Finding the Nondominated Set and Efficient Integer Vectors for a Class of Three-Objective Mixed-Integer Linear Programs

References

• Alves MJ, Costa JP (2016) Graphical exploration of the weight space in three-objective mixed integer linear programs. Eur. J. Oper. Res. 248(1):72–83.Crossref, Google Scholar
• Aneja YP, Nair KP (1979) Bicriteria transportation problem. Management Sci. 25(1):73–78.Link, Google Scholar
• Boland N, Charkhgard H, Savelsbergh M (2015) A criterion space search algorithm for biobjective mixed integer programming: The triangle splitting method. INFORMS J. Comput. 27(4):597–618.Link, Google Scholar
• Ceyhan G (2020a) Solver for a class of multi-objective mixed integer linear programs (MOMILPs). Accessed May 16, 2022, https://github.com/gokhanceyhan/momilp.git.Google Scholar
• Ceyhan G (2020b) A study of the day-ahead energy market auctions from a multi-objective perspective. PhD thesis, Department of Industrial Engineering, Middle East Technical University, Ankara, Turkey.Google Scholar
• Ceyhan G, Köksalan M, Lokman B (2019) Finding a representative nondominated set for multi-objective mixed integer programs. Eur. J. Oper. Res. 272(1):61–77.Crossref, Google 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.Crossref, Google Scholar
• Dächert K, Klamroth K, Lacour R, Vanderpooten D (2017) Efficient computation of the search region in multi-objective optimization. Eur. J. Oper. Res. 260(3):841–855.Crossref, Google Scholar
• Daskin MS, Maass KL (2015) The p-median problem. Laporte G, Nickel S, Saldanha da Gama F, eds. Location Science (Springer, Cham, Switzerland), 21–45.Crossref, Google Scholar
• Derinkuyu K, Tanrisever F, Kurt N, Ceyhan G (2019) Optimizing day-ahead electricity market prices: Increasing the total surplus for energy exchange Istanbul. Manufacturing Service Oper. Management 22(4):700–716.Link, Google Scholar
• Euphemia (2019) Euphemia Public Description. Accessed May 16, 2022, https://www.nemo-committee.eu/assets/files/euphemia-public-description.pdf.Google 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.Crossref, Google Scholar
• Fischetti M, Glover F, Lodi A (2005) The feasibility pump. Math. Programming 104(1):91–104.Crossref, Google Scholar
• Görmez N, Köksalan M, Salman FS (2011) Locating disaster response facilities in istanbul. J. Oper. Res. Soc. 62(7):1239–1252.Crossref, Google Scholar
• Hooker J (2011) Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction (John Wiley & Sons, New York).Google Scholar
• Kalita Z, Datta D (2017) Multi-objective optimization of the multi-floor facility layout problem. Agarwal PK, Gupta M, eds. Proc. 2017 Internat. Conf. Adv. Mech. Indust. Automation Management Systems (AMIAMS) (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 64–68.Google 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.Crossref, Google Scholar
• Lokman B, Köksalan M (2013) Finding all nondominated points of multi-objective integer programs. J. Global Optim. 57(2):347–365.Crossref, Google Scholar
• Masin M, Bukchin Y (2008) Diversity maximization approach for multiobjective optimization. Oper. Res. 56(2):411–424.Link, Google Scholar
• Naccache P (1978) Connectedness of the set of nondominated outcomes in multicriteria optimization. J. Optim. Theory Appl. 25(3):459–467.Crossref, Google Scholar
• O’Neill RP, Sotkiewicz PM, Hobbs BF, Rothkopf MH, Stewart WR Jr (2005) Efficient market-clearing prices in markets with nonconvexities. Eur. J. Oper. Res. 164(1):269–285.Crossref, Google 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.Link, Google 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.Crossref, Google Scholar
• Soylu B (2018) The search-and-remove algorithm for biobjective mixed-integer linear programming problems. Eur. J. Oper. Res. 268(1):281–299.Crossref, Google 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.Link, Google Scholar
• Wiecek MM, Ehrgott M, Engau A (2016) Continuous multiobjective programming. Greco S, Ehrgott M, Figueira J, eds. Multiple Criteria Decision Analysis (Springer, New York), 739–815.Crossref, 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.Crossref, Google Scholar