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Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty

Author

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  • Ivan Contreras

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain)

  • Remei Calm

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain)

  • Miguel A. Sainz

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain)

  • Pau Herrero

    (Centre for Bio-Inspired Technology, Imperial College London, London SW7 2AZ, UK)

  • Josep Vehi

    (Modeling, Identification and Control Engineering (MICELab) Research Group, Institut d’Informatica i Aplicacions, Universitat de Girona, 17003 Girona, Spain
    Centro de Investigación Biomédica en Red de Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM), 17003 Girona, Spain)

Abstract

Complex systems are usually affected by various sources of uncertainty, and it is essential to account for mechanisms that ensure the proper management of such disturbances. This paper introduces a novel approach to solve symbolic regression problems, which combines the potential of Grammatical Evolution to obtain solutions by describing the search space with context-free grammars, and the ability of Modal Interval Analysis (MIA) to handle quantified uncertainty. The presented methodology uses an MIA solver to evaluate the fitness function, which represents a novel method to manage uncertainty by means of interval-based prediction models. This paper first introduces the theory that establishes the basis of the proposed methodology, and follows with a description of the system architecture and implementation details. Then, we present an illustrative application example which consists of determining the outer and inner approximations of the mean velocity of the water current of a river stretch. Finally, the interpretation of the obtained results and the limitations of the proposed methodology are discussed.

Suggested Citation

  • Ivan Contreras & Remei Calm & Miguel A. Sainz & Pau Herrero & Josep Vehi, 2021. "Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:631-:d:517991
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    References listed on IDEAS

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    1. Baraldi, Piero & Podofillini, Luca & Mkrtchyan, Lusine & Zio, Enrico & Dang, Vinh N., 2015. "Comparing the treatment of uncertainty in Bayesian networks and fuzzy expert systems used for a human reliability analysis application," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 176-193.
    2. Anthony Brabazon & Michael O’Neill, 2004. "Evolving technical trading rules for spot foreign-exchange markets using grammatical evolution," Computational Management Science, Springer, vol. 1(3), pages 311-327, October.
    3. Hossein Karshenas & Concha Bielza & Pedro Larrañaga, 2015. "Interval-based ranking in noisy evolutionary multi-objective optimization," Computational Optimization and Applications, Springer, vol. 61(2), pages 517-555, June.
    4. Shary, Sergey P., 1995. "Solving the linear interval tolerance problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 53-85.
    5. Iván Contreras & Silvia Oviedo & Martina Vettoretti & Roberto Visentin & Josep Vehí, 2017. "Personalized blood glucose prediction: A hybrid approach using grammatical evolution and physiological models," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-16, November.
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