arXiv subjects

Bernard T. Agyeman

Publications and source records attributed to Bernard T. Agyeman.

15 recordsLinked to original sources

arXiv2026

A Hybrid Reinforcement and Self-Supervised Learning Aided Benders Decomposition Algorithm

We propose a hybrid reinforcement and self-supervised learning framework for accelerating generalized Benders decomposition (GBD). In this framework, a graph based reinforcement learning agent operates on a bipartite representation of the master problem and, together with a verification mechanism, determines the integer variable assignments that solve the master problem. These assignments are then used as inputs to a KKT informed neural network, trained via self supervision to predict primal dual solutions that approximately satisfy the Karush Kuhn Tucker conditions of the subproblem. The predicted solutions are used to construct Benders cuts directly. The framework is evaluated on a mixed integer nonlinear programming case study, where it achieves a 57.5% reduction in solution time relative to classical GBD while consistently recovering optimal solutions across all test instances.

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arXiv2026

Feasibility-Aware Imitation Learning for Benders Decomposition

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.

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arXiv2025

Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition

This work introduces an end-to-end graph-based agent for accelerating the computational efficiency of Benders Decomposition. The agent's policy is parameterized by a graph neural network which takes as input a bipartite graph representation of the master problem and proposes a candidate solution. The agent is trained using a two-stage approach that combines imitation (IL) and reinforcement learning (RL). IL is used to mimic a solver and obtain a warm-start policy which is then finetuned using RL with a reward signal that balances feasibility and computational efficiency. We augment the agent with a verification mechanism that checks the agent's prediction for feasibility and solution quality. The framework is evaluated in two case studies: (i) an illustrative mixed-integer nonlinear program, where it reduces the solution time by 42% without loss of solution quality, and (ii) a closed-loop irrigation scheduling problem, where it achieves a 23% time reduction without compromising water use efficiency.

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arXiv2025

Learning to control inexact Benders decomposition via reinforcement learning

Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf application to online settings can be computationally inefficient due to the repeated solution of the master problem. An approach to reduce the solution time is to solve the master problem to local optimality. However, identifying the level of suboptimality at each iteration that minimizes the total solution time is nontrivial. In this paper, we propose the application of reinforcement learning to determine the best optimality gap at each GBD iteration. First, we show that the inexact GBD can converge to the optimal solution given a properly designed optimality gap schedule. Next, leveraging reinforcement learning, we learn a policy that minimizes the total solution time, balancing the solution time per iteration with optimality gap improvement. In the resulting RL-iGBD algorithm, the policy adapts the optimality gap at each iteration based on the features of the problem and the solution progress. In numerical experiments on a mixed-integer economic model predictive control problem, we show that the proposed RL-enhanced iGBD method achieves substantial reductions in solution time.

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arXiv2025

Sensitivity-Informed Parameter Selection for Improved Soil Moisture Estimation from Remote Sensing Data

Improving the accuracy of soil moisture estimation is required for advancing irrigation scheduling and water conservation efforts. Central to this task are soil hydraulic parameters, which govern moisture dynamics but are rarely known precisely and must therefore be inferred from observational data. In large-scale agricultural fields, estimating the complete set of these parameters is often impractical due to the sparse and noisy nature of available measurements. To address this challenge, this work develops a framework that uses sensitivity analysis and orthogonal projection to identify parameters that are both reliably estimable from available data. These parameters, together with the spatial distribution of soil moisture, are jointly estimated by assimilating observational data into a cylindrical-coordinate version of the Richards equation using an extended Kalman filter. The soil moisture measurements are obtained from microwave remote sensors mounted on center pivot irrigation systems - an emerging and practical technology for capturing field-scale variability. Numerical simulations and field experiments conducted on a large-scale site in Lethbridge, Alberta, Canada, demonstrate that the proposed method improves soil moisture estimation accuracy by 24-43% and enhances predictive model performance by 50%. Furthermore, the estimated parameters - particularly saturated hydraulic conductivity - exhibit good agreement with experimental measurements.

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arXiv2024

ReLU Surrogates in Mixed-Integer MPC for Irrigation Scheduling

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.

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arXiv2024

A semi-centralized multi-agent RL framework for efficient irrigation scheduling

This paper proposes a Semi-Centralized Multi-Agent Reinforcement Learning (SCMARL) approach for irrigation scheduling in spatially variable agricultural fields, where management zones address spatial variability. The SCMARL framework is hierarchical in nature, with a centralized coordinator agent at the top level and decentralized local agents at the second level. The coordinator agent makes daily binary irrigation decisions based on field-wide conditions, which are communicated to the local agents. Local agents determine appropriate irrigation amounts for specific management zones using local conditions. The framework employs state augmentation approach to handle non-stationarity in the local agents' environments. An extensive evaluation on a large-scale field in Lethbridge, Canada, compares the SCMARL approach with a learning-based multi-agent model predictive control scheduling approach, highlighting its enhanced performance, resulting in water conservation and improved Irrigation Water Use Efficiency (IWUE). Notably, the proposed approach achieved a 4.0% savings in irrigation water while enhancing the IWUE by 6.3%.

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arXiv2024

Performance triggered adaptive model reduction for soil moisture estimation in precision irrigation

Accurate soil moisture information is crucial for developing precise irrigation control strategies to enhance water use efficiency. Soil moisture estimation based on limited soil moisture sensors is crucial for obtaining comprehensive soil moisture information when dealing with large-scale agricultural fields. The major challenge in soil moisture estimation lies in the high dimensionality of the spatially discretized agro-hydrological models. In this work, we propose a performance-triggered adaptive model reduction approach to address this challenge. The proposed approach employs a trajectory-based unsupervised machine learning technique, and a prediction performance-based triggering scheme is designed to govern model updates adaptively in a way such that the prediction error between the reduced model and the original model over a prediction horizon is maintained below a predetermined threshold. An adaptive extended Kalman filter (EKF) is designed based on the reduced model for soil moisture estimation. The applicability and performance of the proposed approach are evaluated extensively through the application to a simulated large-scale agricultural field.

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arXiv2023

Optimizing the switching operation in monoclonal antibody production: Economic MPC and reinforcement learning

Monoclonal antibodies (mAbs) have emerged as indispensable assets in medicine, and are currently at the forefront of biopharmaceutical product development. However, the growing market demand and the substantial doses required for mAb clinical treatments necessitate significant progress in its large-scale production. Most of the processes for industrial mAb production rely on batch operations, which result in significant downtime. The shift towards a fully continuous and integrated manufacturing process holds the potential to boost product yield and quality, while eliminating the extra expenses associated with storing intermediate products. The integrated continuous mAb production process can be divided into the upstream and downstream processes. One crucial aspect that ensures the continuity of the integrated process is the switching of the capture columns, which are typically chromatography columns operated in a fed-batch manner downstream. Due to the discrete nature of the switching operation, advanced process control algorithms such as economic MPC (EMPC) are computationally difficult to implement. This is because an integer nonlinear program (INLP) needs to be solved online at each sampling time. This paper introduces two computationally-efficient approaches for EMPC implementation, namely, a sigmoid function approximation approach and a rectified linear unit (ReLU) approximation approach. It also explores the application of deep reinforcement learning (DRL). These three methods are compared to the traditional switching approach which is based on a 1% product breakthrough rule and which involves no optimization.

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arXiv2023

Integrating machine learning paradigms and mixed-integer model predictive control for irrigation scheduling

The agricultural sector currently faces significant challenges in water resource conservation and crop yield optimization, primarily due to concerns over freshwater scarcity. Traditional irrigation scheduling methods often prove inadequate in meeting the needs of large-scale irrigation systems. To address this issue, this paper proposes a predictive irrigation scheduler that leverages the three paradigms of machine learning to optimize irrigation schedules. The proposed scheduler employs the k-means clustering approach to divide the field into distinct irrigation management zones based on soil hydraulic parameters and topology information. Furthermore, a long short-term memory network is employed to develop dynamic models for each management zone, enabling accurate predictions of soil moisture dynamics. Formulated as a mixed-integer model predictive control problem, the scheduler aims to maximize water uptake while minimizing overall water consumption and irrigation costs. To tackle the mixed-integer optimization challenge, the proximal policy optimization algorithm is utilized to train a reinforcement learning agent responsible for making daily irrigation decisions. To evaluate the performance of the proposed scheduler, a 26.4-hectare field in Lethbridge, Canada, was chosen as a case study for the 2015 and 2022 growing seasons. The results demonstrate the superiority of the proposed scheduler compared to a traditional irrigation scheduling method in terms of water use efficiency and crop yield improvement for both growing seasons. Notably, the proposed scheduler achieved water savings ranging from 6.4% to 22.8%, along with yield increases ranging from 2.3% to 4.3%.

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arXiv2023

Control invariant set enhanced safe reinforcement learning: improved sampling efficiency, guaranteed stability and robustness

Reinforcement learning (RL) is an area of significant research interest, and safe RL in particular is attracting attention due to its ability to handle safety-driven constraints that are crucial for real-world applications. This work proposes a novel approach to RL training, called control invariant set (CIS) enhanced RL, which leverages the advantages of utilizing the explicit form of CIS to improve stability guarantees and sampling efficiency. Furthermore, the robustness of the proposed approach is investigated in the presence of uncertainty. The approach consists of two learning stages: offline and online. In the offline stage, CIS is incorporated into the reward design, initial state sampling, and state reset procedures. This incorporation of CIS facilitates improved sampling efficiency during the offline training process. In the online stage, RL is retrained whenever the predicted next step state is outside of the CIS, which serves as a stability criterion, by introducing a Safety Supervisor to examine the safety of the action and make necessary corrections. The stability analysis is conducted for both cases, with and without uncertainty. To evaluate the proposed approach, we apply it to a simulated chemical reactor. The results show a significant improvement in sampling efficiency during offline training and closed-loop stability guarantee in the online implementation, with and without uncertainty.

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arXiv2022

Impact of sensor placement in soil water estimation: A real-case study

One of the essential elements in implementing a closed-loop irrigation system is soil moisture estimation based on a limited number of available sensors. One associated problem is the determination of the optimal locations to install the sensors such that good soil moisture estimation can be obtained. In our previous work, the modal degree of observability was employed to address the problem of optimal sensor placement for soil moisture estimation of agro-hydrological systems. It was demonstrated that the optimally placed sensors can improve the soil moisture estimation performance. However, it is unclear whether the optimal sensor placement can significantly improve the soil moisture estimation performance in actual applications. In this work, we investigate the impact of sensor placement in soil moisture estimation for an actual agricultural field in Lethbridge, Alberta, Canada. In an experiment on the studied field, 42 soil moisture sensors were installed at different depths to collect the soil moisture measurements for one growing season. A three-dimensional agro-hydrological model with heterogeneous soil parameters of the studied field is developed. The modal degree of observability is applied to the three-dimensional system to determine the optimal sensor locations. The extended Kalman filter (EKF) is chosen as the data assimilation tool to estimate the soil moisture content of the studied field. Soil moisture estimation results for different scenarios are obtained and analyzed to investigate the effects of sensor placement on the performance of soil moisture estimation in the actual applications.

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arXiv2021

LSTM-based model predictive control with discrete inputs for irrigation scheduling

The development of well-devised irrigation scheduling methods is desirable from the perspectives of plant quality and water conservation. In this article, a model predictive control (MPC) with discrete actuators is developed for irrigation scheduling, where a long short-term memory (LSTM) model of the soil-water-atmosphere system is used to evaluate the objective of ensuring optimal water uptake in crops while minimizing total water consumption and irrigation costs. A heuristic method involving a sigmoid function is used in this framework to enhance the computational efficiency of the scheduler. The scheduling scheme is applied to homogeneous and spatially variable fields and the results indicate that the LSTM-based MPC with discrete actuators is able to prescribe optimal or near-optimal irrigation schedules that are typical of irrigation practice.

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arXiv2021

Knowledge-based optimal irrigation scheduling of agro-hydrological systems

The typical agricultural irrigation scheduler provides information on how much to irrigate and when to irrigate. The accurate and effective scheduler decision for a large agricultural field is still an open research problem. In this work, we address the high dimensionality of the agricultural field and propose a systematic approach to provide optimum irrigation amount and irrigation time for three-dimensional agro-hydrological systems. The water dynamics of the agro-hydrological system are represented using a cylindrical three-dimensional Richards Equation. We introduce a structure-preserving model reduction technique to decrease the dimension of the system model. Using the reduced model, the optimization-based closed-loop scheduler is designed in model predictive control (MPC) environment. The closed-loop approach can handle weather disturbances and provide improved yield and water conservation. The primary objective of the proposed scheduler is to ensure maximum yield, minimum water consumption and maximize the time between the two irrigation events, which results in less electricity usage. The proposed approach is applied to three different scenarios to show the effectiveness and superiority of the proposed framework.

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arXiv2020

Soil moisture map construction using microwave remote sensors and sequential data assimilation

Microwave remote sensors mounted on center pivot irrigation systems provide a feasible approach to obtain soil moisture information, in the form of water content maps, for the implementation of closed-loop irrigation. Major challenges such as significant time delays in the soil moisture measurements, the inability of the sensors to provide soil moisture information in instances where the center pivot is stationary, and the inability of the sensors to provide soil moisture information in the root zone reduce the usability of the water content maps in the effective implementation of closed-loop irrigation. In this paper, we seek to address the aforementioned challenges and consequently describe a water content map construction procedure that is suitable for the implementation of closed-loop irrigation. Firstly, we propose the cylindrical coordinates version of the Richards equation (field model) which naturally models fields equipped with a center pivot irrigation system. Secondly, measurements obtained from the microwave sensors are assimilated into the field model using the extended Kalman filter to form an information fusion system, which will provide frequent soil moisture estimates and predictions in the form of moisture content maps. The utility of the proposed information fusion system is first investigated with simulated microwave sensor measurements. The information fusion system is then applied to a real large-scale agriculture field where we demonstrate the its ability to address the challenges. Three performance evaluation criteria are used to validate the soil moisture estimates and predictions provided by the proposed information fusion system.

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