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IEEE Conference on Decision and Control

作者： Shamisa Shoja Daniel Arnström Daniel Axehill Department of Electrical Engineering Division of Automatic Control Linköping University Sweden

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Model predictive control (MPC) with linear cost function for hybrid systems requires the solution of a mixed-integer linear program (MILP) at each sampling time. The branch and bound (B&B) method is a commonly used tool for solving mixed-integer problems. In this work, we present an algorithm to exactly certify the computational complexity of a standard B&B-based MILP solver. By the proposed method, guarantees on worst-case complexity bounds, e.g., the worst-case iterations or size of the B&B tree, are provided. This knowledge is a fundamental requirement for the implementation of MPC in a real-time system. Different node selection strategies, including best-first, are considered when certifying the complexity of the B&B method. Furthermore, the proposed certification algorithm is extended to consider warm-starting of the inner solver in the B&B. We illustrate the usefulness of the proposed algorithm by comparing against the corresponding online MILP solver in numerical experiments using both cold-started and warm-started LP solvers.

关键词： Cost function Prediction algorithms Real-time systems Partitioning algorithms mixed integer linear programming Computational complexity Certification

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QAOA-Assisted Benders' Decomposition for mixed-integer linear programming

QAOA-Assisted Benders' Decomposition for Mixed-integer Linea...

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IEEE International Conference on Communications (ICC)

作者： Zhongqi Zhao Lei Fan Yuanxiong Guo Yu Wang Zhu Han Lajos Hanzo Department of Electrical and Computer Engineering University of Houston Houston TX USA Department of Engineering Technology University of Houston Houston TX USA Department of Information Systems and Cyber Security University of Texas at San Antonio San Antonio TX USA Department of Computer and Information Sciences Temple University Philadelphia PA USA School of Electronics and Computer Science University of Southampton Southampton UK

ISBN: (数字)9781728190549

ISBN: (纸本)9781728190556

Benders' decomposition (BD) algorithm constitutes a powerful mathematical programming method of solving mixed-integer linear programming (MILP) problems with a specific block structure. Nevertheless, BD still needs to solve an NP-hard quasi-integer programming master problem (MAP), which motivates us to harness the popular variational quantum algorithm (VQA) to assist BD. More specifically, we choose the popular quantum approximate optimization algorithm (QAOA) of the VQA family. We transfer the BD's MAP into a digital quantum circuit associated with a physically tangible problem-specific ansatz; and then solve it with the aid of a state-of-the-art digital quantum computer. Next, we evaluate the computational results and discuss the feasibility of the proposed algorithm. The hybrid approach advocated, which utilizes both classical and digital quantum computers, is capable of tackling many practical MILP problems in communication and networking, as demonstrated by a pair of case studies.

关键词： Performance evaluation Quantum computing Quantum algorithm programming Approximation algorithms mixed integer linear programming Quantum circuit

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On the Equivalence Between mixed-integer linear and linear programming Problems in MPC for Photovoltaic Plants with Energy Storage

On the Equivalence Between Mixed-Integer Linear and Linear P...

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IEEE ANDESCON

作者： Rodrigo Graves Angel L. Cedeño Cùsar Silva Juan C. Agüero Departamento de Electronica Universidad Tecnica Federico Santa Maria Valparaiso Chile

ISBN: (数字)9798350355284

ISBN: (纸本)9798350355291

This paper investigates the equivalence between a class of mixed-integer linear and linear programming prob-lems. By utilizing the addition of slack variables theorem, we demonstrate that certain optimization problems arising in Model Predictive Control strategies, which involve logical constraints, can be solved as linear programming problems. Consequently, the equivalent linear programming problem can be solved using the standard and numerically efficient method named the Sim-plex method, as opposed to mixed-integer linear programming problems for which the best solution method is not clear. As a case study, we address the control problem of photovoltaic plants with energy storage systems. We design a model-based predictive control scheme based on our proposed equivalent linear programming problem to maximize economic benefits derived from energy delivered by both photovoltaic panels and energy storage systems to the grid in a deregulated electricity market, achieved by managing the charge and discharge of the energy storage. Additionally, the proposed scheme allows for the consideration of rate-based variable efficiency in the energy stor-age system model, offering a more comprehensive implementation compared to the previous approach in the literature, where only an ideal battery was considered. Furthermore, simulations reveal that the proposed control methodology reduces the execution time of model-predictive control iterations compared to another approach based on mixed-integer linear programming schemes with similar considerations, thereby enhancing the scalability of the solution.

关键词： Photovoltaic systems Economics Transforms linear programming Electricity supply industry Batteries mixed integer linear programming Optimization Standards Predictive control

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An Optimal Bus Scheduling Model Based on mixed-integer linear programming

An Optimal Bus Scheduling Model Based on Mixed-Integer Linea...

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IEEE Joint International Information Technology and Artificial Intelligence Conference (ITAIC)

作者： Ge Meng Yongxuan Lai Fan Yang School of Informatics Xiamen University China Xiamen University China

ISBN: (数字)9781728152448

ISBN: (纸本)9781728152455

The bus company mainly relies on the experienced scheduling personnel to prepare the time plate of the bus line manually in advance, and then conFigure the vehicles. However, this kind of scheduling method often cause a waste of bus seat resources only by experience. In this paper, we propose a vehicles scheduling model called MILPS (mixed-integer linear programming Model of Scheduling) to minimise the gap between the demand and supply of bus seats. In the first phase, we first analyze the historical trajectory data of taxis in Xiamen and select the two most popular stations as the starting and ending points of bus routes, then generate the service area between them by rectangle. In the second phase, we derive several criteria to build bus scheduling model based on mixed-integer linear programming. Finally, we use CPLEX optimizer to solve this MILP problem. Experimental results show that the proposed scheme can effectively reduce the waste of bus seat resources (>76.8% reduction) and significantly improve the delivery ratio (>71.5%).

关键词： Conferences Companies mixed integer linear programming Trajectory Personnel Information technology Public transportation

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Optimal operation of building microgrids - comparison with mixed-integer linear and continuous non-linear programming approaches

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COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING 2018年第2期37卷 603-616页

作者： Reinbold, Vincent Dinh, Van-Binh Tenfen, Daniel Delinchant, Benoit Saelens, Dirk Katholieke Univ Leuven Leuven Belgium Grenoble Univ Grenoble France Inst Fed Educ Ciencia & Tecnol Santa Catarina Florianopolis SC Brazil Grenoble Univ Grenoble Elect Engn Lab G2Elab Grenoble France

PurposeThis paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon. Design/methodology/approachA general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models. FindingsResults show that both approaches are relevant for solving the energy management problem of the building MG. Originality/valueIntroduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

关键词： Microgrid mixed integer linear programming Optimal operation Sequential quadratic programming

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linear or mixed integer programming in long-term energy systems modeling - A comparative analysis for a local expanding heating system

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ENERGY 2023年 283卷

作者： Vilen, Karl Ahlgren, Erik O. Chalmers Univ Technol Dept Space Earth & Environm Div Energy Technol SE-41396 Gothenburg Sweden

Most computer models used in energy systems optimization modeling studies are formulated using linear equations. However, since linear formulations do not always well reflect real-world conditions, they may not always be adequate as policy and support tools. This is particularly the case for local system studies attempting to represent technologies at the individual scale, as in the case for local heating system modeling. Thus, the aim of this paper is to investigate differences in the resulting heating solutions and model solution times for a local expanding heating system. Three different investment cost structures for individual and district heating solutions for the heating of new housing are investigated using linear and mixed integer linear programming. The results show that the use of district heating is higher for the cost structures that use mixed integer linear programming than it is for the linear cost structures. This result is attributed mainly to the fact that individual air-to-water heat pumps benefit from the linear equation formulation due to its high coefficient of performance during summertime. This finding is important to consider when modeling local energy systems. The solution time is, however, significantly shorter for the linear formulations than for the mixed integer linear formulations.

关键词： Housing District heating Local energy system modeling TIMES mixed integer linear programming linear programming

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Integrated Optimization Planning of Multiple Energy Stations for Low Carbon Operation

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CSEE Journal of Power and Energy Systems 2025年第2期11卷 815-825页

作者： Weijie Dong Keyan Liu Wanxing Sheng Beijing Information Science&Technology University Beijing 100192China China Electric Power Research Institute Beijing 100192China

Under the background of low-carbon demand, an integrated energy system is the main direction of energy system development. Integrated Energy System (IES) breaks through technical, market and management barriers of traditional energy systems, and it makes unified planning and scheduling for electricity, gas, heat, cold, etc. However, IES contains a variety of energy forms, and those energy forms are coupled with each other. Its planning and operation are challenging problems. Therefore, this paper proposes an IES planning model, which comprehensively considers optimization of the equipment configuration, interconnection of multiple energy stations, renewable energy integration, and optimal operation strategy. During the planning decision-making, planners can use this model to analyze and evaluate the impact of various factors on the planning indicators. Using the proposed model, an IES composed of several buildings in a street block is planned in detail and the effectiveness of the proposed planning model and its solution method is proved. The case study results show the total cost and carbon emission of the model considering both energy station interconnection and RES integration are reduced by 20.2% and 41.5%.

关键词： Carbon emission energy bus model integrated energy system planning mixed integer linear programming multiple energy station interconnection renewable energy integration

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Rolling stock rescheduling in high-speed railway networks via a nested Benders decomposition approach

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2025年 171卷

作者： Li, Denghui Zhao, Jun Peng, Qiyuan Wang, Dian Zhong, Qingwei Southwest Jiaotong Univ Sch Transportat & Logist Chengdu 611756 Sichuan Peoples R China Southwest Jiaotong Univ Natl United Engn Lab Integrated & Intelligent Tran Chengdu 611756 Sichuan Peoples R China Hefei Univ Technol Sch Automot & Transportat Engn Hefei 230009 Anhui Peoples R China Civil Aviat Flight Univ China Coll Air Traff Management Guanghan 618307 Sichuan Peoples R China

This paper addresses a rolling stock rescheduling problem (RSRP) during disruptions in a high-speed railway network, focusing on decisions related to the reassignment of physical rolling stock units to trips, deadheading schedules, and maintenance plans and schedules, while taking into account deadheading trips and maintenance requirements. A mixed integer linear programming (MILP) model is formulated, leveraging a directed acyclic graph to represent all feasible connections for each rolling stock unit. The objective is to minimize the weighted sum of canceled trips, schedule deviations, and various service quality and cost indicators. An exact nested Benders decomposition (NBD) algorithm is developed to solve this model. In the algorithm, the RSRP is first decomposed into an outer integer master problem (OMP) and an outer integer subproblem (OSP). The OMP is then divided into an inner integer master problem (IMP) and an inner integer subproblem (ISP), and is solved using the logic-based Benders decomposition (LBBD) algorithm, where strengthened feasibility cuts and optimality cuts, as well as valid inequalities, are added to the IMP to enhance the algorithm's performance. The OSP, a feasibility problem, is further decomposed into many easier problems at each depot. Subsequently, three implementations including two branch-and-check type approaches and one LBBD approach are customized to solve the outer decomposition problem. We also propose a three-stage approach to solve the IMP, ISP, and OSP, sequentially. The approaches are tested on a set of instances constructed from the high-speed railway network in China. The results show that the approaches can quickly find (near-)optimal solutions for tested instances within a short computation time of several minutes, making it suitable for real-time rolling stock rescheduling applications.

关键词： High-speed railway transportation Rolling stock rescheduling Deadheading mixed integer linear programming Nested Benders decomposition

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Seniority-based surgery scheduling and team assignment

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SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES 2025年第2期50卷 1-8页

作者： Didem Batur Sir, G. Oner, Nurhan Erol, Serpil Gazi Univ Fac Engn Dept Ind Engn Ankara Turkiye Gen Directorate PTT Ankara Turkiye

Crucial resources for surgical operations are obviously operating rooms and surgical teams. It is essential to ensure the equitable assignment of operations to both operating rooms and surgical teams, taking into account the capacities, resting periods, and cleaning times. Additionally, the varying levels of expertise required for different types of surgeries should be considered. In this study, we focus on these challenges within the context of surgery scheduling and team assignment problems. We propose a mathematical model-based solution approach for operating room planning that aligns surgical teams with the specific requirements of various procedures, consistent with real life applications. Key considerations include appropriate workload distribution, sufficient rest times, and opportunities for surgeon training. By utilizing the methodology presented in this study, we effectively assign daily planned operations to the appropriate operating rooms and surgical teams. The proposed procedure is successfully applied to real data from the otorhinolaryngology department of a public hospital, as well as to randomly generated test problems. This study provides exact solutions for the aforementioned surgery scheduling and team assignment issues.

关键词： Operating room scheduling surgical team assignment surgery types surgeon seniority mixed integer linear programming

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A Customized Local Energy Trading Approach Using a Comprehensive Set of Performance Indices

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IEEE ACCESS 2025年 13卷 9413-9429页

作者： Patnaik, Smitali Cali, Umit Noras, Maciej A. Univ North Carolina Charlotte Dept Engn Technol & Construct Management Charlotte NC 28223 USA Norwegian Univ Sci & Technol NTNU Dept Elect Power Engn N-7491 Trondheim Norway Univ York Sch Phys Engn & Technol York YO10 5DD England

This paper presents a customized local energy trading approach using a comprehensive set of performance indices (i.e. Community Savings, Self-Consumption, Self-Sufficiency, Fairness Index, Individual Household Savings) for evaluation of the trading practices. The simulations performed on historical data sets compared dispatch mechanisms based on mixed integer linear programming (MILP) and techniques originating from Auction-Based approaches. The intent was to use performance metrics in building Local Energy Market (LEM) trading solutions based on a given set of limited inputs and use them to optimize pricing or trading dispatch to get the best consumer returns. Modeling results indicate that the Auction-Based Model performed better than the MILP methods in terms of all performance indices and had potential to provide participants with higher levels of savings.

关键词： Pricing Batteries Indexes Costs Resource management Peer-to-peer computing Optimization Load modeling Electricity Data models Distributed energy resources mixed integer linear programming auction peer-to-peer energy trading optimization photovoltaic self-sufficiency self-consumption fairness index

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