Grey Wolf Optimizer for Parameter Estimation of Enzymatic Reaction in Biodiesel Synthesis

Abstract

Computational models are used to help us to understand the mechanisms of a complex process in nature. Before building the model, we need to know the characteristic of samples which are described in the form of measure named parameters. Usually, the value of parameters is unknown and we need to investigate those value to know the compatibility between the artificial model and real circumstances. Many optimization methods have been introduced to estimate those parameters, but some of them meet the difficulties caused by the nonlinear type of function model. Many objective functions of the estimation parameter are multimodal, high dimensional, and have many local optima, so the estimation process using traditional optimization method is not suggested. In this article, we use Grey Wolf Optimizer (GWO), as one of the metaheuristic artificial intelligence algorithm, which is inspired by leadership hierarchy and hunting behavior of a pack of wolves. GWO is applied to estimate the parameters in a model of enzymatic reaction in biodiesel synthesis. Biodiesel is renewable fuel that can solve the energy crisis and pollution. While the process of biodiesel synthesis occurs, some enzyme in the biodiesel substances react to each other and it can be modeled into ODEs (Ordinary Differential Equations) system. The kinetic parameters inside them are needed to be estimated. After the parameter are estimated, the fourth-order Runge-Kutta method is used to solve the system. The result is evaluated by analyzing the objective function which minimizes the Sum of Squared Errors (SSE). The small value of SSE and the narrow range of both parameter of model and estimation shows that GWO is effective to be the proposed method for parameter estimation and model selection problems.