CWCA: Complex-valued encoding water cycle algorithm.

Since the meta-heuristic water cycle algorithm (WCA) was presented, it has been used extensively in scientific computation and engineering optimization. The aims of this study are to improve the exploration and exploitation capabilities of the WCA algorithm, accelerate its convergence speed, and enhance its calculation accuracy. In this paper, a novel complex-valued encoding WCA (CWCA) is proposed. The positions of rivers and streams are divided into two parts, that is, the real part and imaginary part, and modified formulas for the new positions of rivers and streams are proposed. To evaluate the performance of the CWCA, 12 benchmark functions and four engineering examples were considered. The experimental results indicated that the CWCA had higher precision and convergence speed than the real-valued WCA and other well-known meta-heuristic algorithms.