Comparison of the efficiency of gray wolf optimizer and imperialist competitive algorithms in an optimal allocation of water in irrigation and drainage networks (case study: Sofi-Chay network)

Introduction:
Water scarcity is one of the most important issues in the 21st century that human societies encounter. Population growth, industrial and agricultural production, rapid urbanization, and severe climate change have had a major impact on limited water resources and the environment in river basins. The optimal allocation of water resources among consumers requires effective measurements of water resources and its integrated management for human and environmental justice. Optimization of water resource allocation is a very complex decision to make in several levels, stages, subjects, objectives, and non-linear communications. With the complexity of water allocation issues, its algorithms have been gradually improved, and the use of intelligent meta-analysis algorithms in optimizing the allocation of water resources from traditional math planning has surpassed. However, the effectiveness of conventional optimization algorithms is not ideal from a variety of perspectives, and issues such as convergence, computational speed, initial sensitivity, etc., due to the complexity and multi-purpose of optimizing water allocation, require further studies to improve the efficiency of the algorithm and obtaining a desirable overall solution.
Material and methods:
The gray wolf algorithm mimics the hierarchy of leadership and the mechanism of hunting gray wolves in nature. In this algorithm, four types of gray wolves, including alpha, beta, delta, and omega have been used to simulate a hierarchy of leadership. Also, the colonial competition algorithm begins with some primary random populations, each of which is called a "country". Some of the best population elements (equivalent to the elites in the genetic algorithm) are chosen as imperialists. The remaining population is considered as a colony. Colonialists, depending on their power, are pulling these colonies into a particular process. In this research, the gray wolf and colonial competition algorithms were used to optimize water resources values during 2000-2012 regarding the Sofi-Chay irrigation and drainage network and Alavian dam to achieve the optimal policy. The Alavian dam in the province of East Azerbaijan, 3km north of Maragheh city, near the village of Alavian, has been constructed on the Sofi-Chai River, and supplies drinking water to the Maragheh, Miandoab, Bonab, Ajbashir, and Malekan counties.
Results and discussion:
The results of the implementation of the gray wolf algorithm, compared to the colonial competition algorithm, were very close to the measured value of the amount of allocated water and this suggests the coherence and efficiency of the gray wolf algorithm in water resources system. According to the RMSE values in all four areas, the gray wolf algorithm was 44% less than the colonial competition algorithm and 64% higher in the Nash-Sutcliff coefficient.
Conclusion:
The results of this study showed that the gray wolf algorithm has a suitable speed for finding the optimal response. In other words, it has a high convergence rate and can find an optimal global optimization problem. The results showed that the gray wolf algorithm yielded better and more acceptable results in water utilization in combination with utilizing surface water and underground water resources.