Pareto optima of multicriteria integer linear programs

INFORMS Journal on Computing

Volumn 21, Issue 1, 2009, Pages 39-48

  De Loera, Jesús A ^a   Hemmecke, Raymond ^b   Köppe, Matthias ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Analysis of algorithms; Combinatorics; Computational complexity; Integer programming; Mathematics; Multicriteria programming

Indexed keywords

EID: 67649992783     PISSN: 10919856     EISSN: 15265528     Source Type: Journal    
DOI: 10.1287/ijoc.1080.0277     Document Type: Article

References (15)

1. Barvinok, A. I. 1994. Polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Math. Oper. Res. 19 769-779.
2. Barvinok, A. I., J. E. Pommersheim. 1999. An algorithmic theory of lattice points in polyhedra. L. J. Billera, A. Björner, C. Greene, R. E. Simion, R. P. Stanley, eds. New Perspectives in Algebraic Combinatorics, Mathematical Sciences Research Institute Publications, Vol. 38. Cambridge University Press, Cambridge, UK, 91-147.
3. Barvinok, A. I., K. Woods. 2003. Short rational generating functions for lattice point problems. J. Amer. Math. Soc. 16 957-979.
4. Blanco, V. 2007. Personal communication, September 3.
5. De Loera, J. A., R. Hemmecke, M. Köppe, R. Weismantel. 2006. Integer polynomial optimization in fixed dimension. Math. Oper. Res. 31 147-153.
6. De Loera, J. A., D. Haws, R. Hemmecke, P. Huggins, B. Sturmfels, R. Yoshida. 2004. Short rational functions for toric algebra and applications. J. Symbolic Comput. 38 959-973.
7. Ehrgott, M., X. Gandibleux. 2000. A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum22 425-460.
8. Emelichev, V. A., V. A. Perepelitsa. 1992. On the cardinality of the set of alternatives in discrete many-criterion problems. Discrete Math. Appl. 2 461-471.
9. Figueira, J., S. Greco, M. Ehrgott, eds. 2005. Multiple Criteria Decision Analysis. State of the Art Surveys. Springer, New York.
10. Isermann, H. 1974. Proper efficiency and the linear vector maximum problem. Oper. Res. 22 189-191.
11. Johnson, D. S., M. Yannakakis, C. H. Papadimitriou. 1988. On generating all maximal independent sets. Inform. Processing Lett. 27119-123.
12. Mora, T., L. Robbiano. 1988. The Gröbner fan of an ideal. J. Symbolic Comput. 6 183-208.
13. Sawaragi, Y., H. Nakayama, T. Tanino, eds. 1985. Theory of Multiobjective Optimization. Academic Press, Orlando, FL.
14. Sergienko, I. V., V. A. Perepelitsa. 1991. Finding the set of alternatives in discrete multi-criterion problems. Cybernetics 3673-683.
15. Woods, K. 2004. Rational generating functions and lattice point sets. Ph.D. thesis, University of Michigan, Ann Arbor.