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Title: Using simulated annealing and variable neighborhood search procedures for estimating the Hubbert diffusion process Authors:  Francisco Torres-Ruiz - University of Granada (Spain) [presenting]
Istoni da Luz-Sant-Ana - Federal Institute of Rio de Janeiro (Brazil)
Patricia Roman-Roman - Universidad de Granada (Spain)
Abstract: A problem of great current interest is how to accurately chart the progress of oil production. It is well known that oil exploration is cyclical and that after the oil production reaches its peak in a specific system, a fatal decline will begin. In this context, M.H. Hubbert developed his peak theory in 1956, based on a bell-shaped curve that bears his name. We consider a stochastic model, based on the theory of diffusion processes, associated with the Hubbert curve. The problem of the maximum likelihood estimation of the parameters for this process is also considered. Since a complex system of equation appears, whose solution cannot be guaranteed via the classical numerical procedures, we suggest the use of metaheuristic optimization algorithms such as Simulated Annealing and Variable Neighborhood Search. Some strategies are suggested for bounding the space of solutions, and a description is provided for the application of the algorithms selected. In the case of the Variable Neighborhood Search algorithm, a hybrid method is proposed in which it is combined with Simulated Annealing. In order to validate the theory developed here, we carry out some studies based on simulated data and consider some real scenarios from crude oil production data in Norway and Kazakhstan.