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Experiments in quadratic 0–1 programming

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Abstract

We present computational experience with a cutting plane algorithm for 0–1 quadratic programming without constraints. Our approach is based on a reduction of this problem to a max-cut problem in a graph and on a partial linear description of the cut polytope.

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References

  • E. Balas and J.B. Mazzola (1984), “Nonlinear 0–1 programming: I. Linearization techniques and II. Dominance relations and algorithms,”Mathematical Programming 30 (1984) 1–45.

    Google Scholar 

  • F. Barahona (1986), “A solvable case of quadratic 0–1 programming,”Discrete Applied Mathematics 13 (1986) 23–26.

    Google Scholar 

  • F. Barahona and A. Casari (1988), “On the magnetization of the ground states in two-dimensional Ising spin glasses,”Computer Physics Communications 49 (1988) 417–421.

    Google Scholar 

  • F. Barahona, M. Grötschel, M. Jünger and G. Reinelt (1988), “An application of combinatorial optimization to statistical physics and circuit layout design,”Operations Research 36 (1988) 493–513.

    Google Scholar 

  • F. Barahona and A.R. Mahjoub (1986), “On the cut polytope,”Mathematical Programming 36(1) (1986) 157–173.

    Google Scholar 

  • M.W. Carter (1984), “The indefinite zero-one quadratic problem,”Discrete Applied Mathematics 7 (1984) 23–44.

    Google Scholar 

  • M.R. Garey and D.S. Johnson (1979),Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).

    Google Scholar 

  • M. Grötschel, M. Jünger and G. Reinelt (1984), “A cutting plane algorithm for the linear ordering problem,”Operations Research 32 (1984) 1195–1220.

    Google Scholar 

  • P.L. Hammer (1965), “Some network flow problems solved with pseudo-Boolean programming,”Operations Research 13 (1965) 388–399.

    Google Scholar 

  • P.L. Hammer, P. Hansen and P. Simeone (1984), “Roof duality, complementation and persistence in quadratic 0–1 optimization,”Mathematical Programming 28 (1984) 121–155.

    Google Scholar 

  • M.W. Padberg and G. Rinaldi (1986), “Optimization of a 532-city symmetric travelling salesman problem by branch and cut,”Operations Research Letters 6 (1987) 1–7.

    Google Scholar 

  • J.C. Picard and H.D. Ratliff (1974), “Minimum cuts and related problems,”Networks 5 (1974) 357–370.

    Google Scholar 

  • A.C. Williams (1985), “Quadratic 0–1 programming using the roof dual with computational results,” RUTCOR Research Report #8-85, The State University of New Jersey (New Brunswick, NJ, 1985).

    Google Scholar 

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This research has been partially supported by Schwerpunktprogramm der Deutschen Forschungs-gemeinschaft “Anwendungsbezogene Optimierung und Steuerung”. Part of the work of the first author was done at the Institut für Operations Research, Universität Bonn, and it was supported by the National Sciences Research Council of Canada and the Deutsche Forschungsgemeinschaft.

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Barahona, F., Jünger, M. & Reinelt, G. Experiments in quadratic 0–1 programming. Mathematical Programming 44, 127–137 (1989). https://doi.org/10.1007/BF01587084

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  • DOI: https://doi.org/10.1007/BF01587084

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