Using a Mixed Integer Programming Tool for Solving the 0–1 Quadratic Knapsack Problem

References

• Beale E. M. L.Introduction to Optimization (1988) (Wiley)Google Scholar
• Billionnet A., Calmels F. Linear programming for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. (1996) 92:310–325Crossref, Google Scholar
• Billionnet A., Elloumi S. Best reduction of the quadratic semi-assignment problem. Discrete Appl. Math. (2001) 109:197–213Crossref, Google Scholar
• Billionnet A., Faye A., Soutif E. An exact algorithm for the 0–1 quadratic knapsack problem. ISMP97, Lausanne, Switzerland, August 1997. (1997) Google Scholar
• Billionnet A., Faye A., Soutif E. A new upper bound for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. (1999) 112:664–672Crossref, Google Scholar
• Caprara A., Pisinger D., Toth P. Exact solution of the quadratic knapsack problem. INFORMS J. Comput. (1999) 11:125–137Link, Google Scholar
• Chaillou P., Hansen P., Mahieu Y. Best network flow bound for the quadratic knapsack problem. Lecture Notes in Mathematics (1986) 226–235No.1403Google Scholar
• Ilog, Inc., CPLEX Division (1998) . CPLEX callable library, Version 6.0. Incline Village, NV, USAGoogle Scholar
• Gallo G., Hammer P. L., Simeone B. Quadratic knapsack problems. Math. Programming Stud. (1980) 12:132–149Crossref, Google Scholar
• Glover F. Improved linear integer programming formulations of nonlinear integer problems. Management Sci. (1975) 22:455–460Link, Google Scholar
• Hammer P. L., Rader Jr D. J. Efficient methods for solving quadratic 0–1 knapsack problems. INFOR (1997) 35:170–182Google Scholar
• Helmberg C., Rendl F., Weismantel R., Cunningham W. H., McCormick S. T., Queyranne M. Quadratic knapsack relaxation using cutting planes and semidefinite programming. Proc. Fifth IPCO Conf., Lecture Notes Comput. Sci. (1996) (Springer Verlag)175–189No.1084Crossref, Google Scholar
• Michelon P., Veuilleux L. Lagrangean methods for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. (1996) 92:326–341Crossref, Google Scholar
• Salkin H. M., Mathur K.Foundations of Integer Programming (1989) (North-Holland, Amsterdam, The Netherlands)Google Scholar