A Neural Network Based Global Optimal Algorithm for Unconstrained Binary Quadratic Programming Problem

  • Shenshen GuEmail author
  • Xinyi Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11302)


Unconstrained binary quadratic programming problem is a classical integer optimization problem and is well known to be NP-hard. In order to improve the performance of global optimal algorithms for unconstrained binary quadratic programming problem, in this paper, we proposed a new exact solution method. By investigating the geometric properties of the original problem, the quality of the algorithms for calculating the upper bound and lower bound are improved. And then, for the new derived upper bound algorithm and lower bound algorithm, their recurrent neural network models are proposed and applied respectively in order to speed up the computation. The numerical results shows that the proposed algorithm of a branch-and-bound type is quite effective and efficient.


Binary quadratic problem Branch-and-bound Recurrent neural network 



The work described in the paper was supported by the National Science Foundation of China under Grant 61503233.


  1. 1.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman. Co., New York (1979)Google Scholar
  2. 2.
    Mcbride, R.D., Yormark, J.S.: An implicit enumeration algorithm for quadratic integer programming. Manage. Sci. 26, 282–296 (1980)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chardaire, P., Sutter, A.: A decomposition method for quadratic zero-one programming. J. Manage. Sci. 41, 704–712 (1995)zbMATHGoogle Scholar
  4. 4.
    Li, D., Sun, X.L.: Nonlinear Integer Programming. Springer, New York (2006).
  5. 5.
    Helmberg, C., Rendl, F.: Solving quadratic (0,1)-problems by semidefinite programs and cutting planes. Math. Program. 82, 291–315 (1998)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Rendl, F., Rinaldi, G., Wiegele, A.: Solving max-cut to optimality by intersecting semidefinite and polyhedral relaxation. Lecture Notes Computer Science, vol. 4513, pp. 295–309 (2007)Google Scholar
  7. 7.
    Pardalos, P.M., Rodgers, G.P.: Computational aspects of a branch-and-bound algorithm for quadratic zero-one programming. Computing 45, 131–144 (1990)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Barahona, F., J\({\rm \ddot{u}}\)nger, M., Reinelt, G.: Experiments in quadratic 0–1 programming. Math. Program. 44, 127–137 (1989)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Boros, E., Hammer, P.L., Tavares, G.: Local search heuristics for unconstrained quadratic binary optimization. Technical report, RUTCOR, Rutgers University, Rut-cor Research Report (2005)Google Scholar
  10. 10.
    Li, D., Sun, X.L., Liu, C.L.: An exact solution method for quadratic 0–1 programming: a geometric approach. Technical report, Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management (2006)Google Scholar
  11. 11.
    Gu, S., Peng, J.: A neural network based algorithm to compute the distance between a point and an ellipsoid. In: 2015 Seventh International Conference on Advanced Computational Intelligence (ICACI), pp. 294–299. IEEE (2015)Google Scholar
  12. 12.
    Gu, S., Peng, J., Zhang, J.: A projection based recurrent neural network approach to compute the distance between a point and an ellipsoid with box constraint. In: Youth Academic Annual Conference of Chinese Association of Automation (YAC), pp. 459–462. IEEE (2016)Google Scholar
  13. 13.
    Yen, Y.: Finding the K shortest loopless paths in a network. Manag. Sci. 17(11), 712–716 (1971)CrossRefGoogle Scholar
  14. 14.
    Bellman, R.: On a routing problem. Quart. Appl. Math. 16, 87–90 (1958)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gu, S., Cui, R.: An efficient algorithm for the subset sum problem based on finite-time convergent recurrent neural network. Neurocomputing 149, 13 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiChina

Personalised recommendations