OPTIMIZATION OF AGRICULTURAL CROP ALLOCATION IN WATER-SCARE REGIONS USING THE FRANK-WOLFE ALGORITHM

Authors

  • Nietbay Uteulievich Uteuliev

    Nukus State Technical University

  • Kuuanyshbay Duisenbaevich Kulmuratov

    Nukus State Technical University

  • Polatbek Jumabaevich Kalkhanov

    University of Innovative Technologies

Keywords: Frank–Wolfe method, nonlinear programming, model, optimization, quadratic function, objective function, conditional gradient method

Abstract

The paper develops a nonlinear programming model for optimizing crop area allocation on a 45-hectare experimental plot in the Chimbay district of Karakalpakstan among four crops – cotton, wheat, melon and mung bean. Unlike conventional linear models, a quadratic objective function is applied that accounts for diminishing marginal productivity and soil salinity. The model incorporates nine groups of constraints, from seasonal water quotas to labour and financial resources, and is solved by the Frank–Wolfe method. Total net profit increased by 20.5% (from 425.6 to 512.8 million UZS) and water use efficiency improved by 18.8%.

References

1. Besbes M., Makhlouf M., Hammami S. Optimal resource allocation in agriculture: a nonlinear programming approach. // European Journal of Operational Research, 2022, 298(3). – P. 1012-1025.

2. Bobojonov I., Lamers J.P.A., Bekchanov M., Djanibekov N., Martius C., Müller M. Optimization of crop allocation under uncertainty: a case study from Uzbekistan. // Agricultural Systems, 2016, 148. – P. 112-121.

3. Chen Y., Zhang W., Li H., Wang J. A nonlinear programming model for optimal irrigation water allocation based on crop water productivity. // Water Resources Management, 2023, 37. -P. 2105-2121.

4. Frank M., Wolfe P. An algorithm for quadratic programming. // Naval Research Logistics Quarterly, 1956, 3(1-2). – P. 95-110.

5. Jaggi M. Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization. // Proceedings of the 30th International Conference on Machine Learning (ICML), 2013, 28. – P. 427-435.

6. Karimov A., Matyakubov B., Hamidov M. Sustainable agricultural practices in Karakalpakstan: challenges of water scarcity. // Sustainability, 2024, 16(1). – P. 88.

7. Karimov A., Matyakubov B., Shirokova Y., Okuyama A. Spatial and temporal variation of soil salinity in the lower reaches of the Amu Darya River. // Arid Land Research and Management, 2021, 35(3). – P. 261-278.

8. Khaydarov S., Matyakubov B., Karimov A. Optimizing crop rotation patterns for water saving in the Aral Sea region. // Central Asian Journal of Water Research, 2022, 8(2). – P. 12-28.

9. Salaev O., Matyakubov B., Karimov A. Climate change impact on water resources and crop yield in the lower reaches of the Amudarya river. //Environmental Science & Policy, 2023, 140. –P. 11-23.

10. Zhu X., Zhang J., Zhang X., Liu J. Mathematical modeling of crop yield response to water deficit: a review. // Agricultural Systems, 2022, 196. – P. 103325.