# Evolutionary Design Optimization of an Alkaline Water Electrolysis Cell for Hydrogen Production
## 3 Set up of the Genetic Algorithm
### Evaluation
\begin{array}{l}A_{0}=\ \frac{1}{1-\frac{CAPEX_{min}\ +\ OPEX_{min}}{ CAPEX_{min}\ +\ OPEX_{max}}}\\ B_{0}=-A_{0}\frac{CAPEX_{min}\ +\ OPEX_{min}}{ CAPEX_{max}\ +\ OPEX_{max}}\end{array}  \tag{47}\]  
The value of these coefficients depends on the initial assumptions. Finally, the Equations (48) and (49) gives the form of the fitness function. \[f(CAPEX,OPEX)=A_{0}\overline{F}\ +\ B_{0} \tag{48}\]  
\[f(CAPEX,OPEX)=A_{0}\frac{CAPEX_{min}\ +\ OPEX_{min}}{CAPEX\ +\ OPEX}\ +\ B_{0} \tag{49}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{4}{c}{_EC (\(\mathbf{\bar{t}}\) kWh\({}^{-1}\))_} \\ \cline{3-6}  & & & \multicolumn{2}{c}{_0.17_} & \multicolumn{2}{c}{_0.3_} \\ \cline{3-6}  & & & \multicolumn{2}{c}{_OPEX\({}_{min}\)_} & \multicolumn{2}{c}{_OPEX\({}_{max}\)_} & \multicolumn{2}{c}{_OPEX\({}_{min}\)_} & \multicolumn{2}{c}{_OPEX\({}_{max}\)_} \\ \cline{3-6}  & & & \multicolumn{2}{c}{_9.48_} & \multicolumn{2}{c}{_13.46_} & \multicolumn{2}{c}{_16.74_} & \multicolumn{2}{c}{_23.76_} \\ \hline \multirow{4}{*}{800} & \multirow{2}{*}{\(\ CAPEX_{min}\)} & \multirow{2}{*}{0.02} & \(\overline{F}=1\) & \(\overline{F}=0.70\) & \(\overline{F}=1\) & \(\overline{F}=0.70\) \\  & & & \(f=1\) & \(f=0.04\) & \(f=1\) & \(f=0.02\) \\ \cline{2-6}  & & & \(\overline{F}=0.98\) & \(\overline{F}=0.69\) & \(\overline{F}=0.99\) & \(\overline{F}=0.69\) \\  & & & \(f=0.92\) & \(f=0\) & \(f=0.96\) & \(f=0\) \\ \hline \multirow{4}{*}{3000} & \multirow{2}{*}{\(\ CAPEX_{min}\)} & \multirow{2}{*}{0.09} & \(\overline{F}=1\) & \(\overline{F}=0.71\) & \(\overline{F}=1\) & \(\overline{F}=0.71\) \\  & & & \(f=1\) & \(f=0.12\) & \(f=1\) & \(f=0.07\) \\ \cline{2-6}  & & & \(\overline{F}=0.92\) & \(\overline{F}=0.67\) & \(\overline{F}=0.95\) & \(\overline{F}=0.68\) \\  & & & \(f=0.77\) & \(f=0\) & \(f=0.86\) & \(f=0\) \\ \hline \multirow{4}{*}{\(IC_{c}\) (\(\mathbf{\bar{c}}\) m\({}^{-2}\))} & \multirow{2}{*}{6000} & \(\ CAPEX_{min}\) & \(0.17\) & \(\overline{F}=0.71\) & \(\overline{F}=1\) & \(\overline{F}=0.71\) \\  & & & \(f=1\) & \(f=0.20\) & \(f=1\) & \(f=0.13\) \\ \cline{2-6}  & & & \(\overline{F}=0.85\) & \(\overline{F}=0.63\) & \(\overline{F}=0.91\) & \(\overline{F}=0.66\) \\  & & & \(f=0.61\) & \(f=0\) & \(f=0.74\) & \(f=0\) \\ \hline \multirow{4}{*}{9000} & \multirow{2}{*}{\(\ CAPEX_{min}\)} & \multirow{2}{*}{0.27} & \(\overline{F}=1\) & \(\overline{F}=0.71\) & \(\overline{F}=1\) & \(\overline{F}=0.71\) \\  & & & \(f=1\) & \(f=0.27\) & \(\overline{F}=1\) & \(f=0.18\) \\ \cline{2-6}  & & & \(\overline{F}=0.80\) & \(\overline{F}=0.60\) & \(\overline{F}=0.88\) & \(\overline{F}=0.64\) \\ \cline{2-6}  & & & \(f=0.50\) & \(f=0\) & \(f=0.65\) & \(f=0\) \\ \hline \multirow{4}{*}{14,000} & \multirow{2}{*}{\(\ CAPEX_{min}\)} & \multirow{2}{*}{0.42} & \(\overline{F}=1\) & \(\overline{F}=0.71\) & \(\overline{F}=1\) & \(\overline{F}=0.71\) \\  & & & \(f=1\) & \(f=0.35\) & \(f=1\) & \(f=0.25\) \\ \cline{2-6}  & & & \(\overline{F}=0.72\) & \(\overline{F}=0.56\) & \(\overline{F}=0.82\) & \(\overline{F}=0.61\) \\ \cline{1-1}  & & & \(f=0.37\) & \(f=0\) & \(f=0.53\) & \(f=0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _CAPEX_ and _OPEX_ minimum and maximum and their associated value of fitness.