Future search algorithm imitates the person living life. If one person finds that his life is not good, he will try to change his living life, and he will imitate a more successful person. To overcome insufficient performances of the basic Future search algorithm, this paper proposed an improved Future search algorithm based on the sine cosine algorithm (FSASCA). The proposed algorithm uses sine cosine algorithm to loop-progressive find the best solution. The searching method of the sine cosine algorithm can make the feasible solution to be re-positioned around another feasible solutions, which can make the proposed algorithm have a strong exploitation ability. Four coefficient factors are added in the basic FSA, and new update methods are introduced in the searching phase. To verify the searching and optimization performances of the proposed algorithm in this paper, this paper also gives data calculation results, Wilcoxon rank sum test , iteration figures, box plot figures, and searching path figures. Experimental results showed that FSASCA has a better iteration speed, the convergence precision, the solving accuracy, the strong competitive, and the high balance.INDEX TERMS Future search algorithm, sine cosine algorithm, optimization problem, function optimization.

Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm’s diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm.