Abstract
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.
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References
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)
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)
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)
Gandomi, A.H., Yang, X.S., Alavi, A.H.: Mixed variable structural optimization using firefly algorithm. Comput. Struct. 89(23–24), 2325–2336 (2011)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Yang, X.S.: Firefly algorithms for multimodal optimization. Lecture Notes Comput. Sci. 5792, 169–178 (2009)
Yang, X.S.: Nature-Inspired Metaheuristic Algorithms 2nd Ed. Luniver Press, Frome UK (2010)
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)
Zechman, E.M., Ranjithan, S.R.: An evolutionary algorithm to generate alternatives (EAGA) for engineering optimization problems. Eng. Optim. 36(5), 539–553 (2004)
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Yeomans, J.S. (2018). An Efficient Computational Procedure for Simultaneously Generating Alternatives to an Optimal Solution Using the Firefly Algorithm. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_12
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DOI: https://doi.org/10.1007/978-3-319-67669-2_12
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