A novel differential crossover strategy based on covariance matrix learning with Euclidean neighborhood for solving real-world problems

Solving real-world optimization problems is considered a challenging task. This is due to the variability of the characteristics in objective functions, the presence of enormous number of local optima within the search space and highly nonlinear constraints with large number of variables. The advances on this type of problems are of capital importance for many researchers to develop new efficient evolutionary algorithms to tackle such problems in an efficient manner with better solutions. For this reason, this work proposes a new crossover technique based on covariance learning with Euclidean neighborhood which has been incorporated in the basic L-SHADE algorithm. The goal of this new technique is to help L-SHADE establish a suitable coordinate system for the crossover operator. This helps enhance L-SHADE capability to solve real world problems with difficult characteristics and nonlinear constraints. The proposed algorithm, namely L-covnSHADE, is tested on one of the challenging benchmarks which is the IEEE CEC'11 on real-world numerical optimization problems. This set consists of 22 real-world problems with diverse stimulating characteristics and a dimensionality ranging from 1 to 240 dimensions. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to the L-SHADE algorithm and other state-of-the-art algorithms including the winner of the CEC2011 competition.