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An algorithm for mixed integer optimization

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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.

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References

  1. 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)

    Google Scholar 

  2. Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0–1 programs. Mathematical Programming 58, 295–324 (1993)

    Google Scholar 

  3. Bertsimas, D., Weismantel, R.: Optimization over integers. Book in preparation, 2002

  4. 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

  5. Gomory, R.E.: An algorithm for the mixed integer problem. Technical Report RM-2597-PR, The RAND Corporation, Santa Monica, CA, 1960

  6. 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

  7. Haus, U.-U., Köppe, M., Weismantel, R.: The integral basis method for integer programming. Mathematical Methods of Operations Research 53(3), 353–361 (2001a)

  8. 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

  9. 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)

    Google Scholar 

  10. 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

  11. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Chichester, 1988

  12. Young, R.D.: A simplified primal (all-integer) integer programming algorithm. Operations Research 16(4), 750–782 (1968)

    Google Scholar 

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Correspondence to Robert Weismantel.

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

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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

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  • DOI: https://doi.org/10.1007/s10107-003-0405-7

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