Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Abstract

Background: We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochasticdeterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.

Reaction Rate Constant Evaluation of Thermal Isomerization of α-Pinene

“…Rodriguez-Fernandez et al [5] studied the same kinetic model for the isomerization of α-pinene and applied a global optimization based on the Scatter Table 2 Table 2, it shows roughly 86%, 76%, 33%, 38%, and 28% higher values. This point is also mentioned by Rodriguez-Fernandez et al [5] that the confidence intervals obtained from the Fisher information matrix show a wider confidence interval.…”

“…This reaction produces four products that are presented in weight fraction in eight intervals each with duplicated results. Hunter et al [17] proposed a kinetic model for this reaction as it is shown in Figure 1 followed by Equations (1) to (5). In this scheme α-pinene (C 1 ) converts to dipentene (C 2 ) and allo-ocimen (C 3 ) in two parallel paths; dipentene is the end-point component but allo-ocimen yields α-and β-pyronene (C 4 ) and involves in an equilibrium reaction with other dimer compounds (C 5 ).…”

“…Kinetic model of the thermal isomerization of α-pinene where C 1 is α-pinene, C 2 is dipenetene, C 3 is allo-ocimene, C 4 is pyrone, and C 5 denotes for other dimer compounds [5]. …”

“…Classical gradient-based optimization methods such as gradient descent and evolutionary algorithms (EA) and Genetic algorithm are applied to minimize the square error between the measured and modeled data points. In an ill-conditioned system of equations, the gradient-based algorithms can trap in local minimums and are usually failed to find the global minimum error [5]. However, the EA methods result in a global optimum.…”

“…Yermakova et al [1] applied gradientbased Gauss-Marquardt iteration method for the kinetic model identification of the thermal isomerization of α-pinene and in order to overcome to the ill-conditioning conditions, they applied regularization techniques that can result in a biased estimation of reaction constants. Rodriguez-Fernandez et al [5] studied the same reaction system and successfully applied a global optimization based on the Scatter Search method and obtained the point estimate of rate constants and the global minimum of the least-square objective function. However, these approaches result in a point estimate of reaction rates without taking into account the uncertainty.…”