An Efficient Computational Procedure for Simultaneously Generating Alternatives to an Optimal Solution Using the Firefly Algorithm

  • Julian Scott YeomansEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 744)


In solving many “real world” mathematical programming applications, it is often preferable to formulate numerous quantifiably good approaches that provide distinct alternative solutions to the particular problem. This is because decision-making frequently involves complex problems possessing incompatible performance objectives and contain competing design requirements which prove very difficult—if not impossible—to capture and quantify at the time that the supporting decision models are actually formulated. There are invariably unmodelled design issues, not apparent at the time of model construction, which can greatly impact the acceptability of the model’s solutions. Consequently, it can prove preferable to generate numerous alternatives providing contrasting perspectives to the problem. These alternatives should be near-optimal with respect to the known modelled objective(s), but be fundamentally dissimilar from each other in terms of their decision variables. This solution approach has been referred to as modelling to generate-alternatives (MGA). This chapter provides an efficient computational procedure for simultaneously generating multiple different alternatives to an optimal solution using the Firefly Algorithm. The efficacy and efficiency of this approach will be illustrated using a two-dimensional, multimodal optimization test problem.


Firefly Algorithm Biologically-inspired metaheuristic Modelling-to-generate-alternatives 


  1. 1.
    Baugh, J.W., Caldwell, S.C., Brill, E.D.: A mathematical programming approach for generating alternatives in discrete structural optimization. Eng. Optim. 28(1), 1–31 (1997)CrossRefGoogle Scholar
  2. 2.
    Brill, E.D., Chang, S.Y., Hopkins, L.D.: Modelling to generate alternatives: the HSJ approach and an illustration using a problem in land use planning. Manag. Sci. 28(3), 221–235 (1982)CrossRefGoogle Scholar
  3. 3.
    Brugnach, M., Tagg, A., Keil, F., De Lange, W.J.: Uncertainty matters: computer models at the science-policy interface. Water Resour. Manage 21, 1075–1090 (2007)CrossRefGoogle Scholar
  4. 4.
    Gandomi, A.H., Yang, X.S., Alavi, A.H.: Mixed variable structural optimization using firefly algorithm. Comput. Struct. 89(23–24), 2325–2336 (2011)CrossRefGoogle Scholar
  5. 5.
    Imanirad, R., Yang, X.S., Yeomans, J.S.: A computationally efficient, biologically-inspired modelling-to-generate-alternatives method. J. Comput. 2(2), 43–47 (2012)Google Scholar
  6. 6.
    Imanirad, R., Yang, X.S., Yeomans, J.S.: A Co-evolutionary, Nature-Inspired Algorithm for the Concurrent Generation of Alternatives. J. Comput. 2(3), 101–106 (2012)Google Scholar
  7. 7.
    Imanirad, R., Yeomans, J.S.: Modelling to generate alternatives using biologically inspired algorithms. In: Yang, X.S. (ed.), Swarm Intelligence and Bio-Inspired Computation: Theory and Applications Elsevier, Amsterdam, Netherlands, pp. 313–333 (2013)Google Scholar
  8. 8.
    Imanirad, R., Yang, X.S., Yeomans, J.S.: Modelling-to-generate-alternatives via the firefly algorithm. J. Appl. Oper. Res. 5(1), 14–21 (2013)Google Scholar
  9. 9.
    Imanirad, R., Yang, X.S., Yeomans, J.S.: A concurrent modelling to generate alternatives approach using the firefly algorithm. Int. J. Decis. Support Syst. Technol. 5(2), 33–45 (2013)CrossRefGoogle Scholar
  10. 10.
    Imanirad, R., Yang, X.S., Yeomans, J.S.: A biologically-inspired metaheuristic procedure for modelling-to-generate-alternatives. Int. J. Eng. Res. Appl. 3(2), 1677–1686 (2013)Google Scholar
  11. 11.
    Janssen, J.A.E.B., Krol, M.S., Schielen, R.M.J., Hoekstra, A.Y.: The effect of modelling quantified expert knowledge and uncertainty information on model based decision making. Environ. Sci. Policy 13(3), 229–238 (2010)CrossRefGoogle Scholar
  12. 12.
    Loughlin, D.H., Ranjithan, S.R., Brill, E.D., Baugh, J.W.: Genetic algorithm approaches for addressing unmodeled objectives in optimization problems. Eng. Optim. 33(5), 549–569 (2001)CrossRefGoogle Scholar
  13. 13.
    Walker, W.E., Harremoes, P., Rotmans, J., Van der Sluis, J.P., Van Asselt, M.B.A., Janssen, P., Krayer von Krauss, M.P.: Defining uncertainty—a conceptual basis for uncertainty management in model-based decision support. Integr. Assess. 4(1), 5–17 (2003)CrossRefGoogle Scholar
  14. 14.
    Yang, X.S.: Firefly algorithms for multimodal optimization. Lecture Notes Comput. Sci. 5792, 169–178 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Yang, X.S.: Nature-Inspired Metaheuristic Algorithms 2nd Ed. Luniver Press, Frome UK (2010)Google Scholar
  16. 16.
    Yeomans, J.S., Gunalay, Y.: Simulation-optimization techniques for modelling to generate alternatives in waste management planning. J. Appl. Oper. Res. 3(1), 23–35 (2011)Google Scholar
  17. 17.
    Zechman, E.M., Ranjithan, S.R.: An evolutionary algorithm to generate alternatives (EAGA) for engineering optimization problems. Eng. Optim. 36(5), 539–553 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.OMIS Area, Schulich School of BusinessYork UniversityTorontoCanada

Personalised recommendations