Optimal management of groundwater abstraction using NSGA-Ⅱ, SPEA-Ⅱ and PESA algorithms (Case study: Silakhor plain)

The groundwater level of Silakhor plain has decreased significantly with the occurrence of successive droughts, industrial growth and increasing water needs. In addition, the cultivation pattern of the region in recent years has tended to cultivate water crops, and the combination of these events raises the need for efficient management in the allocation of limited water resources in the region. In this study, in order to sustainable management of groundwater resources, the optimal cultivation pattern of major crops in Silakhor plain has been determined, with the aim of maximizing farmers' net income and available water and land constraints. In this regard, two approaches to using Linear Programming (LP) and using Multi-Objective Meta Heuristic Algorithms in different exploitation scenarios have been investigated and the performance of different penalty functions in algorithms has been evaluated. Also, how to change the optimal cultivation pattern by increasing groundwater exploitation has been studied.

In the first step, after modeling the rainfall of the last 10 years using Artificial Neural Network (ANN) and Genetic Programming (GP) and selecting a better model in terms of accuracy, rainfall for the next three years was forecasted and groundwater recharge was estimated. Then, for each crop year, 100 different exploitation scenarios were considered according to the groundwater recharge and water exploitation in previous years. In the second step, using LP with the aim of maximizing farmers' incomes and available water and land constraints, the optimal cultivation pattern was obtained in the determined exploitation scenarios. Finally, in order to unbound the problem, the mentioned constraints were implemented as static, dynamic and classified dynamic penalty functions in MATLAB software. Then, the performance of three algorithms NSGA-Ⅱ, SPEA-Ⅱ and PESA-Ⅱ with the objective functions of maximizing farmers' incomes and minimizing penalty functions, to achieve the optimal cultivation pattern obtained from LP was examined.

The results of this study indicate that although with the increase of groundwater exploitation, farmers' incomes increase in the optimal cultivation pattern; However, in the exploitation of more than 223.5, 222.2 and 225.1 million m3 for the cropping years 2020-2021, 2021-2022 and 2022-2023, respectively, the limitation of the total arable land in Silakhor plain prevents the increase of crop cultivation and the area under cultivation of crops remains constant and consequently the income of farmers does not change. The results of the study of algorithms and penalty functions also show that in this problem, the best performance among the algorithms belongs to SPEA-Ⅱ, PESA-Ⅱ and NSGA-Ⅱ algorithms, respectively, with an average number of iterations of 12.1, 14.5 And is 17.8. Among the penalty functions in all three algorithms, the best performance belongs to the classified dynamic, dynamic and static penalty functions with an average number of repetitions of 13.1, 13.7 and 17.5, respectively.

In general, it can be seen that the optimization of the cultivation pattern in different exploitation scenarios provides a comprehensive view to the authorities for the sustainable management of valuable and limited water resources and its optimal allocation. In this regard, the use of SPEA-Ⅱ algorithm with classified dynamic penalty function in determining the optimal cultivation pattern leads to desirable results.