Differential evolution for population diversity mechanism based on covariance matrix.

Differential evolution (DE) is a heuristic global search algorithm based on population. It has exhibited great adaptability in solving continuous-domain problems, but sometimes suffered from insufficient local search ability and being trapped in local optimum when dealing with complicated optimization problems. To solve these problems, an improved differential evolution algorithm with population diversity mechanism based on covariance matrix (CM-DE) is proposed. First, a new parameter adaptation strategy is used to adapt the control parameters, in which the scale factor F is updated according to the improved wavelet basis function in the early stage and Cauchy distribution in the later stage and the crossover rate C R is generated according to normal distribution. The diversity of population and convergence speed are improved by employing the method above. Second, the perturbation strategy is incorporated into crossover operator to enhance the search ability of DE. Finally, the covariance matrix of the population is constructed, where the variance in the covariance matrix is used as indicator to measure the similarity between individuals in the population in order to prevent the algorithm from falling into local optimum resulted by low population diversity. The CM-DE is compared with the state-of-art DE variants including LSHADE (Tanabe and Fukunaga, 2014), jSO [1] , LPalmDE [2] , PaDE [3] and LSHADE-cnEpSin [4] under 88 test functions from CEC2013 [5] , CEC2014 [6] and CEC2017 (Wu et al., 2017) test suites. From the experiment results, it is obvious that among 30 benchmark functions from CEC2017 on 50D optimization, the CM-DE algorithm has 22, 20, 24, 23, 28 better performances comparing with LSHADE, jSO, LPalmDE, PaDE, and LSHADE-cnEpsin. For CEC2017 on 30D optimization, the proposed algorithm secures better performance on 19 out of 30 benchmark functions in terms of convergence speed. In addition, a real-world application is also used to verify the feasibility of the proposed algorithm. The experiment results validate the highly competitive performance in terms of solution accuracy and convergence speed. • A new parameter adaptation mechanism is proposed to adjust the scale factor F and crossover rate CR. The experiment results show that the new parameter adaptation mechanism improves the exploration ability of the proposed algorithm. • In order to prevent prematureness, a perturbation strategy is incorporated into the crossover strategy, which firstly constructs a new crossover operation between the mutant vector and target vector based on the t-distribution probability density function; secondly, the information of the outstanding individuals is used to guide the search direction. • By calculating the covariance matrix of the population, the variance in the covariance matrix is used to determine the diversity of individuals in the current population. In the iterative process, a counter is set to count the number of variances in each dimension that is less than the set condition. When the counter meets the predefined threshold, a simple competition mechanism is used to increase the diversity of the population by perturbing the t-distribution or the Cauchy distribution for all stagnant individuals. [ABSTRACT FROM AUTHOR]