Constrained decision-making problems are pervasive across various disciplines.

Constrained decision-making problems are pervasive across various disciplines.

This paper introduces a novel Large Language Models (LLMs)-assisted agent that automatically converts natural-language descriptions of power system optimization scenarios into compact, solver-ready formulations and generates corresponding solutions. In contrast to approaches that rely solely on LLM to produce solutions directly, the proposed method focuses on discovering a mathematically compatible formulation that can be efficiently solved by off-the-shelf optimization solvers. Directly using LLMs to produce solutions often leads to infeasible or suboptimal results, as these models lack the numerical precision and constraint-handling capabilities of established optimization solvers. The pipeline integrates a domain-aware prompt and schema with an LLM, enforces feasibility through systematic validation and iterative repair, and returns both solver-ready models and user-facing results. Using the unit commitment problem as a representative case study, the agent produces optimal or near-optimal schedules along with the associated objective costs. Results demonstrate that coupling the solver with task-specific validation significantly enhances solution reliability. This work shows that combining AI with established optimization frameworks bridges high-level problem descriptions and executable mathematical models, enabling more efficient decision-making in energy systems

The Unit Commitment (UC) problem is a classic challenge in the optimal scheduling of power systems. Years of research and practice have shown that formulating reasonable unit commitment plans can significantly improve the economic efficiency of power systems' operations. In recent years, with the introduction of technologies such as machine learning and the Lagrangian relaxation method, the solution methods for the UC problem have become increasingly diversified, but still face challenges in terms of accuracy and robustness. This paper proposes a Function Space Search (FunSearch) method based on large language models. This method combines pre-trained large language models and evaluators to creatively generate solutions through the program search and evolution process while ensuring their rationality. In simulation experiments, a case of unit commitment with \(10\) units is used mainly. Compared to the genetic algorithm, the results show that FunSearch performs better in terms of sampling time, evaluation time, and total operating cost of the system, demonstrating its great potential as an effective tool for solving the UC problem.

Ensuring that the outputs of neural networks satisfy specific constraints is crucial for applying neural networks to real-life decision-making problems. In this paper, we consider making a batch of neural network outputs satisfy bounded and general linear constraints. We first reformulate the neural network output projection problem as an entropy-regularized linear programming problem. We show that such a problem can be equivalently transformed into an unconstrained convex optimization problem with Lipschitz continuous gradient according to the duality theorem. Then, based on an accelerated gradient descent algorithm with numerical performance enhancement, we present our architecture, GLinSAT, to solve the problem. To the best of our knowledge, this is the first general linear satisfiability layer in which all the operations are differentiable and matrix-factorization-free. Despite the fact that we can explicitly perform backpropagation based on automatic differentiation mechanism, we also provide an alternative approach in GLinSAT to calculate the derivatives based on implicit differentiation of the optimality condition. Experimental results on constrained traveling salesman problems, partial graph matching with outliers, predictive portfolio allocation and power system unit commitment demonstrate the advantages of GLinSAT over existing satisfiability layers. Our implementation is available at \url{https://github.com/HunterTracer/GLinSAT}.

The Unit Commitment (UC) problem is a key optimization task in power systems to forecast the generation schedules of power units over a finite time period by minimizing costs while meeting demand and technical constraints. However, many parameters required by the UC problem are unknown, such as the costs. In this work, we estimate these unknown costs using simulation-based inference on an illustrative UC problem, which provides an approximated posterior distribution of the parameters given observed generation schedules and demands. Our results highlight that the learned posterior distribution effectively captures the underlying distribution of the data, providing a range of possible values for the unknown parameters given a past observation. This posterior allows for the estimation of past costs using observed past generation schedules, enabling operators to better forecast future costs and make more robust generation scheduling forecasts. We present avenues for future research to address overconfidence in posterior estimation, enhance the scalability of the methodology and apply it to more complex UC problems modeling the network constraints and renewable energy sources.

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train a machine learning model that predicts high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. We also introduce an algorithm to reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.

Security-Constrained Unit Commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via Mixed-Integer Linear Programming, sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning (ML) techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions and affine subspaces where the optimal solution is likely to lie, leading to significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that, using the proposed techniques, SCUC can be solved on average 12 times faster than conventional methods, with no negative impact on solution quality.