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Constructing Uncertainty Sets From Covariates in Power Systems

IEEE Transactions on Power Systems 2025年

作者： Bertsimas, Dimitris Koukouvinos, Thodoris Koulouras, Angelos Georgios Massachusetts Institute of Technology Operations Research Center United States

Robust optimization (RO) immunizes against uncertainties in power systems through uncertainty sets that control the robustness and conservativeness of the underlying optimization problem. Despite earlier work in their structure and properties, there are few suggestions on calibrating their size. In this paper, we propose a method to determine (predict) the uncertainty set size using machine learning models and mixed- integer optimization (MIO), leveraging historical data that consist of covariates or features. In essence, we utilize covariates to simultaneously predict the uncertain parameters and construct an uncertainty set around the nominal prediction based on the confidence in the prediction itself. In addition, we introduce optional amendments to our framework so that the uncertainty set bounds are covariate-dependent and also develop an outer approximation scheme for efficiently solving the underlying MIO problem in larger datasets. We apply our framework to uncertainty sets for available wind resource capacity in the Adaptive Robust Unit Commitment (ARUC) problem. We show that our approach gives lower probabilities of constraint violation than commonly used statistical approaches, without necessarily exhibiting an increase in the cost. © 1969-2012 IEEE.

关键词： mixed-integer linear programming

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The aperiodic facility layout problem with time-varying demands and an optimal master-slave solution approach

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第17期59卷 5216-5235页

作者： Xiao, Yiyong Zhang, Yue Kulturel-Konak, Sadan Konak, Abdullah Xu, Yuchun Zhou, Shenghan Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China Penn State Berks Management Informat Syst Reading PA USA Penn State Berks Informat Sci & Technol Reading PA USA Aston Univ Sch Engn & Appl Sci Birmingham W Midlands England

In many seasonal industries, customer demands are constantly changing over time, and accordingly the facility layout should be re-optimized in a timely manner to adapt to changing material handling patterns among manufacturing departments. This paper investigates the aperiodic facility layout problem (AFLP) that involves arranging facilities layout and re-layout aperiodically in a dynamic manufacturing environment during a given planning horizon. The AFLP is decomposed into a master problem and a combination set of static facility layout problems (FLPs, the slave problems) without loss of optimality, and all problems are formulated as mixed-integer linear programming (MILP) models that can be solved by MIP solvers for small-sized problems. An exact backward dynamic programming (BDP) algorithm with a computational complexity of O(n(2)) is developed for the master problem, and an improved linear programming based problem evolution algorithm (PEA-LP) is developed for the traditional static FLP. Computational experiments are conducted on two new problems and twelve well-known benchmark problems from the literature, and the experimental results show that the proposed solution approach is promising for solving the AFLP with practical sizes of problem instances. In addition, the improved PEA-LP found new best solutions for five benchmark problems.

关键词： Facility layout mixed-integer linear programming dynamic programming optimization evolutionary algorithm

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A two-echelon location-routing problem with synchronisation

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2021年第1期72卷 145-160页

作者： Mirhedayatian, Seyed Mostafa Crainic, Teodor Gabriel Guajardo, Mario Wallace, Stein W. NHH Norwegian Sch Econ Dept Business & Management Sci N-5045 Bergen Norway Univ Montreal CIRRELT Ctr Ville Montreal PQ Canada

Motivated by an actual problem of a national postal service company, we introduce and define a new two-echelon location-routing problem (2E-LRP). The 2E-LRP is defined in a two-echelon distribution system where products are transported from origins to destinations through intermediate facilities. A major question that arises in a two-echelon distribution system is how to synchronise the flows of the two echelons at intermediate facilities. The synchronisation is important due to limited storage space or waiting times for transshipments at the intermediate facilities. In our new 2E-LRP, the activities in the two echelons are organised into two waves;a delivery wave, where products are sent from the primary facility to the customers through the intermediate facilities, and a following pickup wave, where the flow of products is reversed. The model only considers temporal constraints, assuming that capacities are never binding;the vehicles are always large enough given the constraints on time. As a solution approach, we propose a decomposition-based heuristic. Besides the solution approach, we propose data-driven schemes for use in combination with the model and we provide the computational results for different sets of instances.

关键词： Two-echelon location-routing synchronisation pickup and delivery waves mixed-integer linear programming

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Exact Methods for the Traveling Salesman Problem with Drone

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TRANSPORTATION SCIENCE 2021年第2期55卷 315-335页

作者： Roberti, Roberto Ruthmair, Mario Vrije Univ Amsterdam Dept Supply Chain Analyt NL-1081 HV Amsterdam Netherlands Univ Vienna Dept Stat & Operat Res A-1090 Vienna Austria

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas;the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows;such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route's completion time when the drone is sufficiently fast.

关键词： traveling salesman problem drones mixed-integer linear programming compact formulation dynamic programming set partitioning branch-and-price

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An Economic Dispatch for a Shared Energy Storage System Using MILP Optimization: A Case Study of a Moroccan Microgrid

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ENERGIES 2023年第12期16卷 4601-4601页

作者： El Barkouki, Bouthaina Laamim, Mohamed Rochd, Abdelilah Chang, Jae-won Benazzouz, Aboubakr Ouassaid, Mohammed Kang, Moses Jeong, Hakgeun Green Energy Pk Reg Rd Kelaa Km 3R206 Benguerir 43150 Morocco Mohammed V Univ Rabat Engn Smart & Sustainable Syst Res Ctr Mohammadia Sch Engineers Rabat 10090 Morocco Univ Hassan 2 LSIB Lab FST Mohammadia 28806 Morocco Hassan II Univ Casablanca Elect Engn & Intelligent Syst Lab ENSET Mohammedia Mohammadia 28830 Morocco Korea Inst Energy Res 152 Gajeong Ro Daejeon 34129 South Korea

Energy storage systems are an effective solution to manage the intermittency of renewable energies, balance supply, and demand. Numerous studies recommend adopting a shared energy storage system (ESS) as opposed to multiple single ESSs because of their high prices and inefficiency. Thus, this study examines a shared storage system in a grid-connected microgrid. By modifying the power outputs of the energy resources, this work intends to implement an economic dispatch of a shared ESS in order to satisfy the power balance and lower the overall cost of electricity. In this context, an optimization problem was formulated and developed using a mixed-integer linear programming (MILP) model. Furthermore, a pilot project (the Solar Decathlon Africa Village) in the Green & Smart Building Park (GSBP), Benguerir, Morocco, was employed to evaluate and verify the proposed approach. Some comparable scenarios were therefore run in a MATLAB environment. The collected findings demonstrate the efficacy of the developed algorithm in terms of optimizing energy cost reductions and enhancing the integration of renewable resources into the Moroccan energy mix.

关键词： shared energy storage system energy management system economic dispatch microgrids mixed-integer linear programming power system

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Alternative Mathematical Models for the Optimal Transmission Switching Problem

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IEEE SYSTEMS JOURNAL 2021年第1期15卷 1245-1255页

作者： Flores, Moises Macedo, Leonardo H. Romero, Ruben Natl Univ Engn Dept Elect Engn Lima 15333 Peru Sao Paulo State Univ Dept Elect Engn BR-15385000 Ilha Solteira SP Brazil

In this article, the optimal transmission switching (OTS) problem is solved in order to optimize the operation cost of an electrical power system. This is accomplished by disconnecting some transmission lines, which enables a change to the profile of the power flow distribution in the system, allowing for increased generation at the buses with lower costs;thus, the hourly operation cost of the generation is minimized to meet the demand of the system. This article presents contributions to topics related to the issue of the high number of transmission lines that are disconnected when the OTS problem is solved, the problem of system islanding, and the causes of Braess's paradox, in the context of the OTS problem. Finally, tests are conducted using the 41-bus southern Brazilian system and the 92-bus Colombian system. The results demonstrate the effectiveness of the proposals for reducing the number of lines disconnected from the system and for avoiding islanding.

关键词： Power transmission lines Proposals Switches Switching circuits Mathematical model Optimization Braess&apos s paradox mixed-integer linear programming optimal transmission switching (OTS) system islanding transmission systems operation planning

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Day-Ahead Scheduling of Power System With Short-Circuit Current Constraints Considering Transmission Switching and Wind Generation

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IEEE ACCESS 2021年 9卷 110735-110745页

作者： Hua, Haocheng Liu, Tianqi He, Chuan Nan, Lu Zeng, Hong Hu, Xiaotong Che, Bin Sichuan Univ Coll Elect Engn Chengdu 610065 Sichuan Peoples R China State Grid Sichuan Elect Power Co Tianfu Power Supply Co Chengdu 610041 Sichuan Peoples R China State Grid Sichuan Elect Power Co Chengdu 610041 Sichuan Peoples R China State Grid Ningxia Elect Power Co Ltd Econ & Technol Res Inst Yinchuan 750004 Ningxia Peoples R China

The expansion of the power network and integration of wind farms pose challenges in the short-circuit current (SCC) problem. Transmission switching performs better in both flexibility and effectiveness compared with other SCC restriction measures, while the power grid security would be threatened as the number of switched-off-lines increases. This paper proposes a day-ahead scheduling model considering commitment of units and N-1 criterion, to avoid the excessive SCC problem caused by wind farms integration. Specially, the SCC calculation model of the grid-connected wind farms is put forward to aggregate wind farms and calculate SCC. A novel SCC formulation considering transmission switching, commitment of units as well as wind farms integration is deduced and converted to SCC constraints. The SCC constrained mixed-integer linear programming (MILP) based day-ahead scheduling model is proposed, which minimizes system operation cost and transmission switching cost. In addition, the N-1 security requirement is considered in the proposed day-ahead scheduling model to ensure system security by avoiding switching off too many lines. Numerical results of a modified IEEE 30-bus system with two wind farms illustrate effectiveness of the proposed model.

关键词： Wind farms Switches Security Analytical models Systems operation Switching circuits Short-circuit currents Short-circuit current wind farm integration transmission switching day-ahead scheduling mixed-integer linear programming

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Timetable coordination in a rail transit network with time-dependent passenger demand

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第1期295卷 183-202页

作者： Yin, Jiateng D'Ariano, Andrea Wang, Yihui Yang, Lixing Tang, Tao Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing Peoples R China Univ Roma Tre Dept Engn Rome Italy

With the expansion of urban rail networks and the increase of passengers demand, the coordination of strongly connected lines becomes more and more important, because passengers transfer several times during their trips and major transfer stations in the rail network often suffer from over-crowdedness, especially during peak-hours. In this paper, we study the optimization of coordinated train timetables for an urban rail network, which is a tactical timetabling problem and includes several operational constraints and time-dependent passenger-related data. We propose a mathematical formulation with the objective of minimizing the crowdedness of stations during peak hours to synchronously generate the optimal coordinated train timetables. By introducing several sets of passenger flow variables, the timetable coordination problem is formulated as a mixed-integer linear programming problem, that is possible to solve to optimum. To capture the train carrying capacity constraints, we explicitly incorporate the number of in vehicle passengers in the modelling framework by considering the number of boarding and alighting passengers as passenger flow variables. To improve the computational efficiency of large-scale instances, we develop an Adaptive Large Neighborhood Search (ALNS) algorithm with a set of destroying and repairing operators and a decomposition-based ALNS algorithm. Real-world case studies based on the operational data of Beijing urban rail network are conducted to verify the effectiveness of timetable coordination. The computational results illustrate that the proposed approaches reduce the level of crowdedness of metro stations by around 8% in comparison with the current practical timetable of the investigated Beijing urban rail network. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Transportation Timetable coordination Rail transit network mixed-integer linear programming Adaptive large neighborhood search

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Optimal insurance contract specification in the upstream sector of the oil and gas industry

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期295卷 718-732页

作者： Torraca, Ana Patricia Fanzeres, Bruno Pontifical Catholic Univ Rio de Janeiro PUC Rio Ind Engn Dept Rio De Janeiro RJ Brazil

The upstream sector of the Oil and Gas (O&G) industry is recognized by its capital-intensive projects and complex and hazardous associated recovery and production processes, thus susceptible for large and financially damaging accidents. In this context, to avoid the risk and impact of high expenses, O&G companies usually acquire insurance contracts. In practice, although the contract format is typically pre-specified, its parameter magnitudes can be adjusted aiming at maximizing the company total wealth. Therefore, this work proposes a holistic methodology to assess the optimal parameter specification of an insurance contract in the upstream sector of the O&G industry. A non-convex stochastic optimization problem is constructed aiming at maximizing a risk-adjusted measure of the policyholder total wealth. The modeling takes into account the uncertainty on the financial loss of an accident by making use of the safety barriers and precursor information framework. The non-convex optimization problem is cast as an equivalent mixed-integer linear programming problem by combining the scenario-based representation approach with a set of binary reformulation procedures. We illustrate the applicability of the proposed methodology with a set of numerical experiments. In a nutshell, we found that the proposed parameter specification methodology resulted in greater predictability when compared to two quantile-based speci-fication policies and an uninsured company. In fact, the second best policy presented a standard deviation 103% higher than the proposed methodology. Furthermore, the model also provided greater protection against extreme events, since the second best policy presented a Conditional Value-at-Risk 41% higher than the proposed methodology. (c) 2021 Elsevier B.V. All rights reserved.

关键词： (R) OR in energy Insurance contract specification mixed-integer linear programming Risk measures Safety barriers

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Domain Partition of the Hydro Production Function for Solving Efficiently the Short-Term Generation Scheduling Problem

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IEEE ACCESS 2021年 9卷 152780-152791页

作者： Brito, Brunno H. Finardi, Erlon C. Takigawa, Fabricio Y. K. Nogueira, Pierry L. R. Morais, Douglas T. S. A. Fernandes, Argemiro Fed Inst Tocantins BR-77020450 Palmas Tocantins Brazil Univ Fed Santa Catarina LabPlan BR-88040900 Florianopolis SC Brazil INESC P&D Brasil BR-11055300 Santos SP Brazil Fed Inst Santa Catarina BR-88020300 Florianopolis SC Brazil Santo Antonio Energia BR-77805412 Porto Velho Rondonia Brazil

Short-term generation scheduling (STGS) is a fundamental task in the operational planning analysis of hydroelectric plants. For the multi-unit case, the STGS is represented as a large-scale nonconvex mixed-integer nonlinear optimization model. Then, considering the (usual) short time for providing a solution, it is vital to exploit all the structural properties of the problem at hand. The main issue for exploiting this problem is the hydro production function (HPF), which is a nonlinear nonconvex relationship between power, head, and turbined outflow of a generating unit (GU). Nevertheless, the HPF usually presents operating regions where the function is convex and regions in which it is concave due to physical reasons. Inspired by sequential convex mixed-integer nonlinear programming techniques, this paper proposes partitioning the domain of the HPF in regions in which it is convex and those in which it is concave. The HPF is approximated by a piecewise linear function using the logarithmic aggregation convex combination (LACC) model in convex regions. In turn, in the concave regions, the HPF is replaced by a convex hull approach, which, combined with symmetry strategies, reduces the number of binary variables in the resulting optimization problem. Using several computational instances of a 50-unit hydroelectric plant, we show that the partitioning-based proposed strategy significantly reduces the computational time compared to two other efficient MILP formulations.

关键词： programming Hydraulic systems Computational modeling Computational efficiency Production Hydroelectric power generation Optimization Short-term hydro generation scheduling hydroelectric power plants domain partitioning mixed-integer linear programming logarithmic aggregate convex combination symmetry-based techniques

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