Parameter Estimation in Neutral Delay Differential Equations Using Genetic Algorithm With Multi-Parent Crossover

Abstract

Neutral delay differential equations (NDDEs) are differential equations containing time lags not only in the states but also in the state derivatives. NDDEs have applications in modeling physical and biological systems. An NDDE model may consist of several parameters, some of which can be determined using available data. Various numerical techniques have been studied to estimate parameters of mathematical models. In this study, parameter estimation is posed as an optimization problem. The use of heuristic algorithms in parameter estimation has gained popularity because of its ease of implementation, requiring only function evaluations. But to our knowledge, heuristic algorithms have never been employed in estimating parameters in NDDE models. In this work, we apply Genetic Algorithm with Multi-Parent Crossover (GA-MPC) to obtain parameter estimates of three NDDE models with a discrete delay. We compare the estimates to those obtained using standard heuristic algorithms. Results show that GA-MPC is capable of consistently identifying model parameters that provide a good fit of the model to the data.

Keywords

• Neutral delay differential equations
• parameter estimation
• genetic algorithm
• bootstrapping
• inverse problem
• heuristic algorithms