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PROCESSES 2023年第10期11卷 2840页

作者： Revelo, Maria F. Tuza, Pablo V. Minist Educ Unidad Educ Rafael Leon Carvajal Dist Educat Intercultural & Bilingue 10D03 Cotacac Coordinac Zonal 1 Cotacachi 100306 Ecuador Univ Tecn Ambato Fac Ciencia Ingn Alimentos & Biotecnol Ambato 180216 Ecuador

In the present work, a modified mixed-integer linear programming model was implemented in Microsoft Excel (R) and minimized using the Solver tool to obtain information to devise a heat exchanger network with multiple utilities from a set of hot and cold streams and selected utilities by hand. Regarding the mixed-integer linear programming problem, the summation of utility energy was added to the model, and this energy was equal to that from the Temperature Interval method and the Grand Composite Curve. Moreover, feasible temperature ranges for heat exchange were considered according to the second law of thermodynamics. Also, the last two temperature intervals from the rank-ordered ones were assigned for water energy balances. An energy balance was introduced into the algorithm for each interval between its temperature and the process pinch temperature in the case of the boiler-feed water. Seven stream sets collected from the literature were used for the mixed-integer linear programming formulation testing, and six of them are presented in this article. Because of boiler-feed water generation and the low cost of utilities, the annualized cost of a heat exchanger network with multiple utilities can be lower than that of a network without multiple utilities.

关键词： pinch heat exchanger network multiple utilities mixed-integer linear programming Microsoft Excel

Exact Complexity Certification of Suboptimal Branch-and-Bound Algorithms for mixed-integer linear programming

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IFAC-PapersOnLine 2023年第2期56卷 7428-7435页

作者： Shamisa Shoja Daniel Axehill Division of Automatic Control Linköping University Sweden

In this paper, we present a method to exactly certify the computational complexity of standard suboptimal branch-and-bound (B&B) algorithms for computing suboptimal solutions to mixed-integer linear programming (MILP) problems. Three well-known approaches for suboptimal B&B are considered. This work shows that it is possible to exactly certify the computational complexity also when these approaches are used. Moreover, it also enables to compute exact bounds on the level of suboptimality actually to be obtained online, also for methods previously without any such guarantees. It additionally provides a novel deeper insight into how they affect the performance of the B&B algorithm in terms of the required computation time and memory storage. The exact bounds on the online worst-case computational complexity (e.g., the accumulated number of LP solver iterations or size of the B&B tree) and the worst-case suboptimality computed with the proposed method are very relevant for real-time applications such as Model Predictive Control (MPC) for hybrid systems. The numerical experiments confirm the correctness of the proposed method, and they demonstrate the usefulness of the certification method for certification of a standard online B&B-based MILP solver employing the three considered suboptimal techniques.

关键词： Numerical methods for optimal control Optimal control of hybrid systems mixed-integer linear programming Branch and bound method Complexity certification Suboptimal solutions

A Timer and mixed integer linear programming Load Shedding Scheme for Resilient DC Microgrids

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IEEE ACCESS 2025年 13卷 6632-6642页

作者： Babagana, Abdulrahman Jimoh, Isah A. Seferi, Yljon Burt, Graeme Univ Strathclyde Inst Energy & Environm Glasgow G1 1XW Scotland

Islanded DC microgrids are vulnerable to voltage instability caused by excessive power demand, which can adversely impact downstream consumers and disrupt overall microgrid operation. Existing load-shedding techniques face limitations such as over-shedding due to fixed voltage thresholds and time delays, predetermined load-shedding actions that fail to account for disturbance magnitude, and delayed stabilization caused by sequential load-shedding steps. To address these challenges, this paper proposes a novel load-shedding strategy for islanded DC microgrids that integrates a short-timer mechanism with mixed integer linear programming (MILP) optimization. The proposed approach reduces reliance on communication systems and achieves optimal load-shedding decisions using local voltage measurements. Simulation results on a DC microgrid model adapted from the IEEE 37-bus network demonstrate the effectiveness of the proposed scheme. The scheme results in a 20% reduction in unnecessary load shedding, an 18% improvement in voltage stabilization (measured as the final voltage after a disturbance), and a 25% decrease in response time compared to conventional methods. The results show that the proposed strategy ensures that the DC bus voltage remains above the critical threshold of 720 V, enhancing system reliability by minimizing voltage transients, reducing regulation time, and maintaining power balance. These improvements highlight the potential of the proposed scheme to support robust, secure, and resilient DC microgrid operation.

关键词： DC microgrid distributed energy resources load shedding mixed-integer linear programming optimization resilience DC microgrid distributed energy resources load shedding mixed-integer linear programming optimization resilience

Scheduling of Multi-Robot Job Shop Systems in Dynamic Environments: mixed-integer linear programming and Constraint programming Approaches

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2023年 115卷

作者： Fatemi-Anaraki, Soroush Tavakkoli-Moghaddam, Reza Foumani, Mehdi Vahedi-Nouri, Behdin Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Tech Univ Munich TUM Sch Management Arcisstr 21 D-80333 Munich Germany Univ Sydney Rio Tinto Ctr Mine Automat Australian Ctr Field Robot Sydney NSW Australia

This paper investigates a dynamic scheduling problem within a job shop robotic cell, wherein multiple robotic arms are responsible for material handling in a U-shaped arrangement. Each robotic arm has ac-cess to specific workstations based on their distance in the cell layout. Therefore, a part may need to be exchanged between several robots according to its process plan. For this purpose, intermediate buffers are positioned between each pair of consecutive robots. Due to the dynamic nature of the problem, new jobs arrive at unpredictable times, which in turn necessitates rescheduling taking the system's current state into account. To tackle this problem, firstly, a mixed-integer linear programming (MILP) model is devised. Secondly, three distinct Speed-up Constraints (SCs) derived from the problem's inherent charac-teristics are designed and implemented to accelerate the MILP model's solving procedure. Afterward, the problem is formulated using Constraint programming (CP) approach. The performance of the CP model and the MILP model in presence of all possible combinations of the SCs are evaluated and compared through solving various random instances. Next, an analysis is performed on the buffers' pick-up crite-rion and how it is affected by the problem's size. Besides, the impact of changes in the robots' speed on the productivity of the cell is assessed. Finally, the extent to which the rescheduling priority affects the output of the model is studied. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Job shop robotic cell Material handling Dynamic scheduling mixed-integer linear programming Constraint programming

Analysis of the Economic Feasibility of Power Substitution Potential at the Industrial Park Level Based on mixed-integer linear programming and Its Application in a Pharmaceutical Park

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Analysis of the Economic Feasibility of Power Substitution P...

2025 International Conference on Electrical Automation and Artificial Intelligence, ICEAAI 2025

作者： Li, Yunfeng Xu, Yutao Xiao, Yong Feng, Qihui Zhao, Yun Zhang, Yuelang CSG Electric Power Research Institute Guangdong Provincial Key Laboratory of Intelligent Measurement and Advanced Metering of Power Grid Guangzhou China Electric Power Research Institute of Guizhou Power Grid Co. Ltd. Guiyang China

ISBN: (纸本)9798331506797

To address the lack of rapid and economical methods for assessing the power substitution potential of enterprises and industrial parks under the dual-carbon goals, this study employs a mixed-integer linear programming (MILP) approach to construct a year-round, 8760-hour simulation and optimization model of the energy system at the industrial park level. A quantitative analysis framework for power substitution potential is proposed. Through a practical analysis of power substitution in a pharmaceutical park in Guizhou, it was found that compared with the traditional gas boiler solution, the optimized power substitution scheme using high-temperature heat pumps could save the target park approximately 95,000 RMB in annual energy costs, reduce unit energy cost by about 3%, and decrease unit energy-related carbon emissions by about 4%. This study provides a scientific method and simulation framework for quantitatively analyzing power substitution potential in industrial parks. © 2025 IEEE.

关键词： energy simulation mixed-integer linear programming Power substitution

Rigid Body Path Planning using mixed-integer linear programming

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arXiv 2024年

作者： Yu, Mingxin Fan, Chuchu The Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP) formulations, suffer from limited scalability with respect to either the size of the workspace or the number of obstacles. In order to address the scalability issue, we propose a three-stage algorithm that first generates a graph of convex polytopes in the workspace free of collision, then poses a large set of small MILPs to generate viable paths between polytopes, and finally queries a pair of start and end configurations for a feasible path online. The graph of convex polytopes serves as a decomposition of the free workspace and the number of decision variables in each MILP is limited by restricting the subproblem within two or three free polytopes rather than the entire free region. Our simulation results demonstrate shorter online computation time compared to baseline methods and scales better with the size of the environment and tunnel width than sampling-based planners in both 2D and 3D environments. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

APOLLO-MILP: AN ALTERNATING PREDICTIONCORRECTION NEURAL SOLVING FRAMEWORK FOR mixed-integer linear programming

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arXiv 2025年

作者： Liu, Haoyang Wang, Jie Geng, Zijie Li, Xijun Zong, Yuxuan Zhu, Fangzhou Hao, Jian Ye Wu, Feng MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition University of Science and Technology of China China Noah’s Ark Lab Huawei Technologies Hong Kong Tianjin University China Shanghai Jiao Tong University China

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap. © 2025, CC BY.

关键词： mixed-integer linear programming

Exact Verification of First-Order Methods via mixed-integer linear programming

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arXiv 2024年

作者： Ranjan, Vinit Gualandi, Stefano Lodi, Andrea Stellato, Bartolomeo

We present exact mixed-integer programming linear formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the objective is to maximize the infinity norm of the fixed-point residual after a given number of iterations. Our approach captures a wide range of gradient, projection, proximal iterations through affine or piecewise affine constraints. We derive tight polyhedral convex hull formulations of the constraints representing the algorithm iterations. To improve the scalability, we develop a custom bound tightening technique combining interval propagation, operator theory, and optimization-based bound tightening. Numerical examples, including linear and quadratic programs from network optimization and sparse coding using Lasso, show that our method provides several orders of magnitude reductions in the worst-case fixed-point residuals, closely matching the true worst-case performance. © 2024, CC BY.

关键词： mixed-integer linear programming

Distributed Asynchronous mixed-integer linear programming with Feasibility Guarantees

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arXiv 2024年

作者： Fina, Luke Petersen, Christopher Hale, Matthew Department of Mechanical and Aerospace Engineering University of Florida GainesvilleFL United States School of Electrical and Computer Engineering Georgia Institute of Technology AtlantaGA United States

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. To solve a MILP, we relax it with a linear program approximation. We first show that if the linear program relaxation satisfies Slater’s condition, then relaxing the problem, solving it, and rounding the relaxed solution produces a point that is guaranteed to satisfy the constraints of the original MILP. Next, we form a Lagrangian saddle point problem that is equivalent to the linear program relaxation, and then we regularize the Lagrangian in both the primal and dual spaces. We then develop a parallelized algorithm to compute saddle points of the regularized Lagrangian, and we show that it is tolerant to asynchrony in the computations and communications of primal and dual variables. Suboptimality bounds and convergence rates are presented for convergence to a saddle point. Simulation results illustrate these theoretical developments in practice, and show that relaxation and regularization combined typically have only a mild impact on the suboptimality of the solution obtained. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

mixed-integer linear programming method for coordination of overcurrent and distance relays incorporating overcurrent relays characteristic selection

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2019年第Sep.期110卷 246-257页

作者： Maleki, Mandi Ghotbi Chabanloo, Reza Mohammadi Taheri, Mohammad Reza Shahid Beheshti Univ Elect Engn Dept AC Tehran Iran

Coordination of overcurrent-overcurrent (OC) and overcurrent-distance (Dis) relays is one of the important issues in sub-transmission and distribution networks. In this paper, three approaches based on mixed-integer linear programming (MILP) is proposed for OC-OC and OC-Dis relays' coordination. Two of these proposed approaches are based on previously presented MILP-based approaches that were introduced for determining time and pickup-current settings in OC-OC relays' coordination problem. These predefined approaches are developed for obtaining optimal types of OC relays in addition to time and pickup-current settings in OC-OC and OC-Dis relays' coordination problem. A new MILP-based approach with less variables than the developed approaches is also proposed. This new approach has the ability to reach the best result in the short simulation time. In the new proposed approach, a cubic term which has two binary variables and one continuous variable must be replaced with a linear term. Therefore, a new linearization method is presented for this purpose. Three proposed approaches are implemented on the IEEE 8-buses and the IEEE 30-buses network. It is illustrated that new proposed approach from the point of view of objective function and simulation time is better than other methods especially for large networks. Therefore, new proposed approach is suitable for employing in the computing software as an efficient algorithm for relays' coordination.

关键词： Distance relay mixed-integer linear programming Overcurrent relay Relays coordination