Generic CP-Supported CMSA for Binary Integer Linear Programs

  • Christian BlumEmail author
  • Haroldo Gambini Santos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11299)


Construct, Merge, Solve & Adapt (CMSA) is a general hybrid metaheuristic for solving combinatorial optimization problems. At each iteration, CMSA (1) constructs feasible solutions to the tackled problem instance in a probabilistic way and (2) solves a reduced problem instance (if possible) to optimality. The construction of feasible solutions is hereby problem-specific, usually involving a fast greedy heuristic. The goal of this paper is to design a problem-agnostic CMSA variant whose exclusive input is an integer linear program (ILP). In order to reduce the complexity of this task, the current study is restricted to binary ILPs. In addition to a basic problem-agnostic CMSA variant, we also present an extended version that makes use of a constraint propagation engine for constructing solutions. The results show that our technique is able to match the upper bounds of the standalone application of CPLEX in the context of rather easy-to-solve instances, while it generally outperforms the standalone application of CPLEX in the context of hard instances. Moreover, the results indicate that the support of the constraint propagation engine is useful in the context of problems for which finding feasible solutions is rather difficult.


  1. 1.
    Achterberg, T.: Constraint Integer Programming. Ph.D. thesis (2007)Google Scholar
  2. 2.
    Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton (2007)zbMATHGoogle Scholar
  3. 3.
    Benoist, T., Estellon, B., Gardi, F., Megel, R., Nouioua, K.: LocalSolver 1.x: a black-box local-search solver for 0–1 programming. 4OR 9(3), 299 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Blum, C.: Construct, merge, solve and adapt: application to unbalanced minimum common string partition. In: Blesa, M.J., Blum, C., Cangelosi, A., Cutello, V., Di Nuovo, A., Pavone, M., Talbi, E.-G. (eds.) HM 2016. LNCS, vol. 9668, pp. 17–31. Springer, Cham (2016). Scholar
  5. 5.
    Blum, C., Blesa, M.J.: A comprehensive comparison of metaheuristics for the repetition-free longest common subsequence problem. J. Heuristics 24, 551–579 (2017)CrossRefGoogle Scholar
  6. 6.
    Blum, C., Pinacho, P., López-Ibáñez, M., Lozano, J.A.: Construct, merge, solve & adapt: a new general algorithm for combinatorial optimization. Comput. Oper. Res. 68, 75–88 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ernst, A.T., Singh, G.: Lagrangian particle swarm optimization for a resource constrained machine scheduling problem. In: 2012 IEEE Congress on Evolutionary Computation, pp. 1–8 (2012)Google Scholar
  8. 8.
    Fischetti, M., Glover, F., Lodi, A.: The feasibility pump. Math. Program. 104(1), 91–104 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fischetti, M., Salvagnin, D.: Feasibility pump 2.0. Math. Program. Comput. 1(2), 201–222 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Fourer, R., Gay, D., Kernighan, B.: AMPL, vol. 117. Boyd & Fraser Danvers (1993)Google Scholar
  11. 11.
    Gamrath, G., Koch, T., Martin, A., Miltenberger, M., Weninger, D.: Progress in presolving for mixed integer programming. Math. Program. Comput. 7, 367–398 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Johnson, E., Nemhauser, G., Savelsbergh, W.: Progress in linear programming-based algorithms for integer programming: an exposition. INFORMS J. Comput. 12, 2–3 (2000)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Koch, T., et al.: Miplib 2010. Math. Program. Comput. 3(2), 103 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kochenberger, G., et al.: The unconstrained binary quadratic programming problem: a survey. J. Comb. Optim. 28(1), 58–81 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lizárraga, E., Blesa, M.J., Blum, C.: Construct, merge, solve and adapt versus large neighborhood search for solving the multi-dimensional knapsack problem: which one works better when? In: Hu, B., López-Ibáñez, M. (eds.) EvoCOP 2017. LNCS, vol. 10197, pp. 60–74. Springer, Cham (2017). Scholar
  16. 16.
    Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097–1100 (1997)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Sandholm, T., Shields, R.: Nogood learning for mixed integer programming. Technical report (2006)Google Scholar
  18. 18.
    Souza Brito, S., Gambini Santos, H., Miranda Santos, B.H.: A local search approach for binary programming: feasibility search. In: Blesa, M.J., Blum, C., Voß, S. (eds.) HM 2014. LNCS, vol. 8457, pp. 45–55. Springer, Cham (2014). Scholar
  19. 19.
    Xy, J., Li, M., Kim, D., Xu, Y.: RAPTOR: optimal protein threading by linear programming. J. Bioinform. Comput. Biol. 1(1), 95–117 (2003)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Artificial Intelligence Research Institute (IIIA-CSIC)BellaterraSpain
  2. 2.Department of Computer ScienceUniversidade Federal de Ouro PretoOuro PretoBrazil

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