The parameters in the biofilm model in the example above were estimated using a heuristic procedure — Genetic Search Algorithm (GSA). The first version of this algorithm was implemented in the C programming language using subroutines adopted from Hunter (1998). The GSA uses the inverse of the mean residual sum of squares (MRSS) computed as the global vari­ance (a2) as a fitness function during parameter optimization using the principles of evolution and natural selection (KrishnaKumar, 1993). The global variance is the main objective function for GSA computed as:

G2 =—— Y((obs — y)2 15.16

n — qt!

where a = average deviation of the model from measured values, yobs = observed variables, y = simulated variables, n = number of observations, and q = degrees of freedom representing number of parameters being evaluated.

15.12 Simulation of the reduced metal Mn+ (Cr6+) in a dual species biofilm culture under a range of hydraulic loading conditions: 24 h HRT (Phase I-VI); 11.7 h HRT (Phase VII-X); 6 h HRT (Phase XI-XIV); 17.9 h HRT (Phase XV-XVIII).

15.13 Simulation of the carbon source (P) and metabolite (U) concentration in a dual species biofilm culture under a range of hydraulic loading conditions: 24 h HRT (Phase I-VI); 11.7 h HRT (Phase VII-X); 6 h HRT (Phase XI-XIV); 17.9 h HRT (Phase XV-XVIII).

In Figs 15.12 and 15.13, parameters were estimated from the data obtained from the operation of the reactor at 24 hours hydraulic retention time (HRT) (Phase I-VI). The rest of the phases (VII-XVIII) were simulated using the optimized parameters. The results show high confidence in the optimization routine as the model accurately tracked the trends in effluent concentrations for both the electron donor (P) and the electron sink (M).