Parameter estimation in S-System Models using Firefly Algorithm with Decoupling Method


by: Raquel C. Cajayon, Carlene P.C. Pilar-Arceo, Eduardo R. Mendoza


An essential element for describing and predicting the dynamic behavior of interacting components within a biochemical system is the formulation of mathematical models. One of the widely used mathematical models is the power-law formalism-based S-systems. However, parameter estimation in S-systems continues to be a difficult challenge because of the nonlinearity and high dimensionality of the underlying coupled systems of ordinary differential equations. Hence it is important to provide efficient and effective novel methods to tackle parameter estimation problem. In this paper, we use decoupling technique on the S-system and then Xin- She Yang’s Firefly Algorithm (FA), a metaheuristic algorithm based on the bioluminescence process which characterizes fireflies, as optimization algorithm in the parameter estimation. FA’s automatic subdivision of the whole population into subgroups and natural capability of dealing with multi-modal optimization are the two major advantages of FA over other algorithms, making FA a good algorithm choice. Using three S-systems of increasing complexity from the MADMan Benchmarking Framework, we assess the performance of the method. Simulation results show that FA-decoupling method is applicable in estimating parameters of the 3 S-system models using noise-free data with concentration error lower than 10-3 and better approximations were recorded for kinetic orders than rate constants. Since FA-decoupling method worked on parameter estimation of S-system models using noise-free data, it is now reasonable to implement the method using datasets with different noise levels to check how the method is affected by the presence of noise.