# Parameter Combination Framework for the Differential Evolution Algorithm
## 3 The Effect of Parameter Distribution on DE Algorithm  
For the population-level parameter control strategy, all individuals share the same parameter value, and the parameter value may vary during the evolutionary process, making the parameter value more suitable for the current evolutionary state of the population. For individual-level parameter control strategy, each individual has its own parameters, and thus the parameter values of the entire population present some distribution characteristics in the parameter space. However, the current individual-level parameter strategies still aim to find the suitable parameter values, such as JADE [13], SHADE [13], and jDE [21], the focus of the current study is not on the parameter combination or distribution. There are few studies specifically focusing on the effects of parameter distribution. In this section, we study the influence of parameter control strategy on parameter distribution and the influence of parameter distribution on algorithm performance by experiments. We chose three individual-level parameter control strategies: the jDE parameter strategy [21], SHADE parameter strategy [13], and a random parameter strategy. The test functions were extracted from the CEC2014 benchmark test function [43] with the maximum number of evaluations 10,000 \(\times\)\(D\). The optimization effect is relevant to operations, operation-related parameters (\(F\), \(CR\)), population size (\(NP\)), and test functions. For comparison, we let the parameter strategy change while the others factors remained the same. The first test was for function f1(30\(D\)), and the \(NP\) was set to 300. We adopted the DE/current-to-pbest/1 [13] mutation operation, binomial crossover operation and the other operations were the same as the classic DE. We observed the running distribution state of all individuals and the corresponding parameter values and intercepted the map, as shown in Figure 1. In each subfigure, the graph above displays the individual distribution, and the graph below displays the corresponding parameter distribution. The population's individual distribution uses the plane of the first and second dimensions of the individual, while the parameter distribution uses the parameter plane on \(F\) and \(CR\). The numbers at the top of each subfigure represent the generation and current optimal value, and red stars represent successful parameters. From Figure 1, the distribution characteristics of the three strategies can be seen, as described below. * The parameters of the random parameter strategy are evenly distributed regardless of the evolutionary state. There are evidently many parameter values that are not beneficial to evolution that affect the efficiency of the strategy. * The population parameter distribution of the jDE parameter strategy gradually coincides with the distribution of successful parameter values along with the evolutionary process; however, the process is slower. * The parameter distribution of the SHADE parameter strategy spreads around a center point, and the distribution is shifted by the difference between the mean of the successful parameter-values and the entire parameter-values. The SHADE parameter strategy enhances a part of the distribution of successful parameter values. The SHADE strategy is superior for f1, while the jDE strategy is prone to converge for many small \(F\) values in the distribution, which impacts exploration. The random strategy displays the worst results for many invalid parameter values. It is evident that parameter distribution affects algorithm performance. The second test involved a mutation strategy of DE/rand/1 and a test function of f2 on 50D. The \(NP\) was set to 100. The other settings are the same as the first test. The intercepted running state is shown in Figure 2, where it can be seen that the distribution characteristics of the three parameter strategies have not changed. However, an entirely different result appears: the SHADE strategy that performed well in the first test fell into a premature convergence.