International Journal of Environmental Science and Development

Abstract—The calibration of a comprehensive mathematical model describing algal dynamics in batch reactors has been attempted. The mathematical model consisted of 29 variables and 40 parameters and was described by 29 stiff differential equations. Of the 40 parameters values, 23 values are not known with certainty and hence need to be adjusted to obtain a good fit between the model simulations and experimental data. Three sets of experimental data were available for model calibration. Each set of data consisted of time series on evaluation of seven variables. Objective was to manipulate the values of the adjustable parameters in the model such that model simulations fit all three sets of experimental data simultaneously with minimum error. The above proposition was formulated as a multi-objective optimization problem and solved using a genetic algorithm called NSGA-II. The code was implemented on MATLAB and Pareto-optimal sets of parameter values were obtained. Model simulations using optimized parameter values do provide a better fit to the experimental data as compared to fits that could be obtained through adjustment of parameter values by trial and error.

Index Terms—Algal growth model, genetic algorithm, multi-objective optimization, Pareto-optimal solution.

Devesh Prakash, Sumit Kumar, and Purnendu Bose are with the Indian Institute of Technology Kanpur, Uttar Pradesh, India (e-mail: pdevesh@iitk.ac.in, sumitkr@iitk.ac.in, pbose@iitk.ac.in).
Amuly Ratn was with the Indian Institute of Technology Kanpur, Uttar Pradesh, India (e-mail: amulyratn@gmail.com).

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Cite: Devesh Prakash, Amuly Ratn, Sumit Kumar, and Purnendu Bose, "Calibration of Algal Growth Model Using Multi-objective Genetic Algorithm," International Journal of Environmental Science and Development vol. 6, no. 12, pp. 901-907, 2015.