Adaptive differential evolution with fitness-based crossover rate for global numerical optimization

Abstract

Abstract Differential evolution (DE) is one of the most efficient evolution algorithms (ES) for dealing with nonlinear, complicated and difficult global optimization problems. The main contribution of this paper can be summarized in three directions: Firstly, a novel crossover rate (CR) generation scheme based on the zscore value of fitness, named fcr, is introduced. For a minimization problem, the proposed CR generation strategy always assigns a smaller CR value to individual with smaller fitness value. Therefore, the parameters of individuals with better fitness are inherited by their offspring with high probability. In the second direction, the control parameters are adjusted by unused bimodal settings in which each parameter setting is selected according to the evolution status of individual. The third direction of our work is introducing the L1 norm distance as the weights for updating the mean value of crossover rate and scale factor. Theoretically, compared with L2 norm, L1-norm is more efficient to suppress outliers in the difference vector. These modifications are first integrated with the mutation strategy of JADE, then a modified version, named JADEfcr, is proposed. In addition, to improve the optimization ability further, another variant LJADEfcr by using a linear population reduction mechanism is considered. So as to confirm and examine the performance of JADEfcr and LJADEfcr, numerical experiments are conducted on 29 optimization problems defined by CEC2017 benchmark. For JADEfcr, its experimental results are made a comparison with twelve state-of-the-art algorithms. The comparative study demonstrates that in terms of robustness, stability and solution quality, JADEfcr are better and highly competitive with these well-known algorithms. For LJADEfcr, its results are compared with JADEfcr and other nine powerful algorithms including four recent algorithms and five top algorithms on CEC2017 competition. Experimental results indicate that LJADEfcr is superior and statistically competitive with these excellent algorithms in terms of robustness, stability and the quality of the obtained solutions.

Keywords

• Differential evolution
• Crossover rate
• Population size reduction
• Bimodal parameter setting