MultiObjectiveAlgorithms.jl: A Julia Package for Solving Multiobjective Optimization Problems

Published Online:https://doi.org/10.1287/ijoc.2025.1449

References

  • AMPL Optimization Inc. (2025) Multiple objective. Accessed June 21, 2025, https://mp.ampl.com/modeling-mo.html.Google Scholar
  • Aneja Y, Nair K (1979) Bicriteria transportation problem. Management Sci. 25(1):73–78.LinkGoogle Scholar
  • Benson H (1998) An outer approximation algorithm for generating all effcient extreme points in the outcome set of a multiple objective linear programming problem. J. Global Optim. 13:1–24.CrossrefGoogle Scholar
  • Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: A fresh approach to numerical computing. SIAM Rev. 59(1):65–98.CrossrefGoogle Scholar
  • Bökler F, Mutzel P (2015) Output-sensitive algorithms for enumerating the extreme nondominated points of multiobjective combinatorial optimization problems. Bansal N, Finocchi I, eds. Algorithms–ESA 2015 (Springer, Berlin, Heidelberg), 288–299.CrossrefGoogle Scholar
  • Bökler F, Nemesch L, Wagner MH (2023) PaMILO: A solver for multi-objective mixed integer linear optimization and beyond. Grothe O, Nickel S, Rebennack S, Stein O, eds. Oper. Res. Proc. 2022, Lecture Notes in Operations Research (Springer, Cham). Google Scholar
  • Borndörfer R, Schenker S, Kutella M, Strunk T (2016) PolySCIP. Greuel G-M, Koch T, Paule P, Sommese AJ, eds. Math. Software—ICMS 2016, Lecture Notes in Computer Science, vol. 9725 (Springer, Cham, Switzerland), 228–234.Google Scholar
  • Bynum ML, Hackebeil GA, Hart WE, Laird CD, Nicholson BL, Siirola JD, Watson JP, Woodruff DL (2021) Pyomo–Optimization Modeling in Python, vol. 67, 3rd ed. (Springer Science & Business Media, Cham, Switzerland).CrossrefGoogle Scholar
  • Chalmet L, Lemonidis L, Elzinga D (1986) An algorithm for the bi-criterion integer programming problem. Eur. J. Oper. Res. 25(2):292–300.CrossrefGoogle Scholar
  • Csirmaz L (2021) Inner approximation algorithm for solving linear multiobjective optimization problems. Optimization 70(7):1487–1511.CrossrefGoogle Scholar
  • Diamond S, Boyd S (2016) CVXPY: A Python-embedded modeling language for convex optimization. J. Machine Learn. Res. 17(1):2909–2913.Google Scholar
  • Dominguez-Rios M, Chicano F, Alba E (2021) Effective anytime algorithm for multiobjective combinatorial optimization problems. Inform. Sci. 565(7):210–228.CrossrefGoogle Scholar
  • Dowson O, Gandibleux X, Kof G (2026) MultiObjectiveAlgorithms.jl: A Julia package for solving multi-objective optimization problems. https://doi.org/10.1287/ijoc.2025.1449.cd, https://github.com/INFORMSJoC/2025.1449.Google Scholar
  • Ehrgott M (2005) Multicriteria Optimization, 2nd ed. (Springer, Berlin).Google Scholar
  • Ehrgott M, Gandibleux X (2000) A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22(4):425–460.CrossrefGoogle Scholar
  • Ehrgott M, Köksalan M, Kadziński M, Deb K (2026) Fifty years of multi-objective optimization and decision-making: From mathematical programming to evolutionary computation. Eur. J. Oper. Res. 330(1):1–25.CrossrefGoogle Scholar
  • Emmerich M, Deutz A (2018) A tutorial on multiobjective optimization: Fundamentals and evolutionary methods. Natural Comput. 17(3):585–609.CrossrefGoogle Scholar
  • GAMS Software GmbH (2025) Multi-objective optimization. Accessed May 21, 2025, https://www.gams.com/50/docs/T_LIBINCLUDE_MOO.html.Google Scholar
  • Gandibleux X, Soleilhac G, Przybylski A, Ruzika S (2017) vOptSolver: An open source software environment for multiobjective mathematical optimization. IFORS2017: 21st Conf. Internat. Federation Oper. Res. Societies (International Federation of Operational Research Societies, Quebec).Google Scholar
  • Gurobi Optimization, LLC (2025a) Gurobi optimizer. Accessed May 21, 2025, https://www.gurobi.com.Google Scholar
  • Gurobi Optimization, LLC (2025b) Multiple objectives. Accessed May 21, 2025, https://docs.gurobi.com/projects/optimizer/en/current/features/multiobjective.html.Google Scholar
  • Haimes Y, Lisdon L, Wismer D (1971) On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Systems Man Cybernetics 3:296–297.Google Scholar
  • Huangfu Q, Hall JAJ (2018) Parallelizing the dual revised simplex method. Math. Programming Comput. 10(1):119–142.CrossrefGoogle Scholar
  • Isermann H (1982) Linear lexicographic optimization. OR Spectrum 4(4):223–228.CrossrefGoogle Scholar
  • Kirlik G, Sayın 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
  • Koenen M, Balvert M, Fleuren H (2023) A renewed take on weighted sum in sandwich algorithms: Modification of the criterion space. Technical report, Center for Economic Research, Tilburg, Netherlands.Google Scholar
  • Legat B, Dowson O, Dias Garcia J, Lubin M (2021) MathOptInterface: A data structure for mathematical optimization problems. INFORMS J. Comput. 34(2):672–689.LinkGoogle Scholar
  • Lubin M, Dowson O, Garcia JD, Huchette J, Legat B, Vielma JP (2023) JuMP 1.0: Recent improvements to a modeling language for mathematical optimization. Math. Programming Comput. 15(3):581–589.CrossrefGoogle Scholar
  • Löhne A, Weiβing B (2017) The vector linear program solver bensolve—Notes on theoretical background. Eur. J. Oper. Res. 260(3):807–813.CrossrefGoogle Scholar
  • MATLAB (2025) paretosearch—Find points in pareto set. Accessed June 29, 2025, https://au.mathworks.com/help/gads/paretosearch.html.Google Scholar
  • Salomon L, Dörfler D, Löhne A (2025) MOCVXPY: A CVXPY extension for multiobjective optimization. Preprint, submitted October 23, https://arxiv.org/abs/2510.21010.Google 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
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