Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs

Discrete Optimization

Volumn 1, Issue 2, 2004, Pages 99-120

  Adams, Warren P ^a   Forrester, Richard J ^b   Glover, Fred W ^c  

^a CLEMSON UNIVERSITY   (United States)

^b DICKINSON COLLEGE   (United States)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

0 1 Quadratic program; Linearization; Reformulation

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUNCTIONS; LAGRANGE MULTIPLIERS; LINEAR PROGRAMMING; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING;

AUXILIARY VARIABLES; BINARY REALIZATIONS; REFORMULATION-LINEARIZATION TECHNIQUE (RLT); REFORMULATIONS;

QUADRATIC PROGRAMMING;

EID: 13944271956     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2004.03.006     Document Type: Article

References (25)

1. W. Adams, R. Forrester, A simple recipe for mixed 0-1 linearizations, Operations Research Letters, to appear.
2. W. Adams, and T. Johnson Improved linear programming-based lower bounds for the quadratic assignment problem DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 16 1994 43 76
3. W. Adams, and H. Sherali A tight linearization and an algorithm for zero-one quadratic programming problems Management Sci. 32 1986 1274 1290
4. W. Adams, and H. Sherali Linearization strategies for a class of zero-one mixed integer programming problems Oper. Res. 38 1990 217 226
5. W. Adams, and H. Sherali Mixed-integer bilinear programming problems Math. Programming 59 1993 279 305
6. J. Benders Partitioning procedures for solving mixed-variables programming problems Numer. Math. 4 1962 238 252
7. A. Billionnet, and F. Calmels Linear programming for the 0-1 quadratic knapsack problem European J. Oper. Res. 92 1996 310 325
8. R. Burkard, and T. Bönniger A heuristic for quadratic Boolean programs with applications to quadratic assignment problems European J. Oper. Res. 13 1983 374 386
9. R. Burkard, and U. Derigs Assignment and matching problems solution methods with FORTRAN-programs Lecture Notes in Economics and Mathematical Systems Vol. 184 1980 Springer Berlin 99 148
10. A. Caprara, D. Pisinger, and P. Toth Exact solution of the quadratic knapsack problem INFORMS J. Comput. 11 1999 125 137
11. F. Glover Improved linear integer programming formulations of nonlinear integer programs Management Sci. 22 1975 455 460
12. F. Glover An improved MIP formulation for products of discrete and continuous variables J. Inform. Optim. Sci. 5 1984 469 471
13. P. Hahn, and T. Grant Lower bounds for the quadratic assignment problem based upon a dual formulation Oper. Res. 46 1998 912 922
14. P. Hahn, W. Hightower, T. Johnson, and M. Guignard-Spielberg Tree elaboration strategies in branch and bound algorithms for solving the quadratic assignment problem Yugoslav J. Oper. Res. 11 2001 41 60
15. T. Johnson, New linear programming-based solution procedures for the quadratic assignment problem, Ph.D. Dissertation, Department of Mathematical Sciences, Clemson University, 1992.
16. L. Kaufman, and F. Broeckx An algorithm for the quadratic assignment problem using Benders' decomposition European J. Oper. Res. 2 1978 207 211
17. J. Krarup, and P. Pruzan Computer aided-layout design Mathematical Programming Study Vol. 9 1978 North-Holland Publishing Company Amsterdam 75 94
18. R. Lougee-Heimer, W. Adams, A conditional logic approach for strengthening mixed 0-1 linear programs, Ann. Oper. Res., to appear.
19. L. Lovász, and S. Schrijver Cones of matrices and set-functions and 0-1 optimization SIAM J. Optim. 1 1991 166 190
20. P. Michelon, and L. Veilleux Lagrangean methods for the 0-1 quadratic knapsack problem European J. Oper. Res. 92 1996 326 341
21. C. Nugent, T. Vollmann, and J. Ruml An experimental comparison of techniques for the assignment of facilities to locations Oper. Res. 16 1968 150 173
22. H. Sherali, and W. Adams A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems SIAM J. Discrete Math. 3 1990 411 430
23. H. Sherali, and W. Adams A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems Discrete Appl. Math. 52 1994 83 106
24. H. Sherali, and W. Adams A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems 1999 Kluwer Academic Publishers Norwell, MA
25. H. Sherali, W. Adams, and P. Driscoll Exploiting special structures in constructing a hierarchy of relaxations for 0-1 mixed integer problems Oper. Res. 46 1998 396 405