# Chaotic Java Approaches to Solving Electromagnetic Optimization Benchmark Problems
## 5 Experimental Study and Discussion
### Results for the Brushless DC Motor Design  
In this case, a population size of 20 and a stopping criterion of 900 evaluations of the objective function in each run of the Jaya approaches were adopted.  
It can be observed in Table 5 that the best solution (boldface) of the CJ in 50 runs converged to the same solution found by sequential quadratic programming (SQP) [24] and ant colony optimization (ACO) [25] (see Table 5), which was considered to be most likely the problem global optimum. All solutions in each run obtained by the Jaya approaches (see Table 5) _were feasible_.  
The best solution, in terms of the best \(\eta\)_value_ obtained by CJ (3, 5, 6, 8, 9, and 10) approaches, was \(D_{s}=201.2\) mm, \(B_{e}=0.6481\) T, \(\delta=2.0437\) A/mm\({}^{2}\), \(B_{d}=1.8\) T, and \(B_{cs}=0.8959\) T. In this case, the obtained total mass was 15 kg. However, in terms of the mean \(\eta\)_values, the best results were obtained by CJ (8)_.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimizer** & **Minimum (10\({}^{-8}\))** & **Mean** \\ \hline CJ (1) & 2.4380 & 3.38 \\ CJ (5) & **2.0566** & 6.60 \\ CJ (8) & 2.1721 & 6.48 \\ GABC (0.1) [19] & 2.2010 & **3.33** \\ GABC (0.3) [19] & 2.0658 & 3.87 \\ Cultural SOMA [20] & 2.4338 & 3.40 \\ TRIBES [21] & 2.0595 & 3.48 \\ QBSO [22] & 3.3990 & 3.57 \\ GHS [23] & 3.8035 & 3.40 \\ \hline \hline \end{tabular}  
Acronyms: Gaussian artificial bee colony (GABC), self-organizing migrating algorithm (SOMA), quantum-behaved brainstorm optimization (QBSO), and Gaussian harmony search algorithm (GHS).  
\end{table}
Table 4: Results in terms of the objective function \(f(s,\ l)\cdot 10^{-8}\). Data in bold font indicates the smaller values.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Optimizer** & **Minimum (Worst)** & **Mean** & **Maximum (Best)** & **Standard** \\ \hline Jaya & 94.67 & 95.17 & 95.31 & 1.67\(\cdot 10^{-3}\) \\ CJ (1) & 94.40 & 95.12 & 95.31 & 1.67\(\cdot 10^{-3}\) \\ CJ (2) & 92.85 & 94.25 & 95.21 & 6.64\(\cdot 10^{-3}\) \\ CJ (3) & 94.32 & 95.23 & **95.32** & 1.63\(\cdot 10^{-3}\) \\ CJ (4) & 92.69 & 93.87 & 95.08 & 7.55\(\cdot 10^{-3}\) \\ CJ (5) & 93.67 & 94.84 & **95.32** & 4.17\(\cdot 10^{-3}\) \\ CJ (6) & 93.10 & 94.91 & **95.32** & 4.58\(\cdot 10^{-3}\) \\ CJ (7) & 93.53 & 94.46 & 95.29 & 5.09\(\cdot 10^{-3}\) \\ CJ (8) & 94.94 & **95.27** & **95.32** & 8.66\(\cdot 10^{-4}\) \\ CJ (9) & 94.14 & 94.97 & **95.32** & 2.89\(\cdot 10^{-3}\) \\ CJ (10) & **94.97** & 95.24 & **95.32** & 8.11\(\cdot 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Optimization results for the brushless DC motor in 50 runs considering the objective function to be maximized, given by max \(\eta=f(D_{s},\ B_{e},\ \delta,\ B_{d},\ B_{cs})-penalty\). Data in bold font indicates the larger values.  
According to the simulation results from Table 6, it was observed that the number of evaluations of the objective function employed in the Jaya method was less than those adopted by GA, PSO, and ACO mentioned in Table 6, except for the efficient nonlinear programming method called SQP.