A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO)

Discrete Optimization

Volumn 5, Issue 2, 2008, Pages 501-529

  Boros, Endre ^a   Hammer, Peter L ^a   Sun, Richard ^b   Tavares, Gabriel ^a  

^a RUTGERS UNIVERSITY   (United States)

^b NOKIA RESEARCH CENTER   (United States)

Author keywords

Network flows; Persistency; Quadratic unconstrained binary optimization; Roof duality

Indexed keywords

BOOLEAN FUNCTIONS; CONSTRAINT THEORY; GRAPH THEORY; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

NETWORK FLOWS; PERSISTENCY; QUADRATIC UNCONSTRAINED BINARY OPTIMIZATION; ROOF DUALITY;

QUADRATIC PROGRAMMING;

EID: 41149100684     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2007.02.001     Document Type: Article

References (44)

1. Adams W.P., and Dearing P.M. On the equivalence between roof duality and lagrangian duality for unconstrained 0-1 quadratic programming. Discrete Applied Mathematics 48 (1994) 1-20
2. Aspvall B., Plass M.F., and Tarjan R.E. A linear time algorithm for testing the truth of certain quantified boolean formulas. Information Processing Letters 8 (1979) 121-123
3. 5. Operations Research Letters 2 (1983) 107-111
4. J.E. Beasley, Heuristic algorithms for the unconstrained binary quadratic programming problem, Tech. Rep., Management School, Imperial College, London, UK, 1998
5. Benson S.J., Ye Y., and Zhang X. Solving large-scale sparse semidefinite programs for combinatorial optimization. SIAM Journal on Optimization 10 2 (2000) 443-461
6. Billionnet A., and Sutter A. Persistency in quadratic 0-1 optimization. Mathematical Programming, Series B 54 1 (1992) 115-119
7. Bonami P., and Minoux M. Exact max-2sat solution via lift-and-project closure. Operations Research Letters 34 (2006) 387-393
8. Boros E., Crama Y., and Hammer P.L. Upper-bounds for quadratic 0-1 maximization. Operations Research Letters 9 (1990) 73-79
9. Boros E., Crama Y., and Hammer P.L. Chvátal cuts and odd cycle inequalities in quadratic 0-1 optimization. SIAM Journal on Discrete Mathematics 5 2 (1992) 163-177
10. E. Boros, P.L. Hammer, A max-flow approach to improved roof-duality in quadratic 0-1 minimization, Research Report RRR 15-1989, RUTCOR, Rutgers University, 1989
11. Boros E., and Hammer P.L. The max-cut problem and quadratic 0-1 optimization, polyhedral aspects, relaxations and bounds. Annals of Operations Research 33 (1991) 151-180
12. Boros E., and Hammer P.L. Pseudo-boolean optimization. Discrete Applied Mathematics 123 (2002) 155-225
13. E. Boros, P.L. Hammer, G. Tavares, Preprocessing of unconstrained quadratic binary optimization, Research Report RRR 10-2006, RUTCOR, Rutgers University, 2006
14. J.M. Bourjolly, Integral and fractional node-packings, and pseudo-boolean programs, Ph.D. Thesis, University of Waterloo, 1986
15. Bourjolly J.M., Hammer P.L., Pulleyblank W.R., and Simeone B. Boolean-combinatorial bounding of maximum 2-satisfiability. Computer Science and Operations Research, Williamsburg, VA 1992 (1999), Pergamon, Oxford 23-42
16. S. Burer, R.D.C. Monteiro, A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization 95 (2) (2003) 329-357
17. Burer S., Monteiro R.D.C., and Zhang Y. Rank-two relaxation heuristics for max-cut and other binary quadratic programs. SIAM Journal on Optimization 12 2 (2001) 503-521
18. Cornuéjols G., and Li Y. Elementary closures for integer programs. Operations Research Letters 28 (2001) 1-8
19. Fujisawa K., Fukuda M., Kojima M., and Nakata K. Numerical evaluation of the sdpa (semidefinite programming algorithm). In: Frenk H., Roos K., Terlaky T., and Zhang S. (Eds). High Performance Optimization (2000), Kluwer Academic Press 267-301
20. Glover F., Alidaee B., Rego C., and Kochenberger G. One-pass heuristics for large-scale unconstrained binary quadratic problems. European Journal of Operational Research 137 2 (2002) 272-287
21. Glover F., Kochenberger G., and Alidaee B. Adaptative memory tabu search for binary quadratic programs. Management Science 44 3 (1998) 336-345
22. Goemans M.X., and Williamson D.P. Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the ACM 42 (1995) 1115-1145
23. Hammer P.L. Pseudo-boolean remarks on balanced graphs. International Series of Numerical Mathematics 36 (1977) 69-78
24. Hammer P.L., Hansen P., and Simeone B. Roof duality, complementation and persistency in quadratic 0-1 optimization. Mathematical Programming 28 (1984) 121-155
25. Hammer P.L., and Kalantari B. A bound on the roof duality gap. Combinatorial Optimization, Lecture Notes in Mathematics 1403 (1989) 254-257
26. Hansen P. Methods of nonlinear 0-1 programming. Annals of Discrete Mathematics 5 (1979) 53-70
27. Hansen P., Lu S.H., and Simeone B. On the equivalence of paved-duality and standard linearization in nonlinear optimization. Discrete Applied Mathematics 29 (1990) 187-193
28. Harary F. On the notion of balance of a signed graph. The Michigan Mathematical Journal 2 (1953-54) 143-146
29. Helmberg C. Numerical evaluation of sbmethod. Mathematical Programming 95 2 (2003) 381-406
30. Helmberg C., and Kiwiel K.C. A spectral bundle method with bounds. Mathematical Programming 93 (2002) 173-194
31. Helmberg C., and Rendl F. A spectral bundle method for semidefinite programming. SIAM Journal on Optimization 10 3 (2000) 673-696
32. Homer S., and Peinado M. Design and performance of parallel and distributed approximation algorithms for maxcut. Journal of Parallel and Distributed Computing 46 (1997) 48-61
33. D.R. Karger, M.S. Levine, Finding maximum flows in undirected graphs seems easier than bipartite matching, in: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, 1998, pp. 69-78
34. Katayama K., and Narihisa H. Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem. European Journal of Operational Research 134 (2001) 103-119
35. S.H. Kim, Y.H. Kim, B.R. Moon, A hybrid genetic algorithm for the max cut problem, in: Genetic and Evolutionary Computation Conference, 2001, pp. 416-423
36. M. Koga, Yagiura, K. Nonobe, T. Imamichi, H. Nagamochi, T. Ibaraki, Efficient branch-and-bound algorithms for weighted max-2-sat, in: Proceedings of the Third International Asian Applied Computing Conference, AACC, Nepal, 2005
37. S.H. Lu, A.C. Williams, Roof duality and linear relaxation for quadratic and polynomial 0-1 optimization, Research Report RRR 8-1987, RUTCOR, Rutgers University, 1987
38. Lu S.H., and Williams A.C. Roof duality for 0-1 nonlinear optimization. Mathematical Programming 37 (1987) 357-360
39. P. Merz, B. Freisleben, Genetic algorithms for binary quadratic programming, in: Proceedings of the 1999 International Genetic and Evolutionary Computation Conference, GECCO'99, 1999, pp. 417-424
40. H.D. Mittelmann, An independent benchmarking of sdp and socp solvers, Mathematical Programming
41. Padberg M. The boolean quadric polytope: Some characteristics, facets and relatives. Mathematical Programming 45 (1989) 139-172
42. Palubeckis G. Multistart tabu search strategies for the unconstrained binary quadratic optimization problem. Annals of Operations Research 131 (2004) 259-282
43. X. Sun, Combinatorial algorithms for boolean and pseudo-Boolean functions, Ph.D. Thesis, RUTCOR, Rutgers University, 1991
44. A.C. Williams, Quadratic 0-1 programming using the roof dual with computational results, Research Report RRR 8-1985, RUTCOR, Rutgers University, December 1985