# A Self-Adaptive Approximated-Gradient-Simulation Method for Black-Box Adversarial Sample Generation
## 2 Related Work
### Differential Evaluation  
Differential evolution (DE) [28], proposed by [PERSON] and [PERSON], is an example of stochastic population-based computing intelligence. Recently, DE has been widely used in diverse fields, such as electrical and power systems [29], pattern recognition [30], artificial neural networks [31], robotics and expert systems [32], manufacturing science [33], image processing [34], and gene regulatory networks [35], because of its comprehensibility, robustness, convergence, and ease of use [36].  
In recent years, researchers have contributed to DE performance improvement [37]. These improvements have mainly focused on mutation strategies, crossover strategies [38], and control parameters (i.e., population size NP, scaling factor F, and crossover rate CR). Extensive studies show that the parameter setting helps to improve DE performance [39]. However, the parameter setting is one of the most persistent challenges in an evolutionary algorithm (EA). An EA with better parameter values may have a greater order of magnitude than one with poor parameter values. In the field of EA, parameter-selection schemes usually include two approaches as follows: one approach is parameter turning, whereby parameter values are carefully picked out before an EA is run and cannot be changed in the process of running; and the other approach is parameter control, whereby parameter values are randomly initialized for the starting run of an EA and can be adjusted in the process of running. In the parameter-turning method, parameter values are set using the experimental method or the trial-and-error method [40]. [PERSON] and [PERSON] indicated that a good initial set of \(F\) is 0.5, and the effective range of \(F\) usually belongs to (0.4, 1). [PERSON] et al. [41] revealed that the global exploitation capability and the speed of convergence are oversensitive to the parameters. [PERSON] et al. [42] stated that \(Cr\) should be between (0, 0.2) when the function is separable, but between (0.9, 1) when the function is non-separable. According to the literature, proper parameters should be set differently for different functions. Therefore, researchers have started to take into account some self-adaptation techniques to automatically search optimal parameters for DE. The SaDE algorithm employed a self-adaptation scheme by learning from historical experiential solutions to control parameters \(F\) and \(Cr\). [PERSON] et al. [43] proposed an adaption algorithm based on fitness for \(F\). The calculation of \(F\) is based on the requirements of a diversified search in the early stage and enhanced search in the later stage, and the formula is as follows (Equation (1)).  
\[F=\left\{\begin{array}{l}\max\left(1,1-\left|\frac{f_{\max}}{f_{\min}}\right| \right)\ \ if\left|\frac{f_{\max}}{f_{\min}}\right|<1\\ \max\left(1,1-\left|\frac{f_{\min}}{f_{\max}}\right|\right)\ \ otherwise\end{array}\right. \tag{1}\]  
where the lower bound for \(F\) is \(l_{min}\) and \(f_{min}\) and \(f_{max}\) are the minimum and maximum function values of the populations in a generation, respectively. The extensive experimental results show that the self-adaptive DE outperforms the standard DE because of the less sensitive parameters in self-adaptive DE.