Understanding the Impact of Constraints: A Rank Based Fitness Function for Evolutionary Methods

  • Eric S. FragaEmail author
  • Oluwamayowa Amusat
Part of the Springer Optimization and Its Applications book series (SOIA, volume 107)


There are design problems where some constraints may be considered objectives as in “It would be great if the solution we obtained had this characteristic.” In such problems, solutions obtained using multi-objective optimisation may help the decision maker gain insight into what is achievable without fully satisfying one of these constraints. A novel fitness function is introduced into a multi-objective population based evolutionary optimisation method, based on a plant propagation algorithm extended to multi-objective optimisation. The optimisation method is implemented and applied to the design of off-grid integrated energy systems for large scale mining operations where the aim is to use local renewable energy generation, coupled with energy storage, to eliminate the need for transporting fuel over large distances. The latter is a desired property and in this chapter is treated as a separate objective. The results presented show that the fitness function provides the desired selection pressure and, when combined with the multi-objective plant propagation algorithm, is able to find good designs that achieve the desired constraint simultaneously.


Multi-objective optimization evolutionary methods plant propagationalgorithm process design integrated energy systems Pareto extremes 



The authors would like to acknowledge the funding provided by the Nigerian government through the Presidential Scholarship for Innovation and Development (PRESSID) scheme.


  1. 1.
    Amusat, O., Shearing, P., Fraga, E.S.: Optimal integrated energy systems design incorporating variable renewable energy sources. In: Roskilly, T., Rajendran, K., Ling-Chin, J. (eds.) Proceedings of Sustainable Thermal Energy Management (SusTEM), pp. 245–253 (2015)Google Scholar
  2. 2.
    Amusat, O., Shearing, P., Fraga, E.S.: System design of renewable energy generation and storage alternatives for large scale continuous processes. In: Gernaey, K.V., Huusom, J.K., Gani, R. (eds.) 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering, pp. 2279–2284. Elsevier B.V., Amsterdam (2015)CrossRefGoogle Scholar
  3. 3.
    Coello Coello, C.A., Landa Becerra, R.: Evolutionary multiobjective optimization in materials science and engineering. Mater. Manuf. Process. 24 (2), 119–129 (2009)Google Scholar
  4. 4.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)CrossRefzbMATHGoogle Scholar
  5. 5.
    Fiandaca, G., Fraga, E.S., Brandani, S.: A multi-objective genetic algorithm for the design of pressure swing adsorption. Eng. Optim. 41 (9), 833–854 (2009)CrossRefGoogle Scholar
  6. 6.
    Merrikh-Bayat, F.: The runner-root algorithm: a metaheuristic for solving unimodal and multimodal optimization problems inspired by runners and roots of plants in nature. Appl. Soft Comput. 33, 292–303 (2015)CrossRefGoogle Scholar
  7. 7.
    Osborn, J., Kawann, C.: Reliability of the US electricity system: Recent trends and current issues. Technical Report, Energy Analysis Department, Ernest Orlando Lawrence Berkeley National Laboratory, LBNL-47043, Berkeley (2001)Google Scholar
  8. 8.
    Pardalos, P.M., Žilinskas, A., Žilinskas, J.: Non-Convex Multi-Objective Optimization. Springer, New York (2016)zbMATHGoogle Scholar
  9. 9.
    Salhi, A., Fraga, E.S.: Nature-inspired optimisation approaches and the new plant propagation algorithm. In: Proceedings of ICeMATH 2011, The International Conference on Numerical Analysis and Optimization, Yogyakarta, pp. K2:1–8 (2011)Google Scholar
  10. 10.
    Törn, A., Žilinskas, A.: Global Optimization. Springer, Berlin (1989)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Process Systems Engineering, Department of Chemical EngineeringUniversity College LondonLondonUK

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