## 3 Optimization Algorithm  
When a battery is being charged, it is important to allow a buffer time for the electrolyte chemical reaction to limit the temperature rise. However, there is no optimum frequency for low switching loss and high charging efficiency in Reflex charging, the switch and battery have different losses at different frequencies. Therefore, to obtain the optimum charging frequency, we used the PSO algorithm [11; 12] and CPSO [13] to search for the optimum Reflex charging frequency. The optimum frequency was calculated using the PSO, improved by the Taguchi method, and a logistic map [3]. The ISE [4] was used to judge the optimum frequency, expressed as Equation (1). ISE represents the aggregate consumption of energy within the designated time for the evaluation of system design performance, and we used \(e(t)\) as the optimum switching loss and switching consumption error at various frequencies. That is the difference of the power of pre-charging circuit, and the output power of stage output in the battery charge is called the error value \(e(t)\) and t is the time.  
\[ISE=\int_{0}^{\infty}\left[e(t)\right]^{2}dt \tag{1}\]  
In the Reflex charge-up method, a reasonable on-and-off pulse width is determined, and the improved PSO is then used to search for the optimum frequency and to select an \(ISE\) function with minimum consumption.  
In velocity-updating Equation (2), the PSO is used to find a current optimal solution of each particle iteratively, set as pbest here. When the iteration of all particles is finished, an optimal solution can be found, set as gbest. The position updating is expressed in Equation (3), the initial position of each particle. Figure 3 is the PSO flow chart.  
Velocity updating equation:  
\[\begin{array}{l}V_{n}(t)=W\times V_{n}(t-1)+C_{1}\times rand\times\\ (pbest-X_{n})+C_{2}\times rand\times(gbest-X_{n})\end{array} \tag{2}\]  
Position updating equation:  
\[X_{n}(t)=X_{n}(t-1)+V_{n}(t) \tag{3}\]  
\(V_{n}\): Particle update rate.  
\(n\): Particle code.  
\(W\): Inertia Weight.  
\(C_{1}\), \(C_{2}\): Learning constants.  
rand: Random number between 0 and 1.  
_pbest_: Optimal solution of current particle up to now.  
_gbest_: The optimal solution of all particles up to now  
\(X_{n}\): Current position of particle.  
Many high-tech products have a high replacement rate and manufacturers strive to improve product quality and to reduce production cost. The Taguchi method, proposed by Dr. [PERSON] (1950), uses a standard simple orthogonal array for the evaluation of experimental design. The number of experiments that need to be conducted is reduced by this simplicity, and design parameters can be optimized with few experiments [14].  
The Taguchi method is used for quality definition, defining the signal-to-noise (S/N) ratio, and in the quality evaluation of products. In this study we used a Taguchi orthogonal array [4] to determine the learning factor of PSO. The system objective function is \(ISE\), so the S/N ratio was calculated according to the data of the \(ISE\). The Taguchi method was used, and the design parameters were substituted in the \(ISE\) obtained by PSO, as shown in reference 4. Finally, the optimum parameters were worked out from reference 4 as \(C_{1}\) is 1, \(C_{2}\) is 1, and \(W\) is 0.75.