# Parameter Combination Framework for the Differential Evolution Algorithm
## 2 Related Works
### Related Works on Parameter Control Strategy for DE  
The first category of parameters is related to operations performed by the individual; parameter control strategies can thus be population-level strategies or individual-level strategies. With a population-level parameter control strategy, the entire population shares the same parameter values. With an individual-level parameter control strategy, each individual has their own parameter value; thus, individuals in the population have different behavioral characteristics. Research on the first parameter category mainly concerns parameters \(F\) and \(CR\). The methods adopted by the parameter control strategy include the following: using fixed value, using random value, changing value according to evolutionary generation, changing value according to individual fitness, changing value according to the population model, test feedback based on statistics, and test feedback based on the single individual evaluation. The parameter control studies of the DE algorithm begin with the random mechanism. This is an individual-level mechanism, and each individual is assigned a random parameter value. The values of the entire population may have distribution characteristics such as uniform distribution [9], normal distribution [26], or Cauchy distribution. Several studies discretized the parameter domain into a value set and randomly extracted from it. The set may be for single parameter [27] or for a combination of several parameters [28]. The strategy of changing parameter values according to evolutionary generation is generally a part of the population-level strategy. The parameter value is set by different functions (or rules) of generation such as linear functions [9] or nonlinear functions [10]. Parameter strategies that vary by individual fitness are individual-level strategies, where parameter values differ for each individual according to their fitness. The authors of [29] consider that the parameter values for individuals with good fitness should be smaller, and vice versa. In [30], the \(F\) value is set with the same idea as [29], however, the \(CR\) is adjusted according to the fitness of the donor vector, which is not a general strategy. In [31] the fitness of donor vector is also be used to adjust the parameter value. Strategies for changing values according to the population model are primarily population-level strategies. The model is constructed according to the entire population and uses the deterministic rules or adaptive method to adjust parameter values for the population. A fuzzy adaptive differential evolution algorithm (FADE) [32] has designed a fuzzy model to adapt parameters \(F\) and \(CR\), and in [33], a two-level parameter adaptation strategy is proposed. The first level involves adjusting the population parameters according to the population model, and in the second level, the individual parameters are adjusted according to the individual's fitness based on the population parameter values. Test feedback strategies based on statistics are primarily adaptive individual-level strategies. An adaptive DE algorithm named JADE [13] uses the results of the last generation to count the mean of the parameter (\(F\) and \(CR\)) of all good individuals by the Lehmer mean, which is used to guide the distribution of parameter values for the next generation. The values of the individual parameters are assigned according to normal distribution for \(CR\) and Cauchy distribution for F based on the mean. Success History based DE (SHADE) [14] improved the JADE strategy by (1) proposing a weighted method for the mean formula, and (2) proposing a history list for storing the successful mean of several recent generations. Many algorithms have used JADE or SHADE parameter strategy directly or with improvement [15; 16; 17; 18; 19; 20]. References [11; 12] discretize the parameter domain and use the results of the previous generation or a period to count the success rate of each discrete parameter value.