# Evolutionary Design Optimization of an Alkaline Water Electrolysis Cell for Hydrogen Production
## 3 Set up of the Genetic Algorithm
### Validation of the Algorithm  
Hypothesis:  
* \(IC_{s}\) = 800 \(\upepsilon\) m\({}^{-2}\)
* \(EC\) = 17\(\upepsilon\) kWh\({}^{-1}\)
* \(b_{an}\) = \(b_{auth}\) = 0.15 V dec\({}^{-1}\)
* \(R_{memb}\) = 3.23 \(\times\) 10\({}^{-5}\) Ohm m\({}^{2}\)[27]  
The calculation has been performed using an Intel Core i7\(-\)6700 HQ CPU @2.60 GHz. The optimization simulation time varies around 5 s. To validate the algorithm, the physics of the model presented in Section 2 will be simplified. The diphasic effect will not be taken into account. In doing so, we can analyze the equations to extract the sensitivities and find the optimal design if the process was not two-phase. The next step is to see if the algorithm finds a better candidate. By analyzing Equations (30) and (31), we can deduce that the current density must be around 1000. As temperature increases the electrical conductivity and decreases the reversible voltage, the algorithm must find the highest possible temperature. Since two-phase phenomena are not taken into account, the pressure proposed by the algorithm must be as low as possible (because it increases the reversible voltage). The same applies to the electrolyte thickness. Indeed, the latter decreases the ohmic resistance. Figure 10 shows the evolution of the fitnesses (a) and the cost function (b) according to generations. In (a) we observe that \(f_{best}\) and \(f_{avg}\) increase greatly in the first 10 generations, we call this phase the exploration. During this phase, the GA searches good locations in the \(DP\) space. It finds very quick good regions in \(DP\), which explains the quick fitness growing, thus the cost dwindling. Between generations 10 and 50 both fitnesses continue to increase but moderately, this in the exploitation phase. During this phase the algorithms attracts most of the population towards the best solution, which explain the reduction of \(f_{best}\) and \(f_{avg}\) difference. Usually, there exist a last phase where the \(f_{avg}\) stagnates below the \(f_{best}\) that continues to slightly increase until reaching a plateau around the end of evolution. This phase is called the convergence one and pursues the search around the best solutions to find slightest increases for \(f_{best}\) (eventually ending up with the global optimum), maintaining \(f_{avg}\) just below \(f_{best}\) using the mutation as permanent genetic stirrer. Unfortunately, we cannot see this last phase that means the evolution is not completed. In Figures 11 and 12 are presented the design parameters evolution path from random (first population) to overall best (last population) values. In (a), both \(h\) parameters (H\({}_{2}\) and O\({}_{2}\)) converge to the smallest available value. This can be explained by the Ohm's law in the monophasic model. Figure 11: Design parameters evolution for the best \(DP\) set solution (in full \(DP\) space and for a single evolution) of the best candidate depending on the generation (**a**) for the anolyte and catholyte thickness \(h_{H2},h_{02}\) (**b**) for electrolyte temperature \(T\). Figure 10: Averaged over 100 evolutions (**a**) fitness and (**b**) cost function evolution according to the generation. In Figures 11 and 12, we note that almost all \(DP\) values converge during the evolution towards their best value, but the parameter \(H_{\textit{dec}}\) (b). Actually, in this simplified model (monophasic), \(H_{\textit{dec}}\) has no influence on the cost function (gaz effects neglected). This first tentative of artificial evolution of alkaline electrolyzer is promising, but we know that it could be improved in two ways:  
* The simplified model does not take into account the two-phase phenomena, which can greatly influence the hydrogen costs (\(F_{c}\)). * The evolution parameters used in this first try are not well adapted to the problem (missing convergence phase to achieve evolution). In the next section we answer these two issues by using the more elaborate two-phase model and by performing a sensitivity analysis of the genetic optimization w.r.t.