An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems

This paper proposes a hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems. The spiral movement of moths in Moth-Flame Optimization algorithm is introduced into the Water Cycle Algorithm to enhance its exploitation ability. In addition, to increase randomization in the new hybrid method, the streams in the Water Cycle Algorithm are allowed to update their position using a random walk (Levy flight). The random walk significantly improves the exploration ability of the Water Cycle Algorithm. The performance of the new hybrid Water Cycle–Moth-Flame Optimization algorithm (WCMFO) is investigated in 23 benchmark functions such as unimodal, multimodal and fixed-dimension multimodal benchmark functions. The results of the WCMFO are compared to the other state-of-the-art metaheuristic algorithms. The results show that the hybrid method is able to outperform the other state-of-the-art metaheuristic algorithms in majority of the benchmark functions. To evaluate the efficiency of the WCMFO in solving complex constrained engineering and real-life problems, three well-known structural engineering problems are solved using WCMFO and the results are compared with the ones of the other metaheuristics in the literature. The results of the simulations revealed that the WCMFO is able to provide very competitive and promising results comparing to the other hybrid and metaheuristic algorithms.