A new linearization method for quadratic assignment problems

Optimization Methods and Software

Volumn 21, Issue 5, 2006, Pages 805-818

  Xia, Yong ^a   Yuan, Ya Xiang ^a  

^a INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Cutting plane; Linearization; Lower bound; Mixed integer linear program; Quadratic assignment problem

Indexed keywords

COMBINATORIAL OPTIMIZATION; INTEGER PROGRAMMING; LINEARIZATION; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

CONTINUOUS RELAXATION; CUTTING PLANES; LINEARIZATION METHODS; LOWER BOUNDS; MIXED INTEGER LINEAR PROGRAM; NUMERICAL RESULTS; QUADRATIC ASSIGNMENT PROBLEMS; QUADRATIC OBJECTIVE FUNCTIONS;

HEURISTIC METHODS;

EID: 84925234382     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780500273077     Document Type: Article

References (20)

1. Adams, W.P. and Johnson, T.A., 1994, Improved linear programming-based lower bounds for the quadratic assignment problem. In: Pardalos, P.M. and Wolkowicz, H. (Eds) Quadratic Assignment and Related Problems, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 16 (Rhode Island: AMS), pp. 43-75.
2. Al-Khayyal, A. and Falk, J.E., 1983, Jointly constrained biconvex programming. Mathematics of Operations Research, 8(2), 273.
3. Anstreicher, K.M., 2003, Recent advances in the solution of quadratic assignment problems. Mathematical Programming, Series B, 97, 24-42.
4. Balinski, M.L. and Russakoff, A., 1974, On the assignment polytope. SIAM Review, 16, 516-525.
5. Bazaraa, M.S. and Sherali, H.D., 1978, New approaches for solving the quadratic assignment problem. Operations Research Verfahren, 32, 29-46.
6. Burkard, R.E., 1991, Locations with spatial interactions: the quadratic assignment problem. In: P.B. Mirchandani and R.L. Francis, (Eds), Discrete Location Theory (New York: Wiley), pp. 387-437.
7. Burkard, R.S. and Bönniger, T., 1983, A heuristic for quadratic Boolean programs with applications to quadratic assignment problems. European Journal of Operational Research, 13, 374-386.
8. Burkard, R.E., C¸ela, E., Pardalos, P.M. and Pitsoulis, L.S., 1998, The quadratic assignment problem. In: D.-Z. Du and P.M. Pardalos (Eds) Handbook of Combinatorial Optimization, Vol. 3 (Dordrecht: Kluwer Academic Publishers), pp. 241-337.
9. Burkard, R.E. and Derigs, U., 1980, Assignment and Matching Problems: Solution Methods with FORTRAN-Programs. In: Lectures Notes in Economics and Mathematical Systems, 184 (Secaucus, NJ: Springer-Verlag New York).
10. Burkard, R.E., Karisch, S.E. and Rendl, F., 1997, QAPLAB - a quadratic assignment problem library. Journal of Global Optimization, 10, 391-403. Available online at: www.opt.math.tu-graz.ac.at/~qaplab.
11. C¸ela, E., 1998, The Quadratic Assignment Problem: Theory and Algorithms (Dordrecht: Kluwer Academic Publishers).
12. Frieze, A.M. and Yadegar, J., 1983, On the quadratic assignment problem. Discrete Applied Mathematics, 5, 89-98.
13. Gilmore, P.C., 1962, Optimal and suboptimal algorithms for the quadratic assignment problem. SIAM Journal on Applied Mathematics, 10, 305-313.
14. Hardy, G.G., Littlewood, J.E. and Pólya, G., 1952, Inequalities (London: Cambridge University Press).
15. Kauffmann, L. and Broeckx, F., 1978, An algorithm for the quadratic assignment problem using Bender's decomposition. European Journal of Operational Research, 2, 204-211.
16. Koopmans, T.C. and Beckmann, M.J., 1957, Assignment problems and the location of economic activities. Econometrica, 25, 53-76.
17. McCormick, P., 1976, Computability of global solution to factorable nonconvex problems. Part I: convex underestimating problems. Mathematical Programming, 10, 147-175.
18. Pardalos, P.M., Rendl, F. and Wolkowicz, H., 1994, The quadratic assignment problem: a survey and recent developments. In: P.M. Pardalos and H. Wolkowicz (Eds) Quadratic Assignment and Related Problems, DIMACS series in Discrete Mathematics and Theoretical Computer Science, Vol. 16 (Rhode Island: AMS), pp. 1-42.
19. Sahni, S. and Gonzalez, T., 1976, P-complete approximation problems. Journal of the Association of Computing Machinery, 23, 555-565.
20. th Conference of CSIAM in Hunan, China.