGoogle Scholar
  • Ruzika S, Wiecek MM (2005) Approximation methods in multiobjective programming. J. Optim. Theory Appl. 126(3):473–501.CrossrefGoogle Scholar
  • Sayin S (2000) Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Math. Programming 87(3):543–560.CrossrefGoogle Scholar
  • Sayin S (2003) A procedure to find discrete representations of the efficient set with specified coverage errors. Oper. Res. 51(3):427–436.LinkGoogle Scholar
  • Sourd F, Spanjaard O (2008) A multiobjective branch-and-bound framework: Application to the biobjective spanning tree problem. INFORMS J. Comput. 20(3):472–484.LinkGoogle Scholar
  • Soylu B (2015) Heuristic approaches for biobjective mixed 0–1 integer linear programming problems. Eur. J. Oper. Res. 245(3):690–703.CrossrefGoogle Scholar
  • Soylu B (2018) The search-and-remove algorithm for biobjective mixed-integer linear programming problems. Eur. J. Oper. Res. 268(1):281–299.CrossrefGoogle Scholar
  • Soylu B, Yildiz GB (2016) An exact algorithm for biobjective mixed integer linear programming problems. Comput. Oper. Res. 72:204–213.CrossrefGoogle Scholar
  • Stanojević M, Vujošević M, Stanojević B (2013) On the cardinality of the nondominated set of multi-objective combinatorial optimization problems. Oper. Res. Lett. 41(2):197–200.CrossrefGoogle Scholar
  • Stidsen T, Andersen KA, Dammann B (2014) A branch and bound algorithm for a class of biobjective mixed integer programs. Management Sci. 60(4):1009–1032.LinkGoogle Scholar
  • Tamby S, Vanderpooten D (2021) Enumeration of the nondominated set of multiobjective discrete optimization problems. INFORMS J. Comput. 33(1):72–85.LinkGoogle Scholar
  • Towns J, Cockerill T, Dahan M, Foster I, Gaither K, Grimshaw A, Hazlewood V, et al. (2014) XSEDE: Accelerating scientific discovery. Comput. Sci. Engrg. 16(5):62–74.CrossrefGoogle Scholar
  • Turgut O, Dalkiran E, Murat AE (2019) An exact parallel objective space decomposition algorithm for solving multi-objective integer programming problems. J. Global Optim. 75(1):35–62.CrossrefGoogle Scholar
  • Vincent T, Seipp F, Ruzika S, Przybylski A, Gandibleux X (2013) Multiple objective branch and bound for mixed 0-1 linear programming. Comput. Oper. Res. 40(1):498–509.CrossrefGoogle Scholar
  • Visée M, Teghem J, Pirlot M, Ulungu E (1998) Two-phases method and branch and bound procedures to solve the biobjective knapsack problem. J. Global Optim. 12:139–155.Google Scholar
  • Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: An analysis and review. IEEE Trans. Evolution Comput. 7(2):117–132.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.