# Parameter Combination Framework for the Differential Evolution Algorithm
## 1 Introduction  
Differential evolution (DE) is a simple and efficient evolutionary algorithm that is used primarily for real-parameter global optimization [1]. It has been successfully applied to many real-world problems [2; 3; 4; 5]; however, the performance of DE algorithms greatly depends on parameter settings, especially in complex optimization problems. It is therefore important to study parameter control strategies for DE algorithms. Parameters of population-based intelligent optimization algorithms can be divided into three categories: (1) operation-related parameters such as scale factor (\(F\)) and crossover probability (\(CR\)), which are used by search operations in classical DE; (2) population size (\(NP\)) and related parameters generated by strategies for dynamically adjusting the population; and (3) high-level strategy parameters: some algorithms use multi-operation, multi-strategy, or multi-population mechanisms, and may introduce new parameters. A number of parameter strategies have been proposed [6; 7; 8]. The first category of parameters has a large influence on the algorithm and has always been the focus of parameter control strategy research. In recent years, the second category of parameters has been gradually paid attention to. The third category of parameters is related to specific high-level strategies and has no universal significance. Different categories employ diverse methods and technologies. Within a category, parameter control strategies also vary and lead to distinct effects for specific problems. Current parameter control strategy research focuses mostly on searching for the most suitable parameter values for the current problem, process, stage, or individual. The methods employed by parameter control strategies may be deterministic rules or adaptive strategies. There are two problems involved in these methods: one is theway to define the concept of suitable parameter values, and the other is how to set the parameter values. For example, some deterministic strategies believe that in the early stage of evolution, the search process should concentrate on exploration, thus larger \(F\) and \(CR\) are suitable parameter value; while in the later stage, the algorithm should focus on exploitation, thus smaller \(F\) and \(CR\) may be more suitable. The corresponding methods have been proposed by some studies such as decreasing the parameter value according to the generation with linear functions or nonlinear functions [9; 10]. Some adaptive strategies consider that the parameter values that make the individual evolution successful are suitable values, and the corresponding parameter control strategies has been proposed in some researches, such as setting parameter values through comparing the success rate of different parameter values [11; 12], statistical successful parameter distribution [13; 14; 15; 16; 17; 18; 19; 20], or retain successful parameter values [21; 22]. There are also a few studies concentrated on exploring the effects of parameter combination. Parameter combination can be the combination of the values of multiple parameters of an algorithm. Some studies discuss the effect of different value combination of \(F\) and \(CR\) for DE, and some parameter control strategies try to reach the best combination value for \(F\) and \(CR\)[22]. Some recent studies considered the three parameter \(F\), \(CR\), and \(NP\) simultaneously [12; 23]. In [24], the authors think that the parameters values space could be decomposed in three regions for different convergence type, however, they also stated that such a decomposition is difficult to be obtained. The authors proposed a parameter control strategy to keep the parameter values in the good convergence region. In addition to the combination of multiple parameters, the combination of multiple parameter values for one parameter in the population is a different idea.