Estimating bounds for quadratic assignment problems associated with Hamming and Manhattan distance matrices based on semidefinite programming

SIAM Journal on Optimization

Volumn 20, Issue 6, 2010, Pages 3408-3426

  Mittelmann, Hans ^a   Peng, Jiming ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Lower bound; Quadratic assignment problem; Relaxation; Semidefinite programming; Singular value decomposition

Indexed keywords

LOWER BOUNDS; QUADRATIC ASSIGNMENT PROBLEMS; RELAXATION; SEMI-DEFINITE PROGRAMMING; SINGULAR VALUES;

DATA STRUCTURES; HAMMING DISTANCE; SINGULAR VALUE DECOMPOSITION;

MATHEMATICAL PROGRAMMING;

EID: 79251483526     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090748834     Document Type: Article

References (36)

1. W. P. Adams and T. A. Johnson, Improved Linear Programming-Based Lower Bounds for the Quadratic Assignment Problem, in Quadratic Assignment and Related Problems, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, P. M. Pardalos and H. Wolkowicz, ed., AMS, Providence, RI, 1994, pp. 43-75.
2. W. P. Adams and H. D. Sherali, A tight linearization and an algorithm for zero-one quadratic programming problems, Manag. Sci., 32 (1986), pp. 1274-1290.
3. K. M. Anstreicher, Recent advances in the solution of quadratic assignment problems, Math. Program., Ser. B, 97 (2003), pp. 27-42.
4. K. M. Anstreicher and N. W. Brixius, A new bound for the quadratic assignment problem based on convex quadratic programming, Math. Program., 80 (2001), pp. 341-357.
5. K. M. Anstreicher, N. W. Brixius, J.-P. Goux, and J. Linderoth, Solving large quadratic assignment problems on computational grids, Math. Program., 91 (2002), pp. 563-588.
6. G. Ben-David and D. Malah, Bounds on the performance of vector-quantizers under channel errors, IEEE Trans. Inform. Theory, 51 (2005), pp. 2227-2235.
7. S. Burer and D. Vandenbussche, Solving lift-and-project relaxations of binary integer programs, SIAM J. Optim., 16 (2006), pp. 726-750.
8. R. E. Burkard, E. Çela, S. E. Karisch, and F. Rendl, QAPLIB-A quadratic assignment problem library, J. Global Optim., 10 (1997), pp. 391-403.
9. N. T. Cheng and N. K. Kingsburg, Robust zero-redundancy vector quantization for noisy channels, in Proceedings of the International Conference on Communications, Boston, 1989, pp. 1338-1342.
10. Y. Ding and H. Wolkowicz, A low-dimensional semidefinite relaxation for the quadratic assignment problem, Math. Oper. Res., 34 (2009), pp. 1008-1022.
11. P. C. Gilmore, Optimal and suboptimal algorithms for the quadratic assignment problem, SIAM J. Appl. Math., 10 (1962), pp. 305-313.
12. M. Grant, S. Boyd, and Y. Ye, CVX Users' Guide, http://www.stanford.edu/ ~boyd/cvx/cvxusrguide.pdf (2007).
13. S. W. Hadley, F. Rendl, and H. Wolkowicz, A new lower bound via projection for the quadratic assignment problem, Math. Oper. Res., 17 (1992), pp. 727-739.
14. P. Hahn and T. Grant, Lower bounds for the quadratic assignment problem based upon a dual formulation, Oper. Res. 46 (1998) pp. 912-922.
15. M. Hannan and J. M. Kurtzberg, Placement techniques, in Design Automation of Digital Systems: Theory and Techniques, Vol. 1, M. A. Breuer, ed., Prentice-Hall, Englewood Cliffs, NJ, 1972, pp. 213-282.
16. L. H. Harper, Optimal assignments of numbers to vertices, J. SIAM, 12 (1964), pp. 131-135.
17. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
18. S. E. Karisch and F. Rendl, Lower bounds for the quadratic assignment problem via triangle decompositions, Math. Program., 71 (1995), pp. 137-152.
19. E. de Klerk and R. Sotirov, Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem, Math. Program., 122 (2010), pp. 225-246.
20. T. Koopmans and M. Beckmann, Assignment problems and the location of economic activities, Econometrica, 25 (1957), pp. 53-76.
21. E. Lawler, The quadratic assignment problem, Manag. Sci., 9 (1963), pp. 586-599.
22. E. M. Loiola, N. M. Maia de Abreu, P. O. Boaventura-Netto, P. Hahn, and T. Querido, A survey for the quadratic assignment problem, European J. Oper. Res., 176 (2007), pp. 657-690.
23. H. Mittelmann, J. Peng, and X. Wu, Graph modeling for quadratic assignment problem associated with the hypercube, AIP Conf. Proc., 1146 (2009), pp. 65-79.
24. C. E. Nugent, T. E. Vollman, and J. Ruml, An experimental comparison of techniques for the assignment of facilities to locations, Oper. Res., 16 (1968), pp. 150-173.
25. L. C. Potter and D. M. Chiang, Minimax nonredundant channel coding, IEEE Trans. Commun., 43 (1995), pp. 804-811.
26. J. Povh and F. Rendl, Copositive and semidefinite relaxations of the quadratic assignment problem, Discrete Optim., 6 (2009), pp. 231-241.
27. F. Rendl and R. Sotirov, Bounds for the quadrtic assignment problem using bundle method, Math. Program., Ser. B, 109 (2007), pp. 505-524.
28. M. Scriabin and R. C. Vergin, Comparison of computer algorithms and visual based methods for plant layout, Manag. Sci., 22 (1975), pp. 172-187.
29. T. Stützle and S. Fernandes, New benchmark instances for the QAP and the experimental analysis of algorithms, in Evolutionary Computation in Combinatorial Optimization: 4th European Conference, EvoCOP 2004, Lecture Notes in Computer Science 3004, J. Gottlieb and G. Raidl, ed., Springer Verlag, Berlin, 2004, pp. 199-209.
30. E. D. Taillard, Comparison of iterative searches for the quadratic assignment problem, Location Sci., 3 (1995), pp. 87-105.
31. K. C. Toh, M. J. Todd, and R. H. Tütüncü, SDPT3-A Matlab software package for semidefinite programming, Optim. Methods Softw., 11 (1999), pp. 545-581.
32. X. Wang, X. Wu, and S. Dumitrescu, On optimal index assignment for MAP decoding of Markov sequences, in 2006 IEEE International Symposium on Information Theory, Seattle, WA, 2006, pp. 2314-2318.
33. X. Wu, private communication, Department of Electrical and Computer Engineering, McMaster University, ON, Canada, 2007.
34. K. Zeger and A. Gersho, Pseudo-gray code, IEEE Trans. Commun., 38 (1990), pp. 2147-2158.
35. X. Zeng, private communication, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, 2008.
36. Q. Zhao, S. E. Karisch, F. Rendl, and H. Wolkowicz, Semidefinite programming relaxations for the quadratic assignment problem, J. Comb. Optim., 2 (1998), pp. 71-109.