ReLU Surrogates in Mixed-Integer MPC for Irrigation Scheduling

TL;DR

This paper introduces ReLU surrogate models to improve the computational efficiency of mixed-integer MPC for irrigation scheduling, achieving significant speedups while maintaining water-saving performance.

Contribution

It presents a novel ReLU surrogate modeling approach that transforms mixed-integer MPC into a more solvable form, enabling large-scale irrigation scheduling with reduced computation time.

Findings

Solution times reduced by up to 99.5%

Comparable water savings to LSTM-based methods

Outperforms triggered irrigation scheduling in efficiency

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.