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Distributed ADMM Approach for the Power Distribution Network Reconfiguration

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arXiv 2024年

作者： Mokhtari, Yacine Coirault, Patrick Moulay, Emmanuel Le Ny, Jerome Larraillet, Didier ISAE-ENSMA Université de Poitiers 2 rue Pierre Brousse Poitiers86073 Cedex 9 France Université de Poitiers 11 bd Marie et Pierre Curie Poitiers86073 Cedex 9 France Department of Electrical Engineering Polytechnique Montréal and GERAD MontrealQCH3T-1J4 Canada SRD Energies 78 Av. Jacques Coeur Poitiers86000 France

The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring radial topology. The growing use of renewable energy and the complexity of managing modern power grids make solving the reconfiguration problem crucial. Distributed algorithms help optimize grid configurations, ensuring efficient adaptation to changing conditions and better utilization of renewable energy sources. This paper introduces a distributed algorithm designed to tackle the problem of power distribution network reconfiguration with a radiality constraint. This algorithm relies on ADMM (Alternating Direction Method of Multipliers), where each agent progressively updates its estimation based on the information exchanged with neighboring agents. We show that every agent is required to solve a linearly constrained convex quadratic programming problem and a Minimum Weight Rooted Arborescence Problem (MWRAP) with local weights during each iteration. Through numerical experiments, we demonstrate the performance of the proposed algorithm in various scenarios, including its application to a 33-bus test system and a real-world network. © 2024, CC BY.

关键词： mixed-integer linear programming

Graph Neural Network-Accelerated Network-Reconfigured Optimal Power Flow

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arXiv 2024年

作者： Pham, Thuan Li, Xingpeng The Department of Electrical and Computer Engineering University of Houston HoustonTX77204 United States

Optimal power flow (OPF) has been used for real-time grid operations. Prior efforts demonstrated that utilizing flexibility from dynamic topologies will improve grid efficiency. However, this will convert the linear OPF into a mixed-integer linear programming network-reconfigured OPF (NR-OPF) problem, substantially increasing the computing time. Thus, a machine learning (ML)-based approach, particularly utilizing graph neural network (GNN), is proposed to accelerate the solution process. The GNN model is trained offline to predict the best topology before entering the optimization stage. In addition, this paper proposes an offline pre-ML filter layer to reduce GNN model size and training time while improving its accuracy. A fast online post-ML selection layer is also proposed to analyze GNN predictions and then select a subset of predicted NR solutions with high confidence. Case studies have demonstrated superior performance of the proposed GNN-accelerated NR-OPF method augmented with the proposed pre-ML and post-ML layers. © 2024, CC BY.

关键词： mixed-integer linear programming

LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages

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arXiv 2024年

作者： Huang, Xuhan Shen, Qingning Hu, Yan Gao, Anningzhe Wang, Benyou The Chinese University of Hong Kong Shenzhen China Shenzhen Research Institute of Big Data China

Large Language Models (LLMs) have demonstrated strong performance across various natural language processing tasks, yet their proficiency in mathematical reasoning remains a key challenge. Addressing the gap between natural and mathematical language requires advanced reasoning capabilities, approaching those of Artificial General Intelligence (AGI). However, the evaluation remains challenging, as perfectly representing reality is inherently elusive, and traditional methods like manual or direct comparison of mathematical statements (Ramamonjison et al., 2023) are insufficient for assessing true modeling ability. We propose a process-oriented framework to evaluate LLMs’ ability to construct mathematical models, using solvers to compare outputs with ground truth. Introducing Mamo, a benchmark with 1,209 questions covering ordinary differential equations, linear programming, and mixed-integer linear programming, we enable automatic evaluation of modeling accuracy. The results show that existing LLMs struggle with complex mathematical modeling tasks, with larger models demonstrating superior performance, while open-source models remain competitive in simpler cases but still fall short of proprietary models in more challenging problems. © 2024, CC BY-SA.

关键词： mixed-integer linear programming

AC-Informed DC Optimal Transmission Switching Problems via Parameter Optimization

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arXiv 2024年

作者： Taheri, Babak Molzahn, Daniel K. School of Electrical and Computer Engineering Georgia Institute of Technology United States

Optimal Transmission Switching (OTS) problems minimize operational costs while treating both the transmission line energization statuses and generator setpoints as decision variables. The combination of nonlinearities from an AC power flow model and discrete variables associated with line statuses makes AC-OTS a computationally challenging mixed-integer Nonlinear Program (MINLP). To address these challenges, the DC power flow approximation is often used to obtain a DC-OTS formulation expressed as a mixed-integer linear Program (MILP). However, this approximation often leads to suboptimal or infeasible switching decisions when evaluated with an AC power flow model. This paper proposes an enhanced DC-OTS formulation that leverages techniques for training machine learning models to optimize the DC power flow model’s parameters. By optimally selecting parameter values that align flows in the DC power flow model with apparent power flows—incorporating both real and reactive components—from AC Optimal Power Flow (OPF) solutions, our method more accurately captures line congestion behavior. Integrating these optimized parameters into the DC-OTS formulation significantly improves the accuracy of switching decisions and reduces discrepancies between DC-OTS and AC-OTS solutions. We compare our optimized DC-OTS model against traditional OTS approaches, including DC-OTS, linear programming AC (LPAC)-OTS, and Quadratic Convex (QC)-OTS. Numeric results show that switching decisions from our model yield better performance when evaluated using an AC power flow model, with up to 44% cost reductions in some cases. © 2024, CC BY-NC-SA.

关键词： mixed-integer linear programming

ON FINITE GROUPS ISOSPECTRAL TO GROUPS WITH ABELIAN SYLOW 2-SUBGROUPS

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arXiv 2024年

作者： Grechkoseeva, M.A. Vasil’Ev, A.V. Sobolev Institute of Mathematics Novosibirsk Russia

The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow 2-subgroups. For every positive integer k, we find k nonabelian simple groups with abelian Sylow 2-subgroups such that their direct product is uniquely determined by its spectrum in the class of all finite groups. On the other hand, we prove that there are infinitely many finite groups having the same spectrum as the direct cube of the small Ree group 2G2(q), q > 3, or the direct fourth power of the sporadic group J1MSC Codes 20D60, 20D06, 20D08 © 2024, CC0.

关键词： mixed-integer linear programming

Interval Abstractions for Robust Counterfactual Explanations

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arXiv 2024年

作者： Jiang, Junqi Leofante, Francesco Rago, Antonio Toni, Francesca Department of Computing Imperial College London 180 Queen’s Gate LondonSW7 2AZ United Kingdom

Counterfactual Explanations (CEs) have emerged as a major paradigm in explainable AI research, providing recourse recommendations for users affected by the decisions of machine learning models. However, CEs found by existing methods often become invalid when slight changes occur in the parameters of the model they were generated for. The literature lacks a way to provide exhaustive robustness guarantees for CEs under model changes, in that existing methods to improve CEs’ robustness are mostly heuristic, and the robustness performances are evaluated empirically using only a limited number of retrained models. To bridge this gap, we propose a novel interval abstraction technique for parametric machine learning models, which allows us to obtain provable robustness guarantees for CEs under a possibly infinite set of plausible model changes ∆. Based on this idea, we formalise a robustness notion for CEs, which we call ∆-robustness, in both binary and multi-class classification settings. We present procedures to verify ∆-robustness based on mixed integer linear programming, using which we further propose algorithms to generate CEs that are ∆-robust. In an extensive empirical study involving neural networks and logistic regression models, we demonstrate the practical applicability of our approach. We discuss two strategies for determining the appropriate hyperparameters in our method, and we quantitatively benchmark CEs generated by eleven methods, highlighting the effectiveness of our algorithms in finding robust CEs. © 2024, CC BY.

关键词： mixed-integer linear programming

A Gauss-Seidel method for solving multi-leader-multi-follower games

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arXiv 2024年

作者： Franci, Barbara Fabiani, Filippo Schmidt, Martin Staudigl, Mathias Department of Advanced Computing Sciences Maastricht University MaastrichtNL–6200 MD Netherlands IMT School for Advanced Studies Lucca Piazza San Francesco 19 Lucca55100 Italy Department of Mathematics Trier University Universitätsring 15 Trier54296 Germany University of Mannheim Department of Mathematics MannheimB6 68159 Germany

We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the Karush–Kuhn–Tucker conditions, we propose a mixed-integer game formulation for solving this challenging class of problems. Besides providing an equivalent reformulation, we design a proximal Gauss–Seidel method with global convergence guarantees in case the game enjoys a potential structure. We finally corroborate the numerical performance of the algorithm on a novel instance of the ride-hail market problem. © 2024, CC BY.

关键词： mixed-integer linear programming

Channel-Aware Throughput Maximization for Cooperative Data Fusion in CAV

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arXiv 2024年

作者： An, Haonan Fang, Zhengru Zhang, Yuang Hu, Senkang Chen, Xianhao Xu, Guowen Fang, Yuguang Department of Computer Science City University of Hong Kong Hong Kong Department of Automation Tsinghua University China Department of Electrical and Electronic Engineering The University of Hong Kong Hong Kong

Connected and autonomous vehicles (CAVs) have garnered significant attention due to their extended perception range and enhanced sensing coverage. To address challenges such as blind spots and obstructions, CAVs employ vehicle-to-vehicle (V2V) communications to aggregate sensory data from surrounding vehicles. However, cooperative perception is often constrained by the limitations of achievable network throughput and channel quality. In this paper, we propose a channel-aware throughput maximization approach to facilitate CAV data fusion, leveraging a self-supervised autoencoder for adaptive data compression. We formulate the problem as a mixed integer programming (MIP) model, which we decompose into two sub-problems to derive optimal data rate and compression ratio solutions under given link conditions. An autoencoder is then trained to minimize bitrate with the determined compression ratio, and a fine-tuning strategy is employed to further reduce spectrum resource consumption. Experimental evaluation on the OpenCOOD platform demonstrates the effectiveness of our proposed algorithm, showing more than 20.19% improvement in network throughput and a 9.38% increase in average precision (AP@IoU) compared to state-of-the-art methods, with an optimal latency of 19.99 ms. © 2024, CC BY.

关键词： mixed-integer linear programming

Feature-Based Interpretable Optimization

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arXiv 2024年

作者： Goerigk, Marc Hartisch, Michael Merten, Sebastian Sharma, Kartikey University of Passau Dr.-Hans-Kapfinger-Str. 30 Passau94032 Germany University of Erlangen–Nuremberg Cauerstraße 11 Erlangen91058 Germany Zuse Institute Berlin Takustr. 7 Berlin14195 Germany

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models used decision trees to map instances to solutions of the underlying optimization model. Based on this work, we investigate how we can use more general optimization rules to further increase interpretability and at the same time give more freedom to the decision maker. The proposed rules do not map to a concrete solution but to a set of solutions characterized by common features. To find such optimization rules, we present an exact methodology using mixed-integer programming formulations as well as heuristics. We also outline the challenges and opportunities that these methods present. In particular, we demonstrate the improvement in solution quality that our approach offers compared to existing frameworks for interpretable optimization and we discuss the relationship between interpretability and performance. These findings are supported by experiments using both synthetic and real-world data. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming