## 8 Conclusions  
The paper showed a way of connecting neural networks with evolutionary algorithms. The neural network was used in order to build a model describing the flotation process. The network learning was carried out with the use of samples from previous empirical measurements of the actual process. The evolutionary algorithm, however, was used to find optimal flotation parameters based on the above model. This combination resulted in obtaining optimal results that go beyond the measurement space used to create the model. The optimisation results of flotation enrichment of Polish copper ores in the Denver flotation machine and in the Jameson cell differ significantly. To some extent, this was influenced by the scope of experiments performed with the use of the second device. Performing a full series of flotation tests could change the final modelling and optimisation results. Different distribution of the size of air bubbles in the flotation chamber in both devices demonstrates the importance of this factor for the flotation results. Above all, the Jameson flotation machine enables the enrichment of fine particle fractions of copper ore, which is significantly hampered in the Denver flotation machine. Such a fine particle size of the feed is even a problem when enriching copper ores in pneumatic-mechanical machines. By entering the full range of empirical data into the cleaning flotation optimisation software (I), the technological optimum was obtained for the following parameters:  
- Flotation machine: Denver  
- Feed: sandstone copper ore,  
- Particle size: 40-71 \(\upmu\)m (d\({}_{\text{opt}}\) = 47 \(\upmu\)m),  
- Cleaning flotation time: 1.308 min,  
- Collector: aqueous solution of ethyl sodium xanthate,  
- Collector dose: 105 g of collector per 1 Mg of the feed. Maintaining the assumed level of the above-mentioned input parameters of the cleaning flotation process (I), it can be assumed that the content of copper-bearing minerals in the flotation concentrate will remain at the level of approximately 27.72%, the recovery will be approximately 97.61%, while the tailings will contain 0.225% of copper. The cleaning flotation process (I) in the injector flotation machine in question will be most effective if the following parameters are used:  
- Particle size: 0-25 \(\upmu\)m,  
- Cleaning flotation time: 30 min,  
- Collector: aqueous solution of isobutyl sodium xanthate,  
- Collector dose: 108.35 g of collector per 1 Mg of the feed. The content of copper-bearing minerals in concentrate will remain at the level of approximately 11.36%, recovery will be approximately 88.87%, and tailings will contain 0.435% of copper. Particle size and the characteristics of the feed being enriched are key factors that guarantee the correct and efficient flotation. The models obtained from NN were burdened with a mean square error of approximately 0.015-0.030. Regardless of the particle size of the feed, the sandstone lithological \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & **Copper** & \multirow{2}{*}{**Particle Size (\(\upmu\)m)**} & **Cleaning flotation** & \multirow{2}{*}{**Collector Type**} & **Collector** & \multirow{2}{*}{**\(\beta\) (\%)**} & \multirow{2}{*}{**\(\upmu\) (\%)**} & \multirow{2}{*}{**\(\upmu\) (\%)**} \\  & **Ore Type** & & & **Time (min)** & & & & \\ \hline AG & D & 0-25 & 30.00 & Z & 108.35 & 11.36 & 0.435 & 88.87 \\ LAB & D & 0.25 & 30.00 & Z & 100.00 & 7.55 & 0.42 & 81.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: The results obtained for the analysis of all cases in the Jameson cell. type guarantees the best enrichment effects for the data range examined. The results of this study confirm the high efficiency of the adopted modelling methods in the description of the flotation process and in the search for the technological optimum for the separation of copper minerals from useless gangue rock. Of course, adding another parameter may improve the quality of the created flotation model.