FDA_CPR: An efficient improved flow direction algorithm with cellular topological structure, potential energy concept and rockfall strategy

Aiming at the problems of Flow Direction Algorithm (FDA), such as premature convergence and tendency to fall into local optimum, this paper proposes an efficient improved version named FDA_CPR. Firstly, the embedding of the topological structure of cellular automata to increase the population diversity of the algorithm. Then, Lévy flight is used to replace the D8 algorithm of FDA and a position update strategy based on Sine Cosine Algorithm to slow down the convergence of the algorithm. Furthermore, a new concept of “potential energy” is introduced to calculate the energy score of the flow and determine the new direction of movement to improve the search efficiency of the algorithm. Finally, a “rockfall strategy” based on dynamic opposite learning is designed to help the algorithm jump out of the local optimum. FDA_CPR is compared with eight well-known algorithms on CEC2017 and several feature selection problems to evaluate its performance. Qualitative analysis, Friedman's test and Wilcoxon signed rank test confirmed the effectiveness of the improvement in different ways. Various experimental results show that FDA_CPR has considerable advantages in solving both discrete and continuous problems, and its comprehensive performance is better than that of FDA and other comparison algorithms.