Optimization of Cropping Pattern through Groundwater Resources Management Using D.E. and PSO Algorithms

Document Type : Research Article

Authors

• M. Komasi ¹
• A. Alizadefard ²

¹ Associate Professor of Civil Engineering Department, Ayatollah Borujerdi University, Iran,

² Civil Engineering Department, Ayatollah Borujerdi University, Iran

https://doi.org/10.22067/jsw.2021.68763.1025

Abstract

Introduction: The occurrence of successive droughts, along with increasing water needs and lack of proper management of water resources has caused a water crisis that has various environmental and economic consequences. In addition to the drought, the change in the cropping pattern towards water crops has also made the water crisis the first critical phenomenon in recent years in the community, which has a direct impact on the agricultural sector as the largest consumer of water. Therefore, optimizing the cropping pattern is one of the most important factors in managing water resources and coping with water shortages. In this study, to determine the optimal cropping pattern of major crops in Silakhor plain in the next three years using two approaches using Linear Programming and Meta-Heuristic Algorithms.
Materials and Methods: In the first step, in order to determine the optimal cropping pattern with the aim of maximizing farmers' incomes in the next three years and the limited water and land available, the amount of rainfall recharge is used as a criterion to determine the water exploitation interval and determine the minimum and maximum exploitation each year. In order to forecast rainfall, SARIMA time series models and Genetic Programming were used considering the data of the last 10 years in both seasonal and monthly modes, and according to RMSE and D.C. criteria, a better model was selected. Then, for each crop year, 100 exploitation scenarios were determined according to the amount of groundwater recharge caused by rainfall and the amount of exploitation in previous years.
In the second step, Linear Programming was used to determine the optimal cropping pattern with the aim of maximizing farmers' incomes and limitations of exploitable water in each scenario and arable land. The price of each product is projected according to the average long-term inflation of the country, i.e., 20%, and the profit from the cultivation of each product was calculated as a proportion of the price of the product in each year by examining the previous years. Finally, the performance of three types of Static, Dynamic, and Classified Dynamics Penalty Functions into two algorithms, Differential Evolution and PSO was investigated to achieve the results obtained from Linear Programming. Static penalty functions use a constant value during the optimization process, whereas in dynamic penalty functions, the fines are modified during the process and depend on the number of generations. In the classified dynamics penalty, groups of violations are also determined, and the penalty of each response is determined according to the amount of violation of the restrictions and the generation number.
Results and Discussion: The results show that with increasing groundwater exploitation, farmers' incomes also increase; However, in the exploitation of more than 223.5, 222.2, and 225.1 million cubic meters for the cropping years 2020-2021, 2021-2022, and 2022-2023, respectively, the limitation of the total arable land has prevented the increase of the area under cultivation, and by increasing exploitation, farmers' incomes remain stable. Also, in order to cultivate four crops of wheat, barley, rice, and corn with the current area under cultivation in Silakhor plain, 142 million cubic meters of water is harvested annually from underground sources. By optimizing the cropping pattern for the four crops studied, with the current water exploitation, the income of farmers in the region will increase by 18%.
In general, the PSO algorithm answers this problem much faster. The average number of iterations of the PSO algorithm to solve each scenario in this problem is 38% of the number of iterations of the Differential Evolution algorithm. Overall, in solving this problem, the PSO algorithm has performed better in 84% of the scenarios. In penalty functions, the best performance in both algorithms belongs to the classified dynamics, dynamic, and static penalty functions, respectively. By changing the penalty function from static to classified dynamics penalty function, the number of iterations of the Differential Evolution algorithm to achieve the Linear Programming solution is reduced by an average of 11%; In contrast, the PSO algorithm did not react significantly to the change in the penalty function, and its repetitions decreased by an average of only 3%.
Conclusion: The results show that the cropping pattern of the region is not optimal, and with the increase of water exploitation, it will move towards the cultivation of water products. Also, by optimizing the cultivation pattern of the region, farmers' incomes can be increased. Examination of Differential Evolution and PSO algorithms with three types of penalty functions also show that using the classified dynamics penalty function in the PSO algorithm can have good results.

Keywords

• Groundwater
• Linear programming
• Metaheuristic algorithms
• Optimization
• Silakhor plain

20.1001.1.20084757.1400.35.3.4.3

Main Subjects

• Irrigation

References

1-       Alabdulkader A.M., Al-Amoud A.I., and Awad F.S. 2012. Optimization of the cropping pattern in Saudi Arabia using a mathematical programming sector model. Agricultural Economics 58(2): 56-60.‏

2-       Amini A., and Mirzaei M. 2014. Consequences of water deficiency crisis and become dry of Zayande-Roud in rural areas (Case study: Baraan plain in eastern Isfahan). Journal of Community Development 5(2):157-180. (In Persian with English abstract)

3-       Birhanu K., Alamirew T., Olumana M.D., Ayalew S., and Aklog D. 2015. Optimizing cropping pattern using chance constraint linear programming for koga irrigation dam, Ethiopia. Irrigation & Drainage Systems Engineering, 10.

4-       Box G.E., Jenkins G.M., and Reinsel G.C. 2011. Time series analysis: forecasting and control. John Wiley & Sons.‏

5-       Chen K.Y., and Wang C.H. 2007. A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan. Expert Systems with Applications 32(1): 254-264.

6-       Coello C.A.C. 2002. Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191(11): 1245-1287.‏

7-       Hekmatnia M., Hosseini S.M., and Safdari M. 2020. Water Resource Management of the Agricultural Sector in Sistan and Baluchestan Province: a Virtual Water Perspective. Journal of Irrigation & Water Engineering 11(41): 137-149. (In Persian with English abstract)

8-       Homaifar A., Qi C.X., and Lai S.H. 1994. Constrained optimization via genetic algorithms. Simulation 62(4): 242-253.

9-       Joines J.A., and Houck C.R. 1994. On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's. p. 579-584. The first IEEE conference on evolutionary computation, June 1994. IEEE world congress on computational intelligence.

10-   Kaur B., Sidhu R.S., and Vatta K. 2010. Optimal crop plans for sustainable water use in Punjab. Agricultural Economics Research Review 23: 273-284.

11-   Kennedy J., and Eberhart R. 1995. Particle swarm optimization. p. 1942-1948. ICNN'95-International Conference on Neural Networks, November 1995.

12-   Komasi M., and Sharghi S. 2019. Recognizing factors affecting decline in groundwater level using wavelet-entropy measure (case study: Silakhor plain aquifer). Journal of Hydroinformatics 21(3): 510-522.

13-   Koza J.R., and Poli R. 1992. Genetic programming: on the programming of computers by means of natural selection. MIT press.

14-   Lu H.W., Huang G.H., and He L. 2010. Development of an interval-valued fuzzy linear-programming method based on infinite α-cuts for water resources management. Environmental Modelling & Software 25(3): 354-361.

15-   Majidi N., Alizadeh A., and Ghorbani M. 2011. Determining The Optimum Cropping Pattern In Same Direction With Water Resources Management Of Mashhad-CHenaran Plain. Journal of Water and Soil 25(4): 776-785. (In Persian with English abstract)

16-   Michalewicz Z. 1995. Genetic algorithms, numerical optimization, and constraints. p. 151-158. The 6^th international conference on genetic algorithms, July 1995. Morgan Kauffman San Mateo.‏

17-   Mohammadian F., Shahnooshi N., Ghorbani M., and Aghel H. 2002. Development of a sustainable crop pattern in Fariman-Torbat Jam plain. Journal of Agricultural Economics 4(2): 1-41. (In Persian)

18-   Moradi H.R., Jalili K., and Bozorg Hadad O. 2017. Optimization of Land and Irrigation Water Allocation Based on Water Balance Approach Using Linear Programming. Journal of Water and Soil 31(2): 372-385. (In Persian with English abstract)

19-   Nourani V., Ranjbar S., and Tootoonchi F. 2016. Change Detection of Hydrological Processes Using Wavelet-Entropy Complexity Measure Case Study: Urmia Lake. Journal of Civil and Environmental Engineering University of Tabriz, 45(3): 75-86. (In Persian with English abstract)

20-   Osama S., Elkholy M., and Kansoh R.M. 2017. Optimization of the cropping pattern in Egypt. Alexandria Engineering Journal, 56(4):557-566.

21-   Parsopoulos K.E., and Vrahatis M.N. 2002. Particle swarm optimization method for constrained optimization problems. Intelligent Technologies–Theory and Application: New Trends in Intelligent Technologies 76(1): 214-220.‏

22-   Price K., Storn R.M., and Lampinen J.A. 2006. Differential evolution: a practical approach to global optimization. Springer Science & Business Media.‏‏

23-   Rabani F., and Alikhani A. 2010. Regional Analysis of Climate Change (Drought) in the Karaj River Basin. Water challenge scientific conference in Qom. (In Persian)

24-   Raju K.S., and Kumar D.N. 2004. Irrigation planning using genetic algorithms. Water Resources Management 18(2): 163-176.

25-   Reddy M.J., and Kumar D.N. 2007. Optimal reservoir operation for irrigation of multiple crops using elitist-mutated particle swarm optimization. Hydrological Sciences Journal 52(4): 686-701.

26-   Selle B., and Muttil N. 2011. Testing the structure of a hydrological model using Genetic Programming. Journal of Hydrology 397(1-2): 1-9.

27-   Shumway R.H., and Stoffer D.S. 2017. Time series analysis and its applications: with R examples. Springer.

28-   Siasar H., & Honar T. 2017. Optimization of Water Allocation Pattern crops Using a Genetic Algorithm. Proceedings of 3^th International Conference on Agricultural Engineering and Natural Resources, July 2017. Ghazvin, Iran. (In Persian with English abstract)

29-   Storn R., and Price K. 1997. Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11(4): 341-359.

30-   Vahidi A. 2012. The Impact of Climate Change and Drought on Iran's Water Resources. Proceedings of 5^th National Conference on Watershed Management and Soil and Water Resources Management, 2012. The Iranian Society of Irrigation & Water Engineering Kerman. Iran. (In Persian)

31-   Yang J.M., Chen Y.P., Horng J.T., and Kao C.Y. 1997. Applying family competition to evolution strategies for constrained optimization. p. 201-211. International conference on evolutionary programming, April 1997. Springer, Berlin, Heidelberg.‏

32-   Yeniay Ö. 2005. Penalty function methods for constrained optimization with genetic algorithms. Mathematical and computational Applications 10(1): 45-56.

33-   Yoosefdoost I., Mohamadrezapuor O., and Ebrahimi M. 2016. Applying Genetic Algorithms in Determining Optimal Cropping Pattern in Different Weather Conditions in Qazvin Plain. Journal of Water Research in Agriculture 30(3): 317-331. (In Persian with English abstract)