Solving Dynamic Optimisation Problems with Known Changeable Boundaries

  • AbdelMonaem F. M. AbdAllahEmail author
  • Daryl L. Essam
  • Ruhul A. Sarker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9592)


Dynamic optimisation problems (DOPs) have become a challenging research topic over the last two decades. In DOPs, at least one part of the problem changes as time passes. These changes may take place in the objective function(s) and/or constraint(s). In this paper, we propose a new type of DOP in which the boundaries of variables change as time passes. This is called a single objective unconstrained dynamic optimisation problem with known changeable boundaries (DOPKCBs). To solve DOPKCBs, we propose three repair strategies. These algorithms have been compared with other repairing techniques from the literature that have been previously used in static problems. In this paper, the results of the conducted experiments and the statistical analysis generally demonstrated that one of the proposed strategies, which uses the overall elite individual (OEI) as a repair strategy, obtained much better results than the other strategies.


Changeable boundaries Dynamic optimisation Genetic algorithm Overall elite individual Repair strategy 


  1. 1.
    Gendreau, M., Potvin, J.-Y., Bräysy, O., Hasle, G., Løkketangen, A.: Metaheuristics for the vehicle routing problem and extensions: a categorized bibliography. In: Golden, B., Raghavan, S., Wasil, E. (eds.) The Vehicle Routing Problem: Latest Advances and New Challenges. Springer, New York (2008)Google Scholar
  2. 2.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006)zbMATHGoogle Scholar
  3. 3.
    Miettinen, K., Ruiz, F., Wierzbicki, A.P.: Introduction to multiobjective optimization: interactive approaches. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 27–57. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Bandyopadhyay, S., Saha, S.: some single - and multiobjective optimization techniques. In: Unsupervised Classification, pp. 17–58. Springer, Heidelberg (2013)Google Scholar
  5. 5.
    Dadkhah, K.: Static optimization. In: Foundations of Mathematical and Computational Economics, pp. 323–346. Springer, Berlin (2011)Google Scholar
  6. 6.
    Branke, J.: Evolutionary Optimization in Dynamic Environments. Kluwer, Dordrecht (2001)Google Scholar
  7. 7.
    Nguyen, T.T., Yangb, S., Branke, J.: Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evol. Comput. 6, 1–24 (2012)CrossRefGoogle Scholar
  8. 8.
    Cruz, C., González, J.R., Pelta, D.A.: Optimization in dynamic environments: a survey on problems, methods and measures. Soft. Comput. 15, 1427–1448 (2011)CrossRefGoogle Scholar
  9. 9.
    Wen-Jun, Z., Xiao-Feng, X., De-Chun, B.: Handling boundary constraints for numerical optimization by particle swarm flying in periodic search space. In: Congress on Evolutionary Computation, CEC 2004, vol. 2302, pp. 2307–2311 (2004)Google Scholar
  10. 10.
    Shi, C., Yuhui, S., Quande, Q.: Experimental study on boundary constraint handling in particle swarm optimization: from population diversity perspective. In: Yuhui, S. (ed.) Recent Algorithms and Applications in Swarm Intelligence Research, pp. 96–124. IGI Global, Hershey (2013)CrossRefGoogle Scholar
  11. 11.
    Padhye, N., Deb, K., Mittal, P.: An Efficient and Exclusively-Feasible Constrained Handling Strategy for Evolutionary Algorithms. Technical Report (2013)Google Scholar
  12. 12.
    Yang, S.: Genetic algorithms with memory- and elitism-based immigrants in dynamic environments. Evol. Comput. 16, 385–416 (2008)CrossRefGoogle Scholar
  13. 13.
    Branke, J., Schmeck, H.: Designing evolutionary algorithms for dynamic optimization problems. In: Advances in Evolutionary Computing: Theory and Applications, pp. 239–262. Springer, Heidelberg (2003)Google Scholar
  14. 14.
    Cobb, H.G.: An investigation into the use of hypermutation as an adaptive operator in genetic algorithms having continuous, time-dependent nonstationary environments. Naval Research Laboratory (1990)Google Scholar
  15. 15.
    Goh, C.-K., Chen Tan, K.: A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans. Evol. Comput. 13, 103–127 (2009)CrossRefGoogle Scholar
  16. 16.
    Grefenstette, J.J.: Genetic algorithms for changing environments. In: Maenner, R., Manderick, B. (eds.) Parallel Problem Solving from Nature, vol. 2, pp. 137–144. North Holland, Amsterdam (1992)Google Scholar
  17. 17.
    Yang, S., Yao, X.: Experimental study on population-based incremental learning algorithms for dynamic optimization problems. Soft. Comput. 9, 815–834 (2005)CrossRefzbMATHGoogle Scholar
  18. 18.
    Nguyen, T.T., Yang, S., Branke, J., Yao, X.: Evolutionary dynamic optimization: methodologies. In: Yang, S., Yao, X. (eds.) Evolutionary Computation for DOPs. SCI, vol. 490, pp. 39–63. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  19. 19.
    Branke, J.: Memory enhanced evolutionary algorithms for changing optimization problems. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 1883, p. 1882 (1999)Google Scholar
  20. 20.
    Moser, I., Chiong, R.: Dynamic function optimization: the moving peaks benchmark. In: Alba, E., Nakib, A., Siarry, P. (eds.) Metaheuristics for Dynamic Optimization. SCI, vol. 433, pp. 37–62. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  21. 21.
    Li, C., Yang, S.: A generalized approach to construct benchmark problems for dynamic optimization. In: Li, X., et al. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 391–400. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Liang, J.J., Suganthan, P.N., Deb, K.: Novel composition test functions for numerical global optimization. In: Proceedings 2005 IEEE, Swarm Intelligence Symposium, SIS 2005, pp. 68–75. (2005)Google Scholar
  23. 23.
    Li, C., Yang, S., Nguyen, T.T., Yu, E.L., Yao, X., Jin, Y., Beyer, H.-G., Suganthan, P.N.: Benchmark Generator for CEC 2009 Competition on Dynamic Optimization (2008)Google Scholar
  24. 24.
    Morrison, R.W.: Performance measurement in dynamic environments. In: GECCO Workshop on Evolutionary Algorithms for Dynamic Optimization Problems, pp. 5–8 (2003)Google Scholar
  25. 25.
    Yang, S., Nguyen, T.T., Li, C.: Evolutionary dynamic optimization: test and evaluation environments. In: Yang, S., Yao, X. (eds.) Evolutionary Computation for DOPs. SCI, vol. 490, pp. 3–37. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  26. 26.
    García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization. J. Heuristics 15, 617–644 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • AbdelMonaem F. M. AbdAllah
    • 1
    Email author
  • Daryl L. Essam
    • 1
  • Ruhul A. Sarker
    • 1
  1. 1.School of Engineering and Information TechnologyUniversity of New South Wales, (UNSW@ADFA)CanberraAustralia

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