Abstract

The calibration of a comprehensive mathematicalmodel describing algal dynamics in batch reactors has beenattempted. The mathematical model consisted of 29 variablesand 40 parameters and was described by 29 stiff differentialequations. Of the 40 parameters values, 23 values are notknown with certainty and hence need to be adjusted to obtain agood fit between the model simulations and experimental data.Three sets of experimental data were available for modelcalibration. Each set of data consisted of time series onevaluation of seven variables. Objective was to manipulate thevalues of the adjustable parameters in the model such thatmodel simulations fit all three sets of experimental datasimultaneously with minimum error. The above propositionwas formulated as a multi-objective optimization problem andsolved using a genetic algorithm called NSGA-II. The code wasimplemented on MATLAB and Pareto-optimal sets ofparameter values were obtained. Model simulations usingoptimized parameter values do provide a better fit to theexperimental data as compared to fits that could be obtainedthrough adjustment of parameter values by trial and error.