Many Differential Evolution algorithms are introduced in the literature to solve optimization problems with diverse set of characteristics. In this paper, we propose an extension of the previously published paper LSHADE-EpSin that was ranked as the joint winner in the real-parameter single objective optimization competition, CEC 2016. The contribution of this work constitutes two major modifications that have been added to enhance the performance: ensemble of sinusoidal approaches based on performance adaptation and covariance matrix learning for the crossover operator. Two sinusoidal waves have been used to adapt the scaling factor: non-adaptive sinusoidal decreasing adjustment and an adaptive sinusoidal increasing adjustment. Instead of choosing one of the sinusoidal waves randomly, a performance adaptation scheme based on earlier success is used in this work. Moreover, covariance matrix learning with Euclidean neighborhood is used for the crossover operator to establish a suitable coordinate system, and to enhance the capability of LSHADE-EpSin to tackle problems with high correlation between the variables. The proposed algorithm, namely LSHADE-cnEpSin, is tested on the IEEE CEC2017 problems used in the Special Session and Competitions on Single Objective Bound Constrained Real-Parameter Single Objective Optimization. The results statistically affirm the efficiency of the proposed approach to obtain better results compared to other state-of-the-art algorithms.

An effective and efficient self-adaptation framework is proposed to improve the performance of the L-SHADE algorithm by providing successful alternative adaptation for the selection of control parameters. The proposed algorithm, namely LSHADE-EpSin, uses a new ensemble sinusoidal approach to automatically adapt the values of the scaling factor of the Differential Evolution algorithm. This ensemble approach consists of a mixture of two sinusoidal formulas: A non-Adaptive Sinusoidal Decreasing Adjustment and an adaptive History-based Sinusoidal Increasing Adjustment. The objective of this sinusoidal ensemble approach is to find an effective balance between the exploitation of the already found best solutions, and the exploration of non-visited regions. A local search method based on Gaussian Walks is used at later generations to increase the exploitation ability of LSHADE-EpSin. The proposed algorithm is tested on the IEEE CEC2014 problems used in the Special Session and Competitions on Real-Parameter Single Objective Optimization of the IEEE CEC2016. The results statistically affirm the efficiency and robustness of the proposed approach to obtain better results compared to L-SHADE algorithm and other state-of-the-art algorithms.