## 3 Results
### Gas Generator Cycle: Comparison of Techniques and Objective Functions
#### 3.2.1 Nelder [PERSON]  
With reference to Figure 4a, the NM technique returned results that met the mission's constraints for two out of three OFs. Therefore, the results for maximizing the Thrust-to-Weight ratio have been excluded. A probable reason for this inability to meet the constraints is due to NM's susceptibility to the initial guess. This technique searches for the local maximum within the vicinity of the initial guess. Therefore, if the initial guess is close to the global maximum, the probability of NM converging on the local maxima is higher than when the initial guess is further away from the global maximum.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Parameters** & **Shahab-3** & **Calculated** & **Optimized** & **Optimized with Similar \(p_{c}\)** \\ \hline GLOW (kg) & 15,832–16,250 & 15,650 & 14,312 & 15,973 \\ Diameter (m) & 1.32–1.35 & 1.06 & 1.03 & 1.07 \\ Length (m) & 15,852–16.0 & 17.45 & 16.89 & 17.58 \\ \(F\) (kN) & 260–262 & 309 & 2.91 & 306 \\ \(I_{sp}\) (s) & 230 & 258 & 266 & 255 \\ \(\Delta t\) (s) & 110 & 110 & 109 & 112 \\ \(p_{c}\) (bar) & 55 & 55 & 79 & 48 \\ L/D & 11.85 & 16.46 & 16.39 & 16.43 \\ T/W & 16.12 & 19.74 & 20.33 & 19.15 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of Shahab-3 performance parameters and dimensions with the research model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **a** & **b** & **c** \\ \hline MR & 2.92 & 0.62 & \(-\)0.14 \\ \(c^{*}\) (m/s) & 1493.41 & 54.97 & \(-\)40.97 \\ C\({}_{F}\) & 0.77 & 0.51 & \(-\)1.07 \\ \(T_{c}\) (K) & 2364.71 & 448.96 & \(-\)199.64 \\ \(\gamma\) & 1.19 & 0.03 & 0.01 \\ M & 20.87 & 2.10 & \(-\)0.69 \\ \(e\) & 0.37 & 0.41 & 0.77 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fitted data for RFNA and RP1; \(p_{c}\) 0.7 bar.  
Figure 3: Optimized Engine Parameters, dimensions and masses for Shahab-3.  
Figure 4: Optimization results for the GG Cycle with mission \(\Delta V\) = 3800 m/s and \(H\) = 120 km using all 7 techniques and 3 OFs. (**a**) Nelder Mead (NM). (**b**) Simulated Annealing (SA). (**c**) Cuckoo Search Algorithm (CSA). (**d**) Particle Swarm Optimization (PSO). (**e**) Pigeon-Inspired Optimization (PIO). (**f**) Genetic Algorithm (GA). (**g**) GA-Swarm.  
Out of these results for NM, the best-performing OF is \(I_{sp}\), as the optimum result both clearly lies within the accepted operating range of \(p_{c}\) for a GG cycle, and occurs at a \(p_{c}\) of 71 bar, which is lower than the minima obtained using GLOW OF. For GLOW OF, there are distinct bands of results at 20, 30 and 40 bar \(p_{c}\), with the minima lying at 97 bar. This minima lies within the operating \(p_{c}\) range for a GG cycle; however, it is relatively higher than the \(p_{c}\) obtained using \(I_{sp}\) as the OF. Using \(I_{sp}\) as an OF provided a relatively larger cluster of results between 11 and 18 bar \(p_{c}\), which is an infeasible operating range for GG cycle. Another smaller band of results between 40 and 45 bar \(p_{c}\) coincided with a similar band of results when using GLOW as the OF. Results of both OFs demonstrate the presence of multiple local minima in the solution space.