Abstract
We present the first criterion space search algorithm, the triangle splitting method, for finding the efficient frontier of a biobjective mixed integer program. The algorithm is relatively easy to implement and converges quickly to the complete set of nondominated points. A computational study demonstrates the efficacy of the triangle splitting method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aneja, Y.P., Nair, K.P.K.: Bicriteria transportation problem. Management Science 27, 73–78 (1979)
Belotti, P., Soylu, B., Wiecek, M.M.: A branch-and-bound algorithm for biobjective mixed-integer programs, http://www.optimization-online.org/DB_HTML/2013/01/3719.html
Benson, H.P., Sun, E.: A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of multiple objective linear program. European Journal of Operational Research 139, 26–41 (2002)
Gardenghi, M., Gómez, T., Miguel, F., Wiecek, M.M.: Algebra of efficient sets for multiobjective complex systems. Journal of Optimization Theory and Applications 149, 385–410 (2011)
Isermann, H.: The enumeration of the set of all efficient solutions for a linear multiple objective program. Operational Research Quarterly 28(3), 711–725 (1977)
Mavrotas, G., Diakoulaki, D.: A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research 107, 530–541 (1998)
Mavrotas, G., Diakoulaki, D.: Multi-criteria branch and bound: A vector maximization algorithm for mixed 0-1 multiple objective linear programming. Applied Mathematics and Computation 171, 53–71 (2005)
Vincent, T., Seipp, F., Ruzika, S., Przybylski, A., Gandibleux, X.: Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for biobjective case. Computers & Operations Research 40(1), 498–509 (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Boland, N., Charkhgard, H., Savelsbergh, M. (2014). The Triangle Splitting Method for Biobjective Mixed Integer Programming. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-07557-0_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07556-3
Online ISBN: 978-3-319-07557-0
eBook Packages: Computer ScienceComputer Science (R0)