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

• For a Richards-type curve a diffusion process is constructed.
• The distribution and main characteristics of the process are analyzed.
• The estimation of the parameters is addressed by maximum likelihood.
• A procedure for bounding the parametric space is established.
• VND and SA algorithms are used for estimating the parameters.

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.