Infeasibility Driven Evolutionary Algorithm for Constrained Optimization

  • Tapabrata Ray
  • Hemant Kumar Singh
  • Amitay Isaacs
  • Warren Smith
Part of the Studies in Computational Intelligence book series (SCI, volume 198)


Real life optimization problems often involve one or more constraints and in most cases, the optimal solutions to such problems lie on constraint boundaries. The performance of an optimization algorithm is known to be largely dependent on the underlying mechanism of constraint handling. Most population based stochastic optimization methods prefer a feasible solution over an infeasible solution during their course of search. Such a preference drives the population to feasibility first before improving its objective function value which effectively means that the solutions approach the constraint boundaries from the feasible side of the search space. In this chapter, we introduce an evolutionary algorithm that explicitly maintains a small percentage of infeasible solutions close to the constraint boundaries during its course of evolution. The presence of marginally infeasible solutions in the population allows the algorithm to approach the constraint boundary from the infeasible side of the search space in addition to its approach from the feasible side of the search space via evolution of feasible solutions. Furthermore, “good” infeasible solutions are ranked higher than the feasible solutions, thereby focusing the search for the optimal solutions near the constraint boundaries. The performance of the proposed algorithm is compared with Non-dominated Sorting Genetic Algorithm II (NSGA-II) on a set of single and multi-objective test problems. The results clearly indicate that the rate of convergence of the proposed algorithm is better than NSGA-II on the studied test problems. Additionally, the algorithm provides a set of marginally infeasible solutions which are of great use in trade-off studies.


Evolutionary Algorithm Constrained Handling Multi-objective Optimization NSGA-II 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bandyopadhyay, S., Saha, S., Maulik, U., Deb, K.: A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Transactions on Evolutionary Computation 12(3), 269–283 (2008)CrossRefGoogle Scholar
  2. 2.
    Bean, J.C., Hadj-Alouane, A.B.: A Dual Genetic Algorithm for Bounded Integer Programs. Technical Report TR 92-53, Department of Industrial and Operations Engineering, The University of Michigan (1992)Google Scholar
  3. 3.
    Coello Coello, C.A.: Constraint-handling using an evolutionary multiobjective optimization technique. Civil engineering and environmental systems 17(4), 319–346 (2000)CrossRefGoogle Scholar
  4. 4.
    Coello Coello, C.A.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191(11-12), 1245–1287 (2002)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Collette, Y., Siarry, P.: Multiobjective optimization Principles and Case Studies. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Czyzak, P., Jaszkiewicz, A.: Pareto simulated annealing - a metaheuristic techinique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis 7(1), 34–47 (1998)MATHCrossRefGoogle Scholar
  7. 7.
    Davis, L. (ed.): Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)Google Scholar
  8. 8.
    Deb, K.: An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering 186(2/4), 311–338 (2000)MATHCrossRefGoogle Scholar
  9. 9.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley and Sons Pvt. Ltd., Chichester (2001)MATHGoogle Scholar
  10. 10.
    Deb, K., Agrawal, S.: Simulated binary crossover for continuous search space. Complex Systems 9, 115–148 (1995)MATHMathSciNetGoogle Scholar
  11. 11.
    Deb, K., Goyal, M.: A combined genetic adaptive search (GeneAS) for engineering design. Computer Science and Informatics 26, 30–45 (1996)Google Scholar
  12. 12.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)CrossRefGoogle Scholar
  13. 13.
    Hadj-Alouane, A.B., Bean, J.C.: A Genetic Algorithm for the Multiple-Choice Integer Program. Operations Research 45, 92–101 (1997)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hamida, S.B., Schoenauer, M.: An adaptive algorithm for constrained optimization problems. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 529–538. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Hamida, S.B., Schoenauer, M.: ASCHEA: new results using adaptive segregational constraint handling. In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 884–889 (May 2002)Google Scholar
  16. 16.
    Hedar, A., Fukushima, M.: Derivative-free filter simulated annealing method for constrained continuous global optimization. Journal of Global Optimization 35(4), 291–308 (2006)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Hinterding, R., Michalewicz, Z.: Your brains and my beauty: parent matching for constrained optimisation. In: Proceedings of 1998 IEEE Conference on Evolutionary Computaion, May 1998, pp. 810–815 (1998)Google Scholar
  18. 18.
    Ho, P.Y., Shimizu, K.: Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Information Sciences 177, 2985–3004 (2007)CrossRefGoogle Scholar
  19. 19.
    Hoffmeister, F., Sprave, J.: Problem-independent handling of constraints by use of metric penalty functions. In: Fogel, L.J., Angeline, P.J., Bäck, T. (eds.) Proceedings of the Fifth Annual Conference on Evolutionary Programming (EP 1996), San Diego, California, February 1996, pp. 289–294. MIT Press, Cambridge (1996)Google Scholar
  20. 20.
    Homaifar, A., Lai, S.H.Y., Qi, X.: Constrained Optimization via Genetic Algorithms. Simulation 62(4), 242–254 (1994)CrossRefGoogle Scholar
  21. 21.
    Isaacs, A., Ray, T., Smith, W.: Blessings of maintaining infeasible solutions for constrained multi-objective optimization problems. In: Proceedings of 2008 IEEE Congress on Evolutionary Computation, Hong Kong, June 2008, pp. 2785–2792 (2008)Google Scholar
  22. 22.
    Ishibuchi, H., Yoshida, T., Murata, T.: Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Transactions on Evolutionary Computing 7(2), 204–223 (2003)CrossRefGoogle Scholar
  23. 23.
    Joines, J., Houck, C.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Fogel, D. (ed.) Proceedings of the first IEEE Conference on Evolutionary Computation, Orlando, Florida, pp. 579–584. IEEE Press, Los Alamitos (1994)CrossRefGoogle Scholar
  24. 24.
    Koziel, S., Michalewicz, Z.: Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation 7(1), 19–44 (1999)CrossRefGoogle Scholar
  25. 25.
    Kuri-Morales, A., Quezada, C.V.: A Universal Eclectic Genetic Algorithm for Constrained Optimization. In: Proceedings 6th European Congress on Intelligent Techniques & Soft Computing, EUFIT 1998, Aachen, Germany, September 1998, pp. 518–522. Verlag Mainz (1998)Google Scholar
  26. 26.
    Mezura-Montes, E., Coello Coello, C.: A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Transactions on Evolutionary Computation 9(1), 1–17 (2005)CrossRefGoogle Scholar
  27. 27.
    Mezura-Montes, E., Coello Coello, C.A.: Constrained Optimization via Multiobjective Evolutionary Algorithms. In: Knowles, J., Corne, D., Deb, K. (eds.) Multiobjective Problems Solving from Nature: From Concepts to Applications. Natural Computing Series. Springer, Heidelberg (2008)Google Scholar
  28. 28.
    Michalewicz, Z.: Genetic Algorithms, Numerical Optimization, and Constraints. In: Eshelman, L.J. (ed.) Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA 1995), July 1995, pp. 151–158. University of Pittsburgh, Morgan Kaufmann Publishers (1995)Google Scholar
  29. 29.
    Michalewicz, Z.: A Survey of Constraint Handling Techniques in Evolutionary Computation Methods. In: McDonnell, J.R., Reynolds, R.G., Fogel, D.B. (eds.) Proceedings of the 4th Annual Conference on Evolutionary Programming, pp. 135–155. The MIT Press, Cambridge (1995)Google Scholar
  30. 30.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)MATHGoogle Scholar
  31. 31.
    Michalewicz, Z., Attia, N.F.: Evolutionary Optimization of Constrained Problems. In: Proceedings of the 3rd Annual Conference on Evolutionary Programming, pp. 98–108. World Scientific, Singapore (1994)Google Scholar
  32. 32.
    Michalewicz, Z., Nazhiyath, G.: Genocop III: A co-evolutionary algorithm for numerical optimization with nonlinear constraints. In: Fogel, D.B. (ed.) Proceedings of the Second IEEE International Conference on Evolutionary Computation, pp. 647–651. IEEE Press, Los Alamitos (1995)CrossRefGoogle Scholar
  33. 33.
    Michalewicz, Z., Schoenauer, M.: Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation 4(1), 1–32 (1996)CrossRefGoogle Scholar
  34. 34.
    Michalewicz, Z., Xiao, J.: Evaluation of Paths in Evolutionary Planner/Navigator. In: Proceedings of the 1995 International Workshop on Biologically Inspired Evolutionary Systems, Tokyo, Japan, May 1995, pp. 45–52 (1995)Google Scholar
  35. 35.
    Powell, D., Skolnick, M.M.: Using genetic algorithms in engineering design optimization with non-linear constraints. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA 1993), San Mateo, California, July 1993, pp. 424–431. University of Illinois at Urbana-Champaign, Morgan Kaufmann Publishers (1993)Google Scholar
  36. 36.
    Ray, T., Tai, K., Seow, K.: Multiobjective design optimization by an evolutionary algorithm. Engineering Optimization 33(4), 399–424 (2001)CrossRefGoogle Scholar
  37. 37.
    Singh, H., Isaacs, A., Ray, T., Smith, W.: A simulated annealing algorithm for constrained multi-objective optimization. In: Proceedings of 2008 IEEE Congress on Evolutionary Computation, Hong Kong, June 2008, pp. 1655–1662 (2008)Google Scholar
  38. 38.
    Surry, P.D., Radcliffe, N.J.: The COMOGA method: Constrained optimisation by multi-objective genetic algorithms. Control and Cybernetics 26(3) (1997)Google Scholar
  39. 39.
    Takahama, T., Sakai, S.: Constrained optimization by applying the /spl alpha/ constrained method to the nonlinear simplex method with mutations. IEEE Transactions on Evolutionary Computation 9(5), 437–451 (2005)CrossRefGoogle Scholar
  40. 40.
    Vieira, D.A.G., Adriano, R.L.S., Krahenbuhl, L., Vasconcelos, J.A.: Handing constraints as objectives in a multiobjective genetic based algorithm. Journal of Microwaves and Optoelectronics 2(6), 50–58 (2002)Google Scholar
  41. 41.
    Vieira, D.A.G., Adriano, R.L.S., Vasconcelos, J.A., Krahenbuhl, L.: Treating constraints as objectives in multiobjective optimization problems using niched pareto genetic algorithm. IEEE Transactions on Magnetics 40(2) (March 2004)Google Scholar
  42. 42.
    Wang, Y., Cai, Z., Guo, G., Zhou, Y.: Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 37(3), 560–575 (2007)CrossRefGoogle Scholar
  43. 43.
    Xiao, J., Michalewicz, Z., Trojanowski, K.: Adaptive Evolutionary Planner/Navigator for Mobile Robots. IEEE Transactions on Evolutionary Computation 1(1), 18–28 (1997)CrossRefGoogle Scholar
  44. 44.
    Xiao, J., Michalewicz, Z., Zhang, L.: Evolutionary Planner/Navigator: Operator Performance and Self-Tuning. In: Proceedings of the 3rd IEEE International Conference on Evolutionary Computation, Nagoya, Japan, May 1996. IEEE Press, Los Alamitos (1996)Google Scholar
  45. 45.
    Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Shaker Verlag, Germany (1999)Google Scholar
  46. 46.
    Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms - A comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tapabrata Ray
    • 1
  • Hemant Kumar Singh
    • 1
  • Amitay Isaacs
    • 1
  • Warren Smith
    • 1
  1. 1.Australian Defence Force AcademyUniversity of New South WalesCanberraAustralia

Personalised recommendations