Two new hybrid algorithms are proposed to improve the performances of the meta-heuristic optimization algorithms, namely the Grey Wolf Optimizer (GWO) and Shuffled Frog Leaping Algorithm (SFLA). Firstly, it advances the hierarchy and position updating of the mathematical model of GWO, and then the SGWO algorithm is proposed based on the advantages of SFLA and GWO. It not only improves the ability of local search, but also speeds up the global convergence. Secondly, the SGWOD algorithm based on SGWO is proposed by using the benefit of differential evolution strategy. Through the experiments of the 29 benchmark functions, which are composed of the functions of unimodal, multimodal, fixed-dimension and composite multimodal, the performances of the new algorithms are better than that of GWO, SFLA and GWO-DE, and they greatly balances the exploration and exploitation. The proposed SGWO and SGWOD algorithms are also applied to the prediction model based on the neural network. Experimental results show the usefulness for forecasting the power daily load. Appl. Sci. 2019, 9, 4514 2 of 22 the process. The algorithm is an effective way to solve global optimization problems, and it has the characteristics of generality, stability, and fast convergence. It includes two criteria, exploration and exploitation. Exploitation reflects the ability of finding the best around a good range, while exploration reflects the ability of searching for new range. At the beginning, it should search the whole range as much as possible, then through using exploitation it searches more carefully around the good solution. But they are contradictory. Too small exploration leads to convergence too fast and easy falling into local optimum; however, too small exploitation makes the algorithm converge too slowly.The No Free Lunch (NFL) theorem considers that there is no meta-heuristic algorithm applying for all optimization problems [1,2]. In other words, an algorithm shows very promising results on a set of issues, but it doesn't perform well on another set of issues. So it needs putting forward a new algorithm to get high performance in certain specific areas.Over the past decades, a large number of meta-heuristics are inspired by natural behaviors [3-5], such as, Genetic Algorithm (GA) [6][7][8], Differential Evolution (DE) Algorithm [9-12], Grey Wolf Optimizer (GWO) Algorithm [13-17], Particle Swarm Optimization (PSO) Algorithm [18-21], Artificial Bee Colony (ABC) Algorithm [22-24], Cat Swarm Optimization (CSO) [25-27], Artificial Fish Swarm Algorithm (AFSA) [28,29], Ant Colony Optimization (ACO) Algorithm [30-34], Shuffled Frog Leaping Algorithm (SFLA) [35-40], Biogeography Based Optimization (BBO) Algorithm [41-43], QUasi-Affine TRansformation Evolutionary (QUATRE) Algorithm [44][45][46][47] and so on. Because they all have some defects, many researchers also introduce hybrid algorithms to improve the defects [48][49][50][51][52][53][54][55].The rest of the paper is organized as follows: some related research works are described in the Secti...