ReLU Surrogates in Mixed-Integer MPC for Irrigation Scheduling

TL;DR

This work tackles the computational burden of daily irrigation scheduling via mixed-integer MPC for large, spatially variable fields. It replaces a mechanistic soil-moisture model with a ReLU neural network surrogate and exploits its MIL formulation to obtain a MIQP, enabling fast, globally solvable optimization. Compared against LSTM surrogates and triggered irrigation, the ReLU-based approach achieves up to near 100% reductions in solution time while maintaining similar or better water savings and IWUE. The study demonstrates practical potential for real-time, scalable irrigation management in agriculture, with avenues for further robustness enhancements such as offset-free MPC and adaptive parameter estimation.

Abstract

Efficient water management in agriculture is important for mitigating the growing freshwater scarcity crisis. Mixed-integer Model Predictive Control (MPC) has emerged as an effective approach for addressing the complex scheduling problems in agricultural irrigation. However, the computational complexity of mixed-integer MPC still poses a significant challenge, particularly in large-scale applications. This study proposes an approach to enhance the computational efficiency of mixed-integer MPC-based irrigation schedulers by employing ReLU surrogate models to describe the soil moisture dynamics of the agricultural field. By leveraging the mixed-integer linear representation of the ReLU operator, the proposed approach transforms the mixed-integer MPC-based scheduler with a quadratic cost function into a mixed-integer quadratic program, which is the simplest class of mixed-integer nonlinear programming problems that can be efficiently solved using global optimization solvers. The effectiveness of this approach is demonstrated through comparative studies conducted on a large-scale agricultural field across two growing seasons, involving other machine learning surrogate models, specifically Long Short-Term Memory (LSTM) networks, and the widely used triggered irrigation scheduling method. The ReLU-based approach significantly reduces solution times -- by up to 99.5\% -- while achieving comparable performance to the LSTM approach in terms of water savings and Irrigation Water Use Efficiency (IWUE). Moreover, the ReLU-based approach maintains enhanced performance in terms of total prescribed irrigation and IWUE compared to the widely-used triggered irrigation scheduling method.

Figures (6)

• Figure 1: A schematic diagram of a spatially variable field with variability in crop and soil. The field is divided into 4 distinct MZs, each with uniform soil and crop properties.
• Figure 2: Study area and its management zone map.
• Figure 3: Predictive performance of the identified ReLU neural networks.
• Figure 4: Prescribed irrigation schedules and the trajectories of root zone soil moisture content for the 2015 season.
• Figure 5: Prescribed irrigation schedules and the trajectories of root zone soil moisture content for the 2022.