Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

• URL: http://arxiv.org/abs/2112.08091v3
• Date: Wed, 17 May 2023 04:04:10 GMT
• Title: Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems
• Authors: Tianyu Zhao, Xiang Pan, Minghua Chen, and Steven H. Low
• Abstract summary: Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to prediction errors. We propose a preventive learning'' framework to guarantee DNN solution for problems with convex and general objective functions without post-versaive inequality constraints. We apply framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation.
• Score: 25.791128241015684
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning'' framework to guarantee DNN solution feasibility for problems with convex constraints and general objective functions without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate inequality constraints used in DNN training, thereby anticipating prediction errors and ensuring the resulting solutions remain feasible. We characterize the calibration magnitudes and the DNN size sufficient for ensuring universal feasibility. We propose a new Adversarial-Sample Aware training algorithm to improve DNN's optimality performance without sacrificing feasibility guarantee. Overall, the framework provides two DNNs. The first one from characterizing the sufficient DNN size can guarantee universal feasibility while the other from the proposed training algorithm further improves optimality and maintains DNN's universal feasibility simultaneously. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100% feasibility and attaining consistent optimality loss ($<$0.19%) and speedup (up to $\times$228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.

Related papers

• Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach [2.943640991628177]
  Constrained optimization problems arise in various engineering system operations such as inventory management electric power grids. This work introduces a learning scheme using Bayesian Networks (BNNs) to solve constrained optimization problems under limited data and restricted model times. We show that the proposed learning method outperforms conventional BNN and deep neural network (DNN) architectures.
  arXiv  Detail & Related papers  (2024-10-04T02:10:20Z)
• Reliable Projection Based Unsupervised Learning for Semi-Definite QCQP with Application of Beamforming Optimization [11.385703484113552]
  In this paper, we investigate a special class of quadratic (QCQP) with semi-definite constraints. We propose a neural network (NN) as a promising method to obtain a high-performing constraint solution. Unsupervised learning is used, so the NN can be effectively efficiently without labels.
  arXiv  Detail & Related papers  (2024-07-04T06:26:01Z)
• Achieving Constraints in Neural Networks: A Stochastic Augmented Lagrangian Approach [49.1574468325115]
  Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. We propose a novel approach to DNN regularization by framing the training process as a constrained optimization problem. We employ the Augmented Lagrangian (SAL) method to achieve a more flexible and efficient regularization mechanism.
  arXiv  Detail & Related papers  (2023-10-25T13:55:35Z)
• Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization [5.412875005737914]
  We propose deeprange dual embedding (DeepLDE) as a fast optimal approximators incorporating neural networks (NNs) We prove the convergence of DeepLDE and primal, nondual-learning method to impose inequality constraints. We show that the proposed DeepLDE solutions achieve the optimal Lag gap among all the smallest NN-based approaches.
  arXiv  Detail & Related papers  (2023-06-11T13:19:37Z)
• Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks [64.23331120621118]
  We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
  arXiv  Detail & Related papers  (2022-04-01T03:31:27Z)
• Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks [52.32646357164739]
  We propose a deep neural network (DNN) to solve the solutions of the optimal power flow (ACOPF) The proposed SIDNN is compatible with a broad range of OPF schemes. It can be seamlessly integrated in other learning-to-OPF schemes.
  arXiv  Detail & Related papers  (2021-03-27T00:45:23Z)
• dNNsolve: an efficient NN-based PDE solver [62.997667081978825]
  We introduce dNNsolve, that makes use of dual Neural Networks to solve ODEs/PDEs. We show that dNNsolve is capable of solving a broad range of ODEs/PDEs in 1, 2 and 3 spacetime dimensions.
  arXiv  Detail & Related papers  (2021-03-15T19:14:41Z)
• Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow [0.0]
  This paper introduces a framework to capture previously intractable optimization constraints and transform them to a mixed-integer linear program. We demonstrate our approach for power system operation considering N-1 security and small-signal stability, showing how it can efficiently obtain cost-optimal solutions.
  arXiv  Detail & Related papers  (2020-03-17T21:01:17Z)
• Self-Directed Online Machine Learning for Topology Optimization [58.920693413667216]
  Self-directed Online Learning Optimization integrates Deep Neural Network (DNN) with Finite Element Method (FEM) calculations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 5 orders of magnitude compared with directly using methods, and outperformed all state-of-the-art algorithms tested in our experiments.
  arXiv  Detail & Related papers  (2020-02-04T20:00:28Z)
• Optimizing Wireless Systems Using Unsupervised and Reinforced-Unsupervised Deep Learning [96.01176486957226]
  Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems.
  arXiv  Detail & Related papers  (2020-01-03T11:01:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.