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.
Key wordsCutting plane algorithm polytopes facets quadratic 0–1 programming
Unable to display preview. Download preview PDF.
- 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