Boundary Search for Constrained Numerical Optimization Problems in ACO Algorithms

  • Guillermo Leguizamón
  • Carlos A. Coello Coello
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4150)


This paper presents a novel boundary approach which is included as a constraint-handling technique in an ant colony algorithm. The necessity of approaching the boundary between the feasible and infeasible search space for many constrained optimization problems is a paramount challenge for every constraint-handling technique. Our proposed technique precisely focuses the search on the boundary region and can be either used alone or in combination with other constraint-handling techniques depending on the type and number of problem constraints. For validation purposes, an ant algorithm is adopted as our search engine. We compare our proposed approach with respect to constraint-handling techniques that are representative of the state-of-the-art in constrained evolutionary optimization using a set of standard test functions.


Search Space Equality Constraint Constrain Optimization Problem Active Constraint Penalty Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bilchev, G., Parmee, I.C.: The ant colony metaphor for searching continuous design spaces. In: Fogarty, T.C. (ed.) AISB-WS 1995. LNCS, vol. 993, pp. 25–39. Springer, Heidelberg (1995)Google Scholar
  2. 2.
    Ling, C., Jie, S., Ling, Q., Hongjian, C.: A method for solving optimization problems in continuous space using ant colony algorithm. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 288–289. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Lei, W., Qidi, W.: Further example study on ant system algorithm based continuous space optimization. In: Proceedings of the 4th Congress on Intelligent and Automation, Shangai, P.R. China, pp. 2541–2545 (2002)Google Scholar
  4. 4.
    Pourtakdoust, S.H., Nobahari, H.: An extension of ant colony systems to continuos optimization problems. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds.) ANTS 2004. LNCS, vol. 3172, pp. 294–301. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Michalewicz, Z., Nazhiyath, G., Michalewicz, M.: A note on usefulness of geometrical crossover for numerical optimization problems. In: L.J.F., et al. (ed.) Proceedings of the Fifth Annual Conference on Evolutionary Programming, pp. 305–311. MIT Press, Cambridge (1996)Google Scholar
  6. 6.
    Keane, A.: Genetic algorithms digest, 8(16) (1994)Google Scholar
  7. 7.
    Schoenauer, M., Michalewicz, Z.: Evolutionary computation at the edge of feasibility. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 245–254. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  8. 8.
    Wu, Z., Simpson, A.: A self-adaptive boundary search genetic algorithm and its application to water distribution systems. Journal of Hidraulic Research 40(2), 191–203 (2002)CrossRefGoogle Scholar
  9. 9.
    Corne, D., Dorigo, M., Glover, F. (eds.): New Ideas in Optimization. McGraw-Hill International, New York (1999)Google Scholar
  10. 10.
    Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4(3), 284–294 (2000)CrossRefGoogle Scholar
  11. 11.
    Hamida, S.B., Schoenauer, M.: ASCHEA: New Results Using Adaptive Segregational Constraint Handling. In: Proceedings of the Congress on Evolutionary Computation 2002 (CEC 2002), Piscataway, New Jersey, vol. 1, pp. 884–889. IEEE Service Center (2002)Google Scholar
  12. 12.
    Liang, J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C., Deb, K.: Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. Technical report, School of Electrical and Electronic Engineering Nanyang Technological University, Singapore (2006),

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Guillermo Leguizamón
    • 1
  • Carlos A. Coello Coello
    • 2
  1. 1.LIDICUniversidad Nacional de San LuisSan LuisArgentina
  2. 2.Electrical Engineering Department, Computer Science SectionEvolutionary Computation Group (EVOCINV) at CINVESTAV-IPNMéxico D.F.México

Personalised recommendations