A Collaborative Approach Based on DCA and VNS for Solving Mixed Binary Linear Programs

  • Sara SamirEmail author
  • Hoai An Le Thi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11431)


This paper addresses the Mixed Binary Linear Programming problems (MBLPs) by a collaborative approach using two component algorithms. The first is DCA (Difference of Convex functions Algorithm), an efficient deterministic algorithm in nonconvex programming framework, and the second is VNS (Variable Neighborhood Search), a well known metaheuristic method. The DCA and VNS are executed in parallel. At the end of each cycle, the best-found solution is exchanged between these algorithms via MPI (Message Passing Interface) library. The next cycle starts with the previous best-found solution as an initial solution. The performance of the proposed approach is tested on a set of benchmarks of the Capacitated Facility Location Problem. Numerical experiments show the efficiency of our approach.


Mixed Binary Linear Programming problems DC programming and DCA Metaheuristics Parallel and distributed programming 


  1. 1.
    Centre de Calcul de l’université de Bourgogne: Bases de la parallélisation par passage de message: MPI (Message Passing Interface) (2016)Google Scholar
  2. 2.
    Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449–467 (2001)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Le Thi, H.A., Pham Dinh, T.: A continuous approach for large-scale constrained quadratic zero-one programming. Optimization 45(3), 1–28 (2001). In honor of Professor ELSTER, Founder of the Journal OptimizationzbMATHGoogle Scholar
  4. 4.
    Le Thi, H.A., Pham Dinh, T.: The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133, 23–46 (2005)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Le Thi, H.A., Pham Dinh, T.: DC programming and DCA: thirty years of developments. Math. Program. 169(1), 5–68 (2018)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Le Thi, H.A., Pham Dinh, T., Muu, L.: Exact penalty in DC programming. Vietnam J. Math. 27(2), 169–178 (1999)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Le Thi, H.A., Pham Dinh, T., Van Ngai, H.: Exact penalty and error bounds in DC programming. J. Glob. Optim. 52(3), 509–535 (2011)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to D.C. programming: theory, algorithm and applications. Acta Mathematica Vietnamica 22(1), 289–355 (1997)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Polacek, M., Hartl, R.F., Doerner, K., Reimann, M.: A variable neighborhood search for the multi depot vehicle routing problem with time windows. J. Heuristics 10(6), 613–627 (2004)Google Scholar
  11. 11.
    Vidović, M., Popović, D., Ratković, B., Radivojević, G.: Generalized mixed integer and VNS heuristic approach to solving the multisize containers drayage problem. Int. Trans. Oper. Res. 24(3), 583–614 (2016)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Yagouni, M., Le Thi, H.A.: A collaborative metaheuristic optimization scheme: methodological issues. In: van Do, T., Le Thi, H.A., Nguyen, N.T. (eds.) Advanced Computational Methods for Knowledge Engineering. AISC, vol. 282, pp. 3–14. Springer, Cham (2014). Scholar
  13. 13.
    Ta, A.S., Le Thi, H.A., Khadraoui, D., Pham Dinh, T.: Solving partitioning-hub location-routing problem using DCA. J. Ind. Manag. Optim. 8(1), 87–102 (2012)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Science and Applications Department, LGIPMUniversity of LorraineMetzFrance

Personalised recommendations