# Design of Gas Cyclone Using Hybrid Particle Swarm Optimization Algorithm
## 7 Conclusions  
This research utilized a hybrid particle swarm optimization approach to design a gas cyclone with design parameters at a low cost. When compared to PSO individually, as \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline Maximum iteration & 1000 \\ Particle size & 40 \\ Dimensions & 7 \\ Probability of crossover range, \(\mathrm{C_{r}}\) & 0.5 \\ \(\mathrm{w}\) & 0.729 \\ \(c_{1}\) & 2 \\ \(c_{2}\) & 2 \\ \hline \end{tabular}
\end{table} 
Table 13: DEPSO Parameters used for design parameter optimization. \begin{table}
\begin{tabular}{c c c c} \hline
**Design Parameters are in the Ratio of \(\mathrm{D_{c}}\)** & **Analytical Method (Stairmand Model)** & **PSO** & **DE** & **Hybrid DEPSO** \\ \hline Overall cyclone height & 4.0 & 3.925 & 3.371 & 3.884 \\ Inlet height, \(\mathrm{a_{o}}\) & 0.5 & 0.491 & 0.494 & 0.489 \\ Gas outlet diameter, \(\mathrm{D_{co}}\) & 0.5 & 0.168 & 0.411 & 0.309 \\ Cylindrical height of cyclone, \(\mathrm{h_{o}}\) & 1.5 & 0.977 & 0.817 & 1.006 \\ Inlet width, \(\mathrm{b_{o}}\) & 0.2 & 0.213 & 0.242 & 0.209 \\ Gas outlet length, \(\mathrm{S_{o}}\) & 0.5 & 0.674 & 1.177 & 1.171 \\ Dust outlet diameter, \(\mathrm{B_{o}}\) & 0.375 & 0.485 & 0.447 & 0.179 \\ Pressure drop (\(\mathrm{Pa}\)) & 1000 & 469.034 & 364.668 & 493.24 \\ Inlet velocity m/s & 19.86 & 11.066 & 9.706 & 11.36 \\ Cut size \(d_{\mathrm{pr}}\) (\(\mathrm{\mu m}\)) & 8.67855 \(\times 10^{-6}\) & \(1.021\times 10^{-5}\) & \(1.26\times 10^{-5}\) & \(9.96\times 10^{-6}\) \\ Cost/s (Naira/s) & - & 297.715 & 218.938 & 230 \\ Overall efficiency & 0.890 & 0.793 & 0.716 & 0.70 \\ Particle size & - & 50 & 70 & 40 \\ \hline \end{tabular}
\end{table} 
Table 14: Design parameters. shown in Table 14, the adoption of a hybridised particle swarm optimization technique produced a lower cost of 230 naira/s, while the use of DE had a cost value of 218.938 naira/s. In this research, it can be concluded that:  
* The PSO algorithm, when applied to complex optimization problems, can be improved via the combination with other algorithms, such as the DE algorithm, thereby improving the distribution of information between candidates, due to the crossover feature present within it. * When both the cognitive component \(c_{1}\) and the social component \(c_{2}\) have the same value, both exploration and exploitation are evenly balanced. Furthermore, the inertia weight, w, when less than one, i.e., w \(<\) 1, has an effect on the distribution of information across the particles. In addition, when inertia weight is less than one, i.e., w \(<\) 1, the velocity of the particle decreases until it reaches zero, thereby causing exploitation to gradually increase and exploration to gradually decrease. In most cases, changing the value of inertia weight, w, during optimization will balance out exploration and exploitation. Some studies, such as [24; 25; 26], have developed an inertia weight application. * When compared to PSO, DEPSO had a better cost value but lower efficiency. * As shown in Table 14, DE and DEPSO algorithms produced suitable results for design purposes with a low cost, while PSO showed the highest cost value. * Due to the problem set being of a minimization type, the efficiency suffers considerably, but if the problem was of a maximization type, of which maximum overall efficiency is required, the cost and overall efficiency would be considerably high, provided that the cost of operation is not the primary focus. * Having made use of the DE/rand/1 strategy with PSO to optimize the cost of operation of the gas cyclone, various other strategies of DE, such as DE/best/1, DE/rand/2, DE/best/2, and DE/target-to-best/1, can also be used. * PSO is a concept which can be used to solve numerous optimization problems and can be improved through combination with other algorithms. Algorithms such as GA, ACO, TLBO, and so forth can, in fact, be explored to form a hybridised PSO algorithm. Some research on such combinations includes [27; 28; 29; 30; 31; 32; 33]. **Author Contributions:** Conceptualization, X.S.