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A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search

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  • Román-Román, P.
  • Torres-Ruiz, F.

Abstract

A stochastic diffusion model related to a reformulation of the Richards growth curve is proposed. The main characteristics of the process are studied, and the problem of maximum likelihood estimation for the parameters of the process is considered. Since a complex system of equations appears whose solution cannot be guaranteed via the classic numerical procedures, we suggest the use of metaheuristic optimization algorithms such as simulated annealing and variable neighborhood search. Given that the space of solutions is continuous and unbounded, some strategies are suggested for bounding it, and a description is provided for the application of the selected algorithms. In the case of the variable neighborhood search algorithm, a hybrid method is proposed in which it is combined with simulated annealing. Some examples based on simulated sample paths are developed in order to test the validity of the bounding method for the space of solutions, and a comparison is made between the application of both methods.

Suggested Citation

  • Román-Román, P. & Torres-Ruiz, F., 2015. "A stochastic model related to the Richards-type growth curve. Estimation by means of simulated annealing and variable neighborhood search," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 579-598.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:579-598
    DOI: 10.1016/j.amc.2015.05.096
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    References listed on IDEAS

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    1. Kahm, Matthias & Hasenbrink, Guido & Lichtenberg-Fraté, Hella & Ludwig, Jost & Kschischo, Maik, 2010. "grofit: Fitting Biological Growth Curves with R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i07).
    2. Vera, J. Fernando & Di­az-Garci­a, Jose A., 2008. "A global simulated annealing heuristic for the three-parameter lognormal maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5055-5065, August.
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    Cited by:

    1. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "T-Growth Stochastic Model: Simulation and Inference via Metaheuristic Algorithms," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    2. Antonio Barrera & Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Two Multi-Sigmoidal Diffusion Models for the Study of the Evolution of the COVID-19 Pandemic," Mathematics, MDPI, vol. 9(19), pages 1-29, September.
    3. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    4. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    5. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    6. Nafidi, Ahmed & El Azri, Abdenbi, 2021. "A stochastic diffusion process based on the Lundqvist–Korf growth: Computational aspects and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 25-38.
    7. Antonio Di Crescenzo & Paola Paraggio & Patricia Román-Román & Francisco Torres-Ruiz, 2023. "Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean," Statistical Papers, Springer, vol. 64(5), pages 1391-1438, October.
    8. Nafidi, A. & Bahij, M. & Achchab, B. & Gutiérrez-Sanchez, R., 2019. "The stochastic Weibull diffusion process: Computational aspects and simulation," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 575-587.

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