Abstract
The recent research on linearization techniques for solving 0-1 quadratic programming problems focuses on providing concise models and tightening constraint bounds. In this paper, we propose a computational enhancement for a linearization technique to make the linearized model much faster to solve. We investigate the computational performance of the proposed approach, by comparing it with other linearization techniques on a class of 0-1 quadratic programming problems. We can further speed up the proposed technique by heuristically tightening the constraint bounds, as demonstrated by solving the uncapacitated single allocation p-hub median problem using the Civil Aeronautics Board data.
Similar content being viewed by others
References
Adams W.P., Forrester R.J.: A simple recipe for concise mixed 0-1 linearizations. Operations Research Letters 33, 55–61 (2005)
Adams W.P., Forrester R.J., Glover F.W.: Comparison and enhancement strategies for linearizing mixed 0-1 quadratic programs. Discrete Optim. 1, 99–120 (2004)
Adams W.P., Sherali H.D.: A tight linearization and an algorithm for zero-one quadratic programming problems. Manag. Sci. 32, 1274–1290 (1986)
Bryan D.L., O’Kelly M.E.: Hub-and-spoke network in air transportation: an analytical review. J. Reg. Sci. 39, 275–295 (1999)
Campbell J.F.: Integer programming formulations of discrete hub location problems. Eur. J. Oper. Res. 72, 387–405 (1994)
Campbell J.F., Ernst A., Krishnamoorthy M.: Hub location problems. In: Hamacher, H., Drezner, Z. (eds) Location theory: applications and theory, pp. 373–406. Springer, New York (2001)
Chaovalitwongse W., Pardalos P.M., Prokoyev O.A.: A new linearization technique for multi-quadratic 0-1 programming problems. Oper. Res. Lett. 32, 517–522 (2004)
Elloumi S., Faye A., Soutif E.: Decomposition and linearization for 0-1 quadratic programming. Ann. Oper. Res. 99, 79–93 (2000)
Ernst A.T., Krishnamoorthy M.: Efficient algorithms for the uncapacitated single allocation p-hub median problem. Locat. Sci. 4, 139–154 (1996)
Glover F.: Improved linear integer programming formulations of nonlinear integer programs. Manag. Sci. 22, 455–460 (1975)
Glover F., Woolsey E.: Further reduction of zero-one polynomial programming problems to zero-one linear programming problems. Oper. Res. 21, 156–161 (1973)
Glover, F., Woolsey, E.: Converting the 0-1 polynomial programming problem to a 0-1 linear program. IRMIS Working paper, 9304, School of Business, Indiana University, Bollomingto, Indiana (1974)
Kaufman L., Broeckx F.: An algorithm for the quadratic assignmnet problem using benders’ decomposition. Eur. J. Oper. Res. 2, 204–211 (1978)
O’Kelly M.: A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32, 393–404 (1987)
Pardalos P.M.: Construction of test problems in quadratic bivalent programming. ACM Trans. Math. Softw. 17, 74–87 (1991)
Sherali H.D., Desai J., Rakha H.: A discrete optimization approach for locating Automatic Vehicle Identification readers for the provision of roadway travel times. Transp. Res. B Methodol. 40, 857–871 (2006)
Sherali H.D., Smith J.C.: An improved linearization strategy for zero-one quadratic programming problems. Optim. Lett. 1, 33–47 (2007)
Skorin-Kapov D., Skorin-Kapov J., O’Kelly M.: Tight linear programming relaxations of uncapacitated p-hub median problems. Eur. J. Oper. Res. 94, 582–593 (1996)
Watters L.: Reduction of integer polynomial programming problems to zero-one linear programming problems. Oper. Res. 15, 1171–1174 (1967)
Zangwill W.I.: Media selection by decision programming. J. Advert. Res. 5, 30–36 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, X., Chen, A., Chaovalitwongse, W.A. et al. An improved linearization technique for a class of quadratic 0-1 programming problems. Optim Lett 6, 31–41 (2012). https://doi.org/10.1007/s11590-010-0249-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-010-0249-z