**5. Optimization Problem**

In this research, to calculate the coefficients of the proposed kinetic and activity models, an optimization problem was formulated to minimize the absolute difference of model results with experimental data. The Genetic Algorithm is a powerful method in global optimization and has been selected to handle formulated optimization problems and obtain the coefficients of kinetic and activity models. Genetic algorithms are the most popular evolutionary algorithm, that is inspired by natural selection of the fittest populations to reproduce and move to the next generation [30]. In each generation the fittest population are attained by three operators, consist of selection, crossover and mutation. In the kinetic section, the reaction rate is calculated numerically and the absolute difference between calculated reaction rate by the model and measured rates are minimized. The considered objective function is as:

$$AMRE = \frac{1}{N} \sum\_{i=1}^{i=N} \frac{\left| y\_{exp}(i) - y\_{model}(i) \right|}{y\_{exp}(i)} \times 100\tag{26}$$

To calculate the coefficients of the considered activity model, the outlet acetylene concentration from guard and lead beds is measured and compared with the calculated acetylene concentration by the model. The considered data consists of 48 data point during the process run time.

is 24.5 nm.
