**3.6 Analysis of results**

Parameter estimation by tabu search is performed by devising different modeling configurations to represent the biofilm reactor. These configurations involve the Edward kinetics and Haldane kinetics with substrate inhibition along with the two and three parameter film thickness expressions. The modeling configuration that is formed by 1D model along with Haldane kinetics and two parameter film thickness expression is referred to 1D-Haldane-2film. Other modeling configurations are formed and abbreviated in the same manner. The effectiveness of these modeling configurations are assessed by comparing the model predictions with experimental data and further by means of performance measures such as cost function (CF) and model efficiency (ME) [28]. A conventional optimization method called Nelder– Mead optimization (NMO) [37, 38] is also employed for comparison with the tabu search. The results are analyzed to find the better suitability of mathematical models using the quantitative performance measures (CF and ME). These results evaluated for 1D and 2D models with Haldane and Edward kinetics involving two film and three film expressions indicate the better suitability of 2D model over 1D model.

**Figure 5.**

*Iterative convergence of parameter estimates by TS and NMO: (a) kinetic parameters, (b) film thickness parameters.*

**Figure 6.**

*Comparison of experimental results with model predicted substrate conversions of 2D model with Edward kinetics.*

*A Metaheuristic Tabu Search Optimization Algorithm: Applications to Chemical… DOI: http://dx.doi.org/10.5772/intechopen.98240*

When the results are analyzed to assess the better suitability optimization algorithm, the analysis of results of different modeling configurations indicate the effectiveness of TS over NMO. The results evaluated to find the usefulness of kinetic models indicate the better suitability of Edward kinetics over Haldane kinetics. The results analyzed to assess the film thickness expressions indicate the appropriateness of the three parameter film thickness expression over two parameter expression. The iterative convergence of parameters estimated by TS and NMO are shown in **Figure 5**. The comparison of the prediction results of 2D model with Edward kinetics and three parameter film thickness expression evaluated using TS and NMO with those of experimental results are shown in **Figure 6**. The analysis of the results show the better performance of TS over NMO for inverse modeling of biofilm reactor. From these results, it is found that the TS involving 2D model, Edward kinetics and three parameter film thickness expression better represents the fixed bed biofilm reactor involved in the treatment of pharmaceutical industry wastewater.
