Differential evolution (DE) is an efficient and robust evolutionary algorithm, which has been widely applied to solve global optimization problems. As we know, crossover operator plays a very important role on the performance of DE. However, the commonly used crossover operators of DE are dependent mainly on the coordinate system and are not rotation-invariant processes. In this paper, covariance matrix learning is presented to establish an appropriate coordinate system for the crossover operator. By doing this, the dependence of DE on the coordinate system has been relieved to a certain extent, and the capability of DE to solve problems with high variable correlation has been enhanced. Moreover, bimodal distribution parameter setting is proposed for the control parameters of the mutation and crossover operators in this paper, with the aim of balancing the exploration and exploitation abilities of DE. By incorporating the covariance matrix learning and the bimodal distribution parameter setting into DE, this paper presents a novel DE variant, called CoBiDE. CoBiDE has been tested on 25 benchmark test functions, as well as a variety of real-world optimization problems taken from diverse fields including radar system, power systems, hydrothermal scheduling, spacecraft trajectory optimization, etc. The experimental results demonstrate the effectiveness of CoBiDE for global numerical and engineering optimization. Compared with other DE variants and other state-of-the-art evolutionary algorithms, CoBiDE shows overall better performance. 
Differential evolution based on covariance matrix learning and bimodal distribution parameter setting