the objective function

The optimal operation of a multi-purpose reservoir is one of the complex and non-linear problems in multi-objective optimization. The limit of water resources and its non-uniform distribution have made the optimal management and utilization of water resources metaheuristic algorithms are suitable optimization methods, so in this study, water cycle algorithms, The gray wolf algorithms, and a combination of these two algorithms were studied in single-objective and multi-objective and compared to find the optimize operation model of Latian and Dez dams. After examining the effectiveness of the single-objective mode of water cycle algorithms, gray wolf, and combination mode using 8 standard benchmark functions and these algorithms were measured by ZDT functions, they were used to solve the problem of optimal operation in the Latian reservoir system. Also, the performance of the algorithms was evaluated using the performance indicators of the reservoir, and these algorithms were assessed using ZDT functions. The results showed that the hybrid algorithm provides a better answer in almost all functions of both the water cycle algorithm and the gray wolf. According to the results obtained from the operation model of Latian Dam, the hybrid algorithm with the value of the objective function of 0.011, provides 98.57% of the downstream needs, the total amount of deficiencies is 1.43%, and with the stability index of 97% and presents the convergence and release curve. It performed better than the two water cycle algorithms and the gray wolf.