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Cuckoo search and firefly algorithms in terms of generalized net theory

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Abstract

In the presented paper, the functioning and the results of the work of two metaheuristic algorithms, namely cuckoo search algorithm (CS) and firefly algorithm (FA), are described using the apparatus of generalized nets (GNs), which is an appropriate and efficient tool for describing the essence of various optimization methods. The two developed GN-models mimic the optimization processes based on the nature of cuckoos and fireflies, respectively. The proposed GN-models execute the two considered metaheuristic algorithms conducting basic steps and performing optimal search. Building upon these two GN-models, a universal GN-model is constructed that can be used for describing and simulating both the CS and the FA by setting different characteristic functions of the GN-tokens. Moreover, the universal GN-model itself can be transformed to each of the herewith presented GN-models by applying appropriate hierarchical operators. In order to validate the proposed universal GN-model, numerical experiments are performed for the operating of the universal GN-model (CS and FA) on benchmark mathematical functions. The obtained results are compared with the results of the GN-model of CS, GN-model of FA, as well as the results of the standard CS and FA.

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Acknowledgements

The work presented here is partially supported by the National Scientific Fund of Bulgaria under Grant DN02/10 “New Instruments for Knowledge Discovery from Data, and their Modelling” (D. Zoteva and K. Atanassov) and by the Program for career development of young scientists, BAS, Grant DFNP-17-136/2017 (O. Roeva and V. Atanassova). This research work did not receive funding.

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Authors and Affiliations

  1. Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Olympia Roeva, Dafina Zoteva, Vassia Atanassova & Krassimir Atanassov

  2. Tijuana Institute of Technology, Tijuana, BC, Mexico

    Oscar Castillo

Authors
  1. Olympia Roeva
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  2. Dafina Zoteva
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  3. Vassia Atanassova
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  4. Krassimir Atanassov
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  5. Oscar Castillo
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Correspondence to Oscar Castillo.

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Roeva, O., Zoteva, D., Atanassova, V. et al. Cuckoo search and firefly algorithms in terms of generalized net theory. Soft Comput 24, 4877–4898 (2020). https://doi.org/10.1007/s00500-019-04241-7

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  • DOI: https://doi.org/10.1007/s00500-019-04241-7

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