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RETHINKING THE CAPACITY OF GRAPH NEURAL NETWORKS FOR BRANCHING STRATEGY

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arXiv 2024年

作者： Chen, Ziang Liu, Jialin Chen, Xiaohan Wang, Xinshang Yin, Wotao Department of Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Statistics and Data Science University of Central Florida OrlandoFL32816 United States Decision Intelligence Lab Damo Academy Alibaba US BellevueWA98004 United States

Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching (SB), the most effective yet computationally expensive heuristic employed in the branch-and-bound algorithm. In the literature, message-passing GNN (MP-GNN), as the simplest GNN structure, is frequently used as a fast approximation of SB and we find that not all MILPs’s SB can be represented with MP-GNN. We precisely define a class of "MP-tractable" MILPs for which MP-GNNs can accurately approximate SB scores. Particularly, we establish a universal approximation theorem: for any data distribution over the MP-tractable class, there always exists an MP-GNN that can approximate the SB score with arbitrarily high accuracy and arbitrarily high probability, which lays a theoretical foundation of the existing works on imitating SB with MP-GNN. For MILPs without the MP-tractability, unfortunately, a similar result is impossible, which can be illustrated by two MILP instances with different SB scores that cannot be distinguished by any MP-GNN, regardless of the number of parameters. Recognizing this, we explore another GNN structure called the second-order folklore GNN (2-FGNN) that overcomes this limitation, and the aforementioned universal approximation theorem can be extended to the entire MILP space using 2-FGNN, regardless of the MP-tractability. A small-scale numerical experiment is conducted to directly validate our theoretical findings. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Power minimization and resource allocation in HetNets with uncertain channel-gains

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arXiv 2024年

作者： Ferreira, Gabriel O. Ravazzi, Chiara Dabbene, Fabrizio Calafiore, Giuseppe C. IEIIT CNR Institute Torino Italy DET Politecnico di Torino Italy CECS VinUniversity Viet Nam

We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city. © 2024, CC BY.

关键词： mixed-integer linear programming

Fair Least Core: Efficient, Stable and Unique Game-Theoretic Reward Allocation in Energy Communities by Row-Generation

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IEEE Transactions on Energy Markets, Policy and Regulation

IEEE Transactions on Energy Markets, Policy and Regulation 2024年

作者： Fioriti, Davide Bigi, Giancarlo Frangioni, Antonio Passacantando, Mauro Poli, Davide University of Pisa Department of Energy Systems Territory and Construction Engineering PI Pisa56122 Italy University of Pisa Dipartimento di Informatica PI Pisa56127 Italy University of Milano-Bicocca Department of Business and Law MI Milan20126 Italy

Energy Communities are increasingly proposed as a tool to boost renewable penetration and maximize citizen participation in energy matters. These policies enable the formation of legal entities that bring together power system members, enabling collective investment and operation of energy assets. However, designing appropriate reward schemes is crucial to fairly foster individuals to join, as well to ensure collaborative and stable aggregation, maximizing community benefits. Cooperative Game Theory, emphasizing coordination among members, has been extensively proposed for ECs and microgrids;however, it is still perceived as obscure and difficult to compute due to its exponential computational requirements. This study proposes a novel framework for stable fair benefit allocation, named Fair Least Core, that provides uniqueness, reproducibility, stability and fairness. A novel row-generation algorithm is also proposed that allows to efficiently compute the imputations for coalitions of practical size. A case study of ECs with up to 100 members shows the stability, reproducibility, fairness and efficiency properties of proposed model. The results also highlight how the market power of individual users changes as the community grows larger, which can steer the development of practical reliable, robust and fair reward allocations for energy system applications © 2023 IEEE.

关键词： mixed-integer linear programming

Upgrading edges in the Maximal Covering Location Problem

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arXiv 2024年

作者： Baldomero-Naranjo, Marta Kalcsics, Jörg Marín, Alfredo Rodríguez-Chía, Antonio M. 11510 Spain School of Mathematics University of Edinburgh EdinburghEH9 3FD United Kingdom Departamento de Estadística e Investigación Operativa Universidad de Murcia Facultad de Matemáticas Murcia30100 Spain

We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets. © 2024, CC BY-NC-ND.

关键词： mixed-integer linear programming

Optimization of Integrated Production and Distribution Planning In the Cement Industry with Multi-Site Plants Model 21

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Optimization of Integrated Production and Distribution Plann...

Proceedings of the 4th Asia Pacific Conference on Research in Industrial and Systems Engineering

作者： Fuadi Sejahtera Teuku Yuri M. Zagloel Zulkarnain Zulkarnain Universitas Indonesia Indonesia

ISBN: (纸本)9781450390385

Each stage of the supply chain must be able to maximize value to achieve supply chain profitability. Handling production planning and distribution planning as a part of the supply chain are carried out to obtain optimal strategies that increase efficiency and reduce the risk of supply chain network failure. Distribution cost problems in the fulfillment of raw materials affect the total production costs as a whole. This paper proposes an integrated production and distribution planning in a multi-site plants model, in order to obtain optimal profit from production in each plant in a different location. This model uses a raw material fulfillment multi-suppliers scheme through a mixture of internal and external sources. mixed-integer linear programming method is used for model optimization by considering production capacity constraints, demand constraints, supply constraints, production costs, logistics costs, and product revenue. Analysis of various demand conditions was applied in the multi-suppliers scheme to see the sensitivity of the parameters.

关键词： mixed-integer linear programming integrated models multi-site plants distribution systems Production systems

Improving Community-Participated Patrol for Anti-Poaching

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arXiv 2024年

作者： Wu, Yufei Xu, Yixuan Even Zhang, Xuming Liu, Duo Zhu, Shibing Fang, Fei Shanghai Jiao Tong University China Carnegie Mellon University United States World Wide Fund For Nature China Heilongjiang Academy of Sciences China

Community engagement plays a critical role in anti-poaching efforts, yet existing mathematical models aimed at enhancing this engagement often overlook direct participation by community members as alternative patrollers. Unlike professional rangers, community members typically lack flexibility and experience, resulting in new challenges in optimizing patrol resource allocation. To address this gap, we propose a novel game-theoretic model for community-participated patrol, where a conservation agency strategically deploys both professional rangers and community members to safeguard wildlife against a best-responding poacher. In addition to a mixed-integer linear program formulation, we introduce a Two-Dimensional Binary Search algorithm and a novel Hybrid Waterfilling algorithm to efficiently solve the game in polynomial time. Through extensive experiments and a detailed case study focused on a protected tiger habitat in Northeast China, we demonstrate the effectiveness of our algorithms and the practical applicability of our model. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Global Optimization of Gaussian Process Acquisition Functions Using a Piecewise-linear Kernel Approximation

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arXiv 2024年

作者： Xie, Yilin Zhang, Shiqiang Paulson, Joel Tsay, Calvin Department of Computing Imperial College London United Kingdom Department of Chemical and Biomolecular Engineering The Ohio State University United States

Bayesian optimization relies on iteratively constructing and optimizing an acquisition function. The latter turns out to be a challenging, non-convex optimization problem itself. Despite the relative importance of this step, most algorithms employ sampling- or gradient-based methods, which do not provably converge to global optima. This work investigates mixed-integer programming (MIP) as a paradigm for global acquisition function optimization. Specifically, our Piecewise-linear Kernel mixed integer Quadratic programming (PK-MIQP) formulation introduces a piecewise-linear approximation for Gaussian process kernels and admits a corresponding MIQP representation for acquisition functions. We analyze the theoretical regret bounds of the proposed approximation, and empirically demonstrate the framework on synthetic functions, constrained benchmarks, and a hyperparameter tuning task. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

A Universal Multi-Vehicle Cooperative Decision-Making Approach in Structured Roads by mixed-integer Potential Game

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arXiv 2024年

作者： Meng, Chengzhen Huang, Zhenmin Ma, Jun The Robotics and Autonomous Systems Thrust The Hong Kong University of Science and Technology Guangzhou China The Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Hong Kong

Due to the intricate of real-world road topologies and the inherent complexity of autonomous vehicles, cooperative decision-making for multiple connected autonomous vehicles (CAVs) remains a significant challenge. Currently, most methods are tailored to specific scenarios, and the efficiency of existing optimization and learning methods applicable to diverse scenarios is hindered by the complexity of modeling and data dependency, which limit their real-world applicability. To address these issues, this paper proposes a universal multi-vehicle cooperative decision-making method in structured roads with game theory. We transform the decision-making problem into a graph path searching problem within a way-point graph framework. The problem is formulated as a mixed-integer linear programming problem (MILP) first and transformed into a mixed-integer potential game (MIPG), which reduces the scope of problem and ensures that no player needs to sacrifice for the overall cost. Two Gauss-Seidel algorithms for cooperative decision-making are presented to solve the MIPG problem and obtain the Nash equilibrium solutions. Specifically, the sequential Gauss-Seidel algorithm for cooperative decision-making considers the varying degrees of CAV interactions and flexibility in adjustment strategies to determine optimization priorities, which reduces the frequency of ineffective optimizations. Experimental evaluations across various urban traffic scenarios with different topological structures demonstrate the effectiveness and efficiency of the proposed method compared with MILP and comparisons of different optimization sequences validate the efficiency of the sequential Gauss-Seidel algorithm for cooperative decision-making. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

A neural network-based approach to hybrid systems identification for control

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arXiv 2024年

作者： Fabiani, Filippo Stellato, Bartolomeo Masti, Daniele Goulart, Paul J. IMT School for Advanced Studies Lucca Piazza San Francesco 19 Lucca55100 Italy Operations Research and Financial Engineering Princeton University PrincetonNJ United States Gran Sasso Science Institute Viale F. Crispi 7 L’Aquila67100 Italy Department of Engineering Science University of Oxford OxfordOX1 3PJ United Kingdom

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We adopt a neural network (NN) architecture that, once suitably trained, yields a hybrid system with continuous piecewise-affine (PWA) dynamics that is differentiable with respect to the network’s parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN’s weights produces a hybrid system model with structural properties that are highly favorable when used as part of a finite horizon optimal control problem (OCP). Specifically, we rely on available results to establish that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming (NLP), in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. Besides being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methods for hybrid systems and it is competitive on nonlinear benchmarks. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming