Abstract.
This paper introduces a new algorithm for solving mixed integer programs. The core of the method is an iterative technique for changing the representation of the original mixed integer optimization problem.
Similar content being viewed by others
References
Aardal, K., Hurkens, C.A.J., Lenstra, A.K.: Solving a system of diophantine equations with lower and upper bounds on the variables. Mathematics of Operations Research 25, 427–442 (2000)
Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0–1 programs. Mathematical Programming 58, 295–324 (1993)
Bertsimas, D., Weismantel, R.: Optimization over integers. Book in preparation, 2002
Gentile, C., Haus, U.-U., Köppe, M., Rinaldi, G., Weismantel, R.: On the way to perfection: A new combinatorial algorithm for stable sets in graphs. To appear in M. Grötschel, editor, The Sharpest Cut, Festschrift in honor of Manfred Padberg, MPS/SIAM, preprint available from URL http://www.math.uni-magdeburg.de/~mkoeppe/art/primstab.ps, 2002
Gomory, R.E.: An algorithm for the mixed integer problem. Technical Report RM-2597-PR, The RAND Corporation, Santa Monica, CA, 1960
Gomory, R.E.: An all-integer integer programming algorithm. In: Muth, J.F., Thompson, G.L. (eds), Industrial Scheduling: (Papers presented at a Conference on ``Factory Scheduling'' held at the Graduate School of Industrial Administration at Carnegie Institute of Technology, May 10–12, 1961), Prentice-Hall international series in management, p. 193–206. Prentice Hall, Englewood Cliffs, N.J., 1963
Haus, U.-U., Köppe, M., Weismantel, R.: The integral basis method for integer programming. Mathematical Methods of Operations Research 53(3), 353–361 (2001a)
Haus, U.-U., Köppe, M., Weismantel, R.: A primal all-integer algorithm based on irreducible solutions. To appear in Mathematical Programming Series~B, preprint available from URL http://www.math.uni-magdeburg.de/~mkoe ppe/art/haus-koeppe-weismantel-ibm-theory-rr.ps,~2001b
Henk, M., Köppe, M., Weismantel, R.: Integral decomposition of polyhedra and some applications in mixed integer programming. Mathematical Programming, Series B 94(2–3), 193–206 (2003)
Köppe, M.: Exact Primal Algorithms for General Integer and Mixed-Integer Linear Programs. Dissertation, Otto-von-Guericke-Universität Magdeburg, 2002. Published by Shaker Verlag, Aachen 2003
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Chichester, 1988
Young, R.D.: A simplified primal (all-integer) integer programming algorithm. Operations Research 16(4), 750–782 (1968)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C11
Rights and permissions
About this article
Cite this article
Köppe, M., Weismantel, R. An algorithm for mixed integer optimization. Math. Program., Ser. B 98, 281–307 (2003). https://doi.org/10.1007/s10107-003-0405-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10107-003-0405-7