A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method

References

• Adelgren N, Belotti P, Gupte A (2014) Efficient storage of Pareto points in biobjective mixed integer programming. CoRR, ePub ahead of print November 24, http://arxiv.org/abs/1411.6538.Google Scholar
• Aneja YP, Nair KPK (1979) Bicriteria transportation problem. Management Sci. 27:73–78.Link, Google Scholar
• Benson HP, Sun E (2002) A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program. Eur. J. Oper. Res. 139:26–41.Crossref, Google Scholar
• Boland N, Charkhgard H, Savelsbergh M (2014) The triangle splitting method for biobjective mixed integer programming. Lee J, Vygen J, eds. Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, Vol. 8494 (Springer International Publishing, Switzerland), 162–173.Crossref, Google Scholar
• Bowman VJ (1976) On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. Thieriez H, Zionts S, eds. Multiple Criteria Decision Making (Springer Verlag, Berlin), 76–85.Crossref, Google Scholar
• Chalmet L, Lemonidis L, Elzinga D (1986) An algorithm for the bi-criterion integer programming problem. Eur. J. Oper. Res. 25:292–300.Crossref, Google Scholar
• Chankong V, Haimes YY (1983) Multiobjective Decision Making Theory and Methodology (Elsevier Science, New York).Google Scholar
• Dächert K, Gorski J, Klamroth K (2012) An augmented weighted Tchebycheff method with adaptively chosen parameters for discrete bicriteria optimization problems. Comput. Oper. Res. 39:2929–2943.Crossref, Google Scholar
• Dolan ED, Moré JJ (2002) Benchmarking optimization software with performance profiles. Math. Programming 91:201–213.Crossref, Google Scholar
• Ehrgott M (2006) A discussion of scalarization technique for multiple objective integer programming. Ann. Oper. Res. 147:343–360.Crossref, Google Scholar
• Evans JP, Steuer RE (1973) A revised simplex method for linear multiple objective programs. Math. Programming 5:54–72.Crossref, Google Scholar
• Hamacher HW, Pedersen CR, Ruzika S (2007) Finding representative systems for discrete bicriterion optimization problems. Oper. Res. Lett. 35:336–344.Crossref, Google Scholar
• Isermann H (1977) The enumeration of the set of all efficient solutions for a linear multiple objective program. Oper. Res. Quart. 28:711–725.Crossref, Google 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. 24:554–564.Link, Google Scholar
• Kirlik G, Sayın S (2014) A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems. Eur. J. Oper. Res. 232:479–488.Crossref, Google Scholar
• Laumanns M, Thiele L, Zitzler E (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. Eur. J. Oper. Res. 169:932–942.Crossref, Google Scholar
• Lokman B, Köksalan M (2013) Finding all nondominated points of multi-objective integer programs. J. Global Optim. 57:347–365.Crossref, Google Scholar
• Lust T, Teghem J (2012) The multiobjective multidimensional knapsack problem: A survey and a new approach. Internat. Trans. Oper. Res. 19:495–520.Crossref, Google Scholar
• Mavrotas G, Figueira JR (2011) Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems. J. Global Optim. 49:589–606.Crossref, Google Scholar
• Özlen M, Azizoğlu M (2009) Multi-objective integer programming: A general approach for generating all non-dominated solutions. Eur. J. Oper. Res. 199:25–35.Crossref, Google Scholar
• Özlen M, Burton BA, MacRae CAG (2014) Multi-objective integer programming: An improved recursive algorithm. J. Optim. Theory Appl. 160:470–482.Crossref, Google Scholar
• Przybylski A, Gandibleux X, Ehrgott M (2008) Two phase algorithms for the bi-objective assignment problem. Eur. J. Oper. Res. 185:509–533.Crossref, Google Scholar
• Ralphs TK, Saltzman MJ, Wiecek MM (2006) An improved algorithm for solving biobjective integer programs. Ann. Oper. Res. 147:43–70.Crossref, Google Scholar
• Sourd F, Spanjaard O (2008) A multiobjective branch-and-bound framework: Application to the biobjective spanning tree problem. INFORMS J. Comput. 20:472–484.Link, Google Scholar
• Steuer RE, Choo E (1983) An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Programming 26:326–344.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. 60:1009–1032.Link, Google Scholar
• Sylva J, Crema A (2004) A method for finding the set of non-dominated vectors for multiple objective integer linear programs. Eur. J. Oper. Res. 158:46–55.Crossref, Google Scholar
• Sylva J, Crema A (2007) A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs. Eur. J. Oper. Res. 180:1011–1027.Crossref, Google Scholar
• Tuyttens D, Teghem J, Fortemps P, Van Nieuwenhuyze K (2000) Performance of the MOSA method for the bicriteria assignment problem. J. Heuristics 6:295–310.Crossref, Google Scholar
• Yu PL, Zeleny M (1975) The set of all nondominated solutions in linear cases and a multicriteria simplex method. J. Math. Anal. Appl. 49:430–468.Crossref, Google Scholar
• Zitzler E, Thiele L (May 1998) An evolutionary algorithm for multiobjective optimization: The strength Pareto approach. Technical Report 43, Computer Engineering and Communication Networks Lab, Swiss Federal Institute of Technology, Zurich.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. Evolutionary Comput. 7:117–132.Crossref, Google Scholar