# Different Object Functions for SWIPT Optimization by SADDE and APSO
## 3 Evolution Algorithm  
In this paper, we use two different evolution algorithms to compare the multiple objective functions. The first evolution algorithm is APSO [21; 27; 28], which is developed from the Particle Swarm Optimization (PSO). PSO was inspired by the social behavior of animals as fish schooling. APSO adjusts the velocity when the best object function is updated, and it converges more rapidly than PSO. As shown in Figure 3, there are six main steps for APSO optimization.  
**Step 1.**_We first set all particles with fixed range which depends on the feed length of the antenna array. The algorithm initializes particle position randomly with a dimensional adjustment._  
**Step 2.**_Evaluate the p-th object value of the objective function, where p is the number sequence in the total population._  
**Step 3.**_Update global best particle and local best particle._  
**Step 4.**_The particles are mutated with ten percent probability. Then update the local best particle and global best particle according to the objective value._  
**Step 5.**_Velocity and position are updated according to the position of the local best and global best particle._  
**Step 6.**_To step 2 or stop operating the algorithm when the present generation is reached._  
The SADDE is developed from Dynamic Differential Evolution (DDE) [21; 26; 29]. In this research, we add some mechanisms to let the adjustment factor self-adapt during the searching. The flowchart of the SADDE algorithm is shown in Figure 4.  
**Step 1.**_We load the setting parameter and initiate the parameter of population randomly. Every population has d dimensional adjustment parameters for the antenna array and those parameters are employed to compute the objective function._  
**Step 2.**_Calculate the objective function and update the best value of the local particle based on the p-th particle's adjustment parameters._  
**Step 3.**_Mutate the trial vector according to the control vector and adjust the control vector for the next generation._  
**Step 4.**_By the preset probability, decide whether to start the crossover mechanism._  
**Step 5.**_Update the position of the global best particle._  
Figure 3: APSO flow chart.  
**Step 6.**_According to the total number of particles and the number of generations, go to Step 2. or stop operating the algorithm._  
Here, consider two different requirements at the same time. One is the \(BER\) and the other is the total harvesting power. If \(BER\) is constrained at \(10^{-5}\), we define \(BER_{w}\) as Equation (8) in order to optimize the objection functions into one.  
\[BER_{W}=\left\{\begin{array}{cc}\frac{10^{-5}}{BER}&,BER>10^{-5}\\ 1&,BER<10^{-5}\end{array}\right. \tag{8}\]  
The total power harvesting can be expressed as  
\[HP_{T}=\sum_{i=1}^{N_{R}}HP_{i}\]  
where \(N_{R}\) is the total number of receivers in the environment. \(HP_{T}\) is expected to be as large as possible. The above two functions have been combined with two different methods. In the first proposed criterion, we set \(BER_{W}\) multiplied by \(HP_{T}\) plus \(HP_{T}\) as the objective function. Thus, \(BER_{W}\) multiplied by \(HP_{T}\) and \(HP_{T}\) has the similar order if the BER is less than \(10^{-5}\). However, from the numerical simulations, this criterion cannot reach the BER constraint of \(10^{-5}\). As a result, we introduce the weighting factor \(W\) in the objective function, as show in Equation (9)  
\[1/(W\times BER_{W}\times HP_{T}+HP_{T}) \tag{9}\]  
However, you must test the weighting factor W case by case beforehand in order to obtain satisfied results. Hence, we propose a second criterion in Equation (10) that only keeps the terms \(BER_{W}\) multiplied by \(HP_{T}\) where W for balancing the required value can be skipped.  
\[1/(BER_{W}\times HP_{T}) \tag{10}\]  
Figure 4: SADDE flow chart.