Abstract
In this study, the capability of recently introduced Moth Swarm Algorithm (MSA) was compared with two robust meta-heuristics of harmony search (HS) algorithm and imperialist competitive algorithm (ICA). First, the performance of these algorithms was assessed by seven benchmark functions having 2–30 dimensions. Next, they were compared in optimization of complex problem of 4-reservoir and 10-reservoir systems operation. Furthermore, the results of these algorithms were compared with nine other metaheuristic algorithms developed by several researchers. Sensitivity analysis was performed to determine the appropriate values of the algorithms parameters. The statistical indices of R2, RMSE, MAE, MSE, NMSE, MAPE, and Willmott's index of agreement were used to compare the algorithms performance. The results showed that the MSA was the superior algorithm in solving all benchmark functions in terms of obtaining the optimal value and saving the CPU usage. ICA and HS were placed in the next orders, respectively. It was found that by increasing the dimensions of the problem, the performance of ICA and HS dropped but the MSA has still performed extraordinary. In addition, the minimum CPU usage and the best solutions for optimal operation of four-reservoir system were obtained by MSA algorithm with values of (269.7s and 308.83) which are very close to the global optimum solution. Corresponding values for ICA and HS were (486.73, 306.47) and (638.61s, 264.61) respectively, which put them in the next ranks. Similar results were observed for ten-reservoir system; the CPU time and optimal value obtained by MSA were (722.5s, 1,195.58) while for ICA and HS were (1,421.62s, 1,136.22) and (1,963.41s, 1,060.76), respectively. The values of R2 and RMSE achieved by MSA were (0.951, 0.528) and (0.985, 0.521) for 4-reservoir and 10-reservoir systems which demonstrated the outstanding performance of this algorithm in optimal operation of multi-reservoir systems. In a general comparison, it was concluded that among the twelve investigated algorithms, MSA was the best, and it is recommended as a robust promising tool in optimal operation of multi-reservoir systems.