arXiv subjects

Prodromos Daoutidis

Publications and source records attributed to Prodromos Daoutidis.

13 recordsLinked to original sources

arXiv2026

Approximate Dynamic Optimization via Deep Neural Operators

This paper addresses the solution of nonlinear dynamic optimization problems that compute optimal manipulated input profiles to enforce desired output profiles. Such trajectory optimization problems commonly arise in chemical process applications, for example, batch processes where optimal temperature or feeding profiles (in case of fed-batch processes) are calculated to enforce time-varying product quality profiles, tightly controlling the reaction rate or rate of heat generation. We propose deep neural operators that approximate function to function mappings as surrogates for the solution of such dynamic optimization problems. We specifically employ deep operator networks (DeepONets) and Fourier-enhanced DeepONets in a batch polymerization reactor case study for which number-average and weight-average molecular weight profiles, together with a final conversion target, are enforced through an optimal temperature program. Our results show that the Fourier-enhanced DeepONet architecture performs very well in approximating the solution of the dynamic optimization problem for different instances, achieving a lower prediction error compared to the standard DeepONet architecture and standard feedforward neural networks.

eess.SY↗

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.

eess.SY↗

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.

math.OC↗

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.

math.OC↗

arXiv2025

Integer L-Shaped Method with Non-Supporting No-Good Optimality Cuts

Two-stage stochastic mixed-integer linear programs with mixed-integer recourse arise in many practical applications but are computationally challenging due to their large size and the presence of integer decisions in both stages. The integer L-shaped method with alternating cuts is a widely used decomposition algorithm for these problems, relying on optimality cuts generated using subproblems to iteratively refine the master problem. A key computational bottleneck in this approach is solving the mixed-integer subproblems to optimality in order to generate separating cuts. This work proposes a modification to the integer L-shaped method with alternating cuts to allow for efficient generation of no-good optimality cuts that are separating for the current master problem solutions without being supporting hyperplanes of the feasible region. These separating cuts are derived from subproblems that are terminated before the optimal solution is found or proven to be optimal, reducing the computational effort required for cut generation. Additionally, an updated optimality cut generation function is proposed to account for the various complexities introduced by this early termination strategy. The effectiveness of the proposed method is demonstrated through two case studies on industrially relevant problems from the literature, which illustrate its advantages in handling large-scale instances with complex mixed-integer subproblems. In these cases, the method achieves substantial reductions in solution time or optimality gap compared to the standard integer L-shaped method with alternating cuts, with performance improvements that increase with mixed-integer subproblem size and complexity.

math.OC↗

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.

math.OC↗

arXiv2025

Topological descriptors for the electron density of inorganic solids

Descriptors play an important role in data-driven materials design. While most descriptors of crystalline materials emphasize structure and composition, they often neglect the electron density - a complex yet fundamental quantity that governs material properties. Here, we introduce Betti curves as topological descriptors that compress electron densities into compact representations. Derived from persistent homology, Betti curves capture bonding characteristics by encoding components, cycles, and voids across varied electron density thresholds. Machine learning models trained on Betti curves outperform those trained on raw electron densities by an average of 33 percentage points in classifying structure prototypes, predicting thermodynamic stability, and distinguishing metals from non-metals. Shannon entropy calculations reveal that Betti curves retain comparable information content to electron density while requiring two orders of magnitude less data. By combining expressive power with compact representation, Betti curves highlight the potential of topological data analysis to advance materials design.

cond-mat.mtrl-sci↗

arXiv2024

Accelerating process control and optimization via machine learning: A review

Process control and optimization have been widely used to solve decision-making problems in chemical engineering applications. However, identifying and tuning the best solution algorithm is challenging and time-consuming. Machine learning tools can be used to automate these steps by learning the behavior of a numerical solver from data. In this paper, we discuss recent advances in (i) the representation of decision-making problems for machine learning tasks, (ii) algorithm selection, and (iii) algorithm configuration for monolithic and decomposition-based algorithms. Finally, we discuss open problems related to the application of machine learning for accelerating process optimization and control.

eess.SY↗

arXiv2023

Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures the structural and functional coupling among the variables and constraints of the problem via an appropriate set of features. Given this representation, a graph classifier is built to determine the best solution method for a given problem. The proposed approach is used to develop a classifier that determines whether a convex Mixed Integer Nonlinear Programming problem should be solved using branch and bound or the outer approximation algorithm. Finally, it is shown how the learned classifier can be incorporated into existing mixed integer optimization solvers.

math.OC↗

arXiv2023

Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize

The repeated solution of large-scale optimization problems arises frequently in process systems engineering tasks. Decomposition-based solution methods have been widely used to reduce the corresponding computational time, yet their implementation has multiple steps that are difficult to configure. We propose a machine learning approach to learn the optimal initialization of such algorithms which minimizes the computational time. Active and supervised learning is used to learn a surrogate model that predicts the computational performance for a given initialization. We apply this approach to the initialization of Generalized Benders Decomposition for the solution of mixed integer model predictive control problems. The surrogate models are used to find the optimal number of initial cuts that should be added in the master problem. The results show that the proposed approach can lead to a significant reduction in solution time, and active learning can reduce the data required for learning.

math.OC↗

arXiv2023

Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition

Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient and robust online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for the efficient solution of such problems. We use machine learning to approximate the effect of the complicating variables on the subproblem by approximating the Benders cuts without solving the subproblem, therefore, alleviating the need to solve the subproblem multiple times. The proposed approach is applied to a mixed integer economic MPC case study on the operation of chemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50x) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition.

math.OC↗

arXiv2023

Automated Characterization and Monitoring of Material Shape using Riemannian Geometry

Shape affects both the physical and chemical properties of a material. Characterizing the roughness, convexity, and general geometry of a material can yield information on its catalytic efficiency, solubility, elasticity, porosity, and overall effectiveness in the application of interest. However, material shape can be defined in a multitude of conflicting ways where different aspects of a material's geometry are emphasized over others, leading to bespoke measures of shape that are not easily generalizable. In this paper, we explore the use of Riemannian geometry in the analysis of shape and show that a Riemannian geometric framework for shape analysis is generalizable, computationally scalable, and can be directly integrated into common data analysis methods. In this framework, material shapes are abstracted as points on a Riemannian manifold. This information can be used to construct statistical moments (e.g., means, variances) and perform tasks such as dimensionality reduction and statistical process control. We provide a practical introduction to the mathematics of shape analysis through Riemannian geometry and illustrate its application on a manufactured/mined granular material dataset provided by Covia Corp. We show that the Riemannian framework can be used to automatically extract and quantify the shape of granular materials in a statistically rigorous manner.

cs.CE↗

arXiv2020

Fast and Stable Nonconvex Constrained Distributed Optimization: The ELLADA Algorithm

Distributed optimization, where the computations are performed in a localized and coordinated manner using multiple agents, is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints and general inter-subsystem interactions remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers (ADMM) for distributed optimization. Specifically, (i) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (ii) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (iii) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence towards stationary solutions and computational complexity of the proposed algorithm, named ELLADA, is established. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.

eess.SY↗