检索结果-内蒙古大学图书馆

mixed-integer linear Optimization via Learning-Based Two-Layer Large Neighborhood Search

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Liu, Wenbo Wang, Akang Yang, Wenguo Shi, Qingjiang University of Chinese Academy of Sciences Beijing China Shenzhen Research Institute of Big Data China The Chinese University of Hong Kong Shenzhen China Tongji University Shanghai China

mixed-integer linear programs (MILPs) are extensively used to model practical problems such as planning and scheduling. A prominent method for solving MILPs is large neighborhood search (LNS), which iteratively seeks improved solutions within specific neighborhoods. Recent advancements have integrated machine learning techniques into LNS to guide the construction of these neighborhoods effectively. However, for large-scale MILPs, the search step in LNS becomes a computational bottleneck, relying on off-the-shelf solvers to optimize auxiliary MILPs of substantial size. To address this challenge, we introduce a two-layer LNS (TLNS) approach that employs LNS to solve both the original MILP and its auxiliary MILPs, necessitating the optimization of only small-sized MILPs using off-the-shelf solvers. Additionally, we incorporate a lightweight graph transformer model to inform neighborhood design. We conduct extensive computational experiments using public benchmarks. The results indicate that our learning-based TLNS approach achieves remarkable performance gains–up to 66% and 96% over LNS and state-of-the-art MILP solvers, respectively. © 2024, CC BY.

关键词： mixed-integer linear programming

RESIDUE CLASS BIASES IN UNRESTRICTED PARTITIONS, PARTITIONS INTO DISTINCT PARTS, AND OVERPARTITIONS

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Schlosser, Michael J. Zhou, Nian Hong Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 ViennaA-1090 Austria School of Mathematics and Statistics The Center for Applied Mathematics of Guangxi Guangxi Normal University Guangxi Guilin541004 China

We prove specific biases in the number of occurrences of parts belonging to two different residue classes a and b, modulo a fixed non-negative integer m, for the sets of unrestricted partitions, partitions into distinct parts, and overpartitions. These biases follow from inequalities for residue-weighted partition functions for the respective sets of partitions. We also establish asymptotic formulas for the numbers of partitions of size n that belong to these sets of partitions and have a symmetric residue class bias (i.e., for 1 ≤ a MSC Codes 05A17 (Primary) 11P81 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Graph Neural Network-Accelerated Network-Reconfigured Optimal Power Flow

学校读者我要写书评

暂无评论

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

Distributed ADMM Approach for the Power Distribution Network Reconfiguration

学校读者我要写书评

暂无评论

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

Analysis of Singapore Electricity Market Clearing Model with Transmission Network Consideration

学校读者我要写书评

暂无评论

Analysis of Singapore Electricity Market Clearing Model with...

IEEE Region 10 Conference

作者： Zhen Shu Shengfeng Zhou Kelvin Tan Kian Hock Gooi Hoay Beng Energy R&D DNV GL School of Electrical and Electronic Engineering Nanyang Technological University

ISBN: (纸本)9781509025985

The analysis of electricity market model plays a very important role in power system planning and market design. It is usually established based on economic deliberation and reliability requirement. This paper investigates the electricity market clearing model (MCM) of Singapore as a representative of Southeast Asia countries. The MCM is formulated as an optimization framework, where the system network topology is properly incorporated. The market clearing policies for energy and ancillary services are explicitly included in the mathematical model. Case studies have been performed on a transmission test system based on local market data. The optimal dispatch for generation production, as well as the locational marginal prices are achieved, providing effective decision-making support for power system planners and operators.

关键词： Singapore wholesale electricity market power system market clearing process electric generation dispatch mixed-integer linear programming

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

学校读者我要写书评

暂无评论

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

学校读者我要写书评

暂无评论

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

学校读者我要写书评

暂无评论

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

Channel-Aware Throughput Maximization for Cooperative Data Fusion in CAV

学校读者我要写书评

暂无评论

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