Mathematical Programming

, Volume 98, Issue 1–3, pp 23–47 | Cite as

Local branching

  • Matteo Fischetti
  • Andrea Lodi


The availability of effective exact or heuristic solution methods for general Mixed-Integer Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a black-box ``tactical'' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic'' level by a simple external branching framework. The procedure is in the spirit of well-known local search metaheuristics, but the neighborhoods are obtained through the introduction in the MIP model of completely general linear inequalities called local branching cuts. The new solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the MIP solver at hand. It alternates high-level strategic branchings to define the solution neighborhoods, and low-level tactical branchings to explore them. The result is a completely general scheme aimed at favoring early updatings of the incumbent solution, hence producing high-quality solutions at early stages of the computation. The method is analyzed computationally on a large class of very difficult MIP problems by using the state-of-the-art commercial software ILOG-Cplex 7.0 as the black-box tactical MIP solver. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the new method exhibits consistently an improved heuristic performance: in 23 out of 29 cases, the MIP solver produced significantly better incumbent solutions when driven by the local branching paradigm.


Mixed integer program heuristic local search branch-and-bound 


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  1. 1.
    Balas, E., Ceria, S., Dawande, M., Margot, F., Pataki, G.: OCTANE: A New Heuristic For Pure 0-1 Programs. Operations Research 49(2), 207–225 (2001)Google Scholar
  2. 2.
    Balas, E., Martin, C.H.: Pivot-And-Complement: A Heuristic For 0-1 Programming. Management Science 26(1), 86–96 (1980)Google Scholar
  3. 3.
    Belotti, P.: Personal communication, 2002Google Scholar
  4. 4.
    Bixby, R.E., Ceria, S., McZeal, C.M., Savelsbergh, M.W.P.: MIPLIB 3.0.∼ bixby/miplib/miplib.html.Google Scholar
  5. 5.
    Caprara, A., Fischetti, M., Toth, P.: A Heuristic Method For The Set Covering Problem. Operations Research 47, 730–743 (1999)Google Scholar
  6. 6.
    Cplex.: ILOG Cplex 7.0 User's Manual and Reference Manual. ILOG, S.A., 2001 ( Scholar
  7. 7.
    Glover, F., Laguna, M.: General Purpose Heuristics For Integer Programming: Part I. Journal of Heuristics 2, 343–358 (1997)Google Scholar
  8. 8.
    Glover, F., Laguna, M.: General Purpose Heuristics For Integer Programming: Part II. Journal of Heuristics 3, 161–179 (1997)Google Scholar
  9. 9.
    Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publisher, Boston, Dordrecht, London, 1997Google Scholar
  10. 10.
    Goessens, J.W., van Hoesel, S., Kroon, L.: A Branch-and-Cut Approach to Line Planning Problems. Working Paper, Erasmus University, 2001Google Scholar
  11. 11.
    Hillier, F.S.: Effcient Heuristic Procedures For Integer Linear Programming With An Interior. Operations Research 17(4), 600–637 (1969)Google Scholar
  12. 12.
    Ibaraki, T., Ohashi, T., Mine, H.: A Heuristic Algorithm For Mixed-Integer Programming Problems. Mathematical Programming Study 2, 115–136 (1974)Google Scholar
  13. 13.
    Kroon, L.: Personal communication, 2002Google Scholar
  14. 14.
    Kroon, L., Fischetti, M.: Crew Scheduling for Netherlands Railways: Destination Customer. In: Voss, S., Daduna, J.R., eds. Computer-Aided Scheduling of Public Transport. Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, 2001, pp. 181–201Google Scholar
  15. 15.
    Løkketangen, A.: Heuristics for 0-1 Mixed-Integer Programming. In: Pardalos, P.M., Resende, M.G.C. eds. Handbook of Applied Optimization, Oxford University Press, 2002, pp. 474–477Google Scholar
  16. 16.
    Løkketangen, A., Glover, F.: Solving Zero/One Mixed Integer Programming Problems Using Tabu Search. European Journal of Operational Research 106, 624–658 (1998)Google Scholar
  17. 17.
    Luzzi, I.: Personal communication, 2001Google Scholar
  18. 18.
    Mannino, C., Parrello, E.: Personal communication, 2002Google Scholar
  19. 19.
    Mladenovíc, N., Hansen, P.: Variable Neighborhood Search. Computers and Operations Research 24, 1097–1100 (1997)Google Scholar
  20. 20.
    Nediak, M., Eckstein, J.: Pivot, Cut, and Dive: A Heuristic for 0-1 Mixed Integer Programming Research Report RRR 53-2001, RUTCOR, Rutgers University, October 2001Google Scholar
  21. 21.
    Polo, C.: Algoritmi Euristici per il Progetto Ottimo di una Rete di Interconnessione. Tesi di laurea in Ingegneria Informatica, Universtità degli Studi di Padova, 2002 (in Italian)Google Scholar
  22. 22.
    TURNI.: User's Manual, Double-Click sas, 2001 ( Scholar
  23. 23.
    Van Vyve, M., Pochet, Y.: A General Heuristic for Production Planning Problems. CORE Discussion Paper 56, 2001Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.DEIUniversity of PadovaPadovaItaly
  2. 2.DEISUniversity of BolognaBolognaItaly

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