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Robust optimal discrete arc sizing for tree-shaped potential networks

COMPUTATIONAL optimization AND APPLICATIONS 2019年第3期73卷 791-819页

作者： Robinius, Martin Schewe, Lars Schmidt, Martin Stolten, Detlef Thuerauf, Johannes Welder, Lara Forschungszentrum Julich Inst Electrochem Proc Engn IEK 3 Wilhelm Johnen Str D-52428 Julich Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Trier Univ Dept Math Univ Sring 15 D-54296 Trier Germany Rhein Westfal TH Aachen Chair Fuel Cells Forschungszentrum Julich Inst Electrochem Proc Engn IEK 3 Wilhelm Johnen Str D-52428 Julich Germany

We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to be NP-complete even on trees. In order to obtain a tractable problem, we introduce a method for generating a finite scenario set such that optimality of a sizing for this finite set implies the sizing's optimality for the originally given infinite set of scenarios. We further prove that the size of the finite scenario set is quadratically bounded above in the number of nodes of the underlying tree and that it can be computed in polynomial time. The resulting problem can then be solved as a standard mixed-integer linear optimization problem. Finally, we show the applicability of our theoretical results by computing globally optimal arc sizes for a realistic hydrogen transport network of Eastern Germany.

关键词： Discrete arc sizing Network design Potential networks Scenario generation Robust optimization mixed-integer linear optimization 90-08 90B10 90C11 90C35 90C90

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Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design (Reprintede from Computers and Chemical Engineering, vol 113, pg 57-85, 2018)

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COMPUTERS & CHEMICAL ENGINEERING 2018年 116卷 422-450页

作者： Letsios, Dimitrios Kouyialis, Georgia Misener, Ruth Imperial Coll London Dept Comp South Kensington SW7 2AZ England

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods. (C) 2018 The Author(s). Published by Elsevier Ltd.

关键词： Minimum number of matches Heat exchanger network design Heuristics Approximation algorithms mixed-integer linear optimization

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Extrapolating curvature lines in rough concept sketches using mixed-integer nonlinear optimization

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optimization AND ENGINEERING 2019年第2期20卷 337-347页

作者： D'Ambrosio, Claudia Lee, Jon Liberti, Leo Ovsjanikov, Maks CNRS LIX Ecole Polytech F-91128 Palaiseau France Univ Michigan Dept IOE Ann Arbor MI 48109 USA

We present several mathematical-optimization formulations for a problem that commonly occurs in geometry processing and specifically in the design of so-called smooth direction fields on surfaces. This problem has direct applications in 3D shape parameterization, texture mapping, and shape design via rough concept sketches, among many others. A key challenge in this setting is to design a set of unit-norm directions, on a given surface, that satisfy some prescribed constraints and vary smoothly. This naturally leads to mixed-integer optimization formulations, because the smoothness needs to be formulated with respect to angle-valued variables, which to compare one needs to fix the discrete jump between nearby points. Previous works have primarily attacked this problem via a greedy ad-hoc strategy with a specialized solver. We demonstrate how the problem can be cast in a standard mathematical-optimization form, and we suggest several relaxations that are especially adapted to modern mathematical-optimization solvers. .

关键词： mixed-integer nonlinear optimization mixed-integer linear optimization Computer graphics Sketching

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Allocation of available transfer capability in planning horizon

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EUROPEAN TRANSACTIONS ON ELECTRICAL POWER 2011年第3期21卷 1437-1454页

作者： Rajabi-Ghahnavieh, A. Fotuhi-Firuzabad, M. Feuillet, R. ENS3E INPG Lab Genie Elect Grenoble F-38402 St Martin Dheres France Sharif Univ Technol Dept Energy Engn Tehran Iran Sharif Univ Technol Dept Elect Engn Tehran Iran

In the United States electricity market standard, when several transmission service requests (TSRs) are made for a specific pair of power injection/extraction points, the independent system operator (ISO) must allocate the available transmission capability (ATC) associated with the pair to the requests. An ATC allocation must determine the amount of accepted requests as well as the priority of the accepted requests during emergencies. The requests could have different types (recallable/non-recallable), tariffs, and time frames and these factors must be properly considered in ATC allocation. This paper proposes a method for optimal ATC allocation in the planning horizon which incorporates the type and tariffs of the requests in a mixed integer linear optimization programming for which the expected net revenue of ATC allocation on a seasonal base has to be maximized. The method also incorporates maintenance and forced outage of power system components as well as the load forecast uncertainty in ATC allocation problem. Once allocation accomplished by solving the optimization problem, the amount of the accepted requests and their priorities to the power system operator during emergencies are determined. The proposed method is applied to the modified IEEE reliability test system (IEEE-RTS) and its performance is evaluated. A comparison is made between the results obtained by the proposed method and those obtained using existing ATC allocation methods. Two approaches are finally presented and evaluated to apply the proposed method for allocating ATC to the requests with a yearly base. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： available transfer capability allocation transmission services deregulated power system mixed-integer linear optimization

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Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design

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COMPUTERS & CHEMICAL ENGINEERING 2018年 113卷 57-85页

作者： Letsios, Dimitrios Kouyialis, Georgia Misener, Ruth Imperial Coll London Dept Comp London SW7 2AZ South Kensingto England

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an N P-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Minimum number of matches Heat exchanger network design Heuristics Approximation algorithms mixed-integer linear optimization

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Modelling and (re-)planning periodic home social care services with loyalty and non-loyalty features

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期277卷 284-299页

作者： Gomes, Maria Isabel Pereira Ramos, Tania Rodrigues Univ Nova Lisboa CMA Fac Sci & Technol P-2829516 Monte De Caparica Caparica Portugal Univ Nova Lisboa Dept Math Fac Sci & Technol P-2829516 Monte De Caparica Caparica Portugal Univ Lisbon Ctr Management Studies Inst Super Tecn CEG IST P-1049001 Lisbon Portugal Inst Univ Lisboa ISCTE IUL Business Res Unit BRU IUL Av Forcas Armadas P-1649026 Lisbon Portugal

The aging population alongside little availability of informal care are two of the several factors leading to an increased need for assisted living support. In this work, we tackle a home social care service problem, motivated by two real case studies where a new loyalty scheme must be considered: within a week, patient-caregiver loyalty should be pursued but, between weeks, the caregivers must rotate among patients (non-loyalty). In addition, a common situation in this kind of service is also addressed: the need of a constant re-planning caused by the leaving of patients and the arrival of new ones. This new plan should be such that minimum disturbance is caused to the visiting hours of current patients, the caregivers' travelling time between visits is minimized, and the workload is balanced among caregivers. A multi-objective optimization approach based on mixed-integer models is developed. Results on the two real case studies show that both institutions can efficiently re-plan their activities without much disturbance on the visits of their patients, and with a patient-caregiver loyalty scheme suiting their needs. (C) 2019 Elsevier B.V. All rights reserved.

关键词： OR in health services Homecare service (Re-)routing and (Re-)scheduling Non-loyalty mixed-integer linear optimization

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Optimizing design and dispatch of a renewable energy system with combined heat and power

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optimization AND ENGINEERING 2022年第3期23卷 1-31页

作者： Hirwa, Jusse Ogunmodede, Oluwaseun Zolan, Alexander Newman, Alexandra M. Colorado Sch Mines 1500 Illinois St Golden CO 80401 USA Natl Renewable Energy Lab Thermal Energy Syst Grp 15013 Denver West Pkwy Golden CO 80401 USA

We embellish a mixed-integer program that prescribes a set of renewable energy, conventional generation, and storage technologies to procure, along with a corresponding dispatch strategy. Specifically, we add combined heat and power to this set. The model minimizes fixed and operational costs less incentives for the use of various technologies, subject to a series of component interoperability and system-wide constraints. The resulting mixed-integer linear program contains hundreds of thousands of variables and constraints. We demonstrate how to efficiently formulate and solve the corresponding instances such that we produce near-optimal solutions in minutes. A previous rendition of the model required hours of solution time for the same instances.

关键词： mixed-integer linear optimization Renewable energy Combined heat and power systems Efficient formulations

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Robust stabilization of polytopic systems via fast and reliable neural network-based approximations

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INTERNATIONAL JOURNAL OF ROBUST AND NONlinear CONTROL 2024年第9期34卷 6180-6201页

作者： Fabiani, Filippo Goulart, Paul J. IMT Sch Adv Studies Lucca Lucca Italy Univ Oxford Dept Engn Sci Oxford England IMT Sch Adv Studies Lucca Piazza S Francesco 19 I-55100 Lucca Italy

We consider the design of fast and reliable neural network-based approximations of traditional stabilizing controllers for linear systems with polytopic uncertainty, including control laws with variable structure and those based on a (minimal) selection policy. Building upon recent approaches for the design of reliable control surrogates with guaranteed structural properties, we develop a systematic procedure to certify the closed-loop stability and performance of a linear uncertain system when a trained rectified linear unit (ReLU)-based approximation replaces such traditional controllers. First, we provide a sufficient condition, which involves the worst-case approximation error between ReLU-based and traditional controller-based state-to-input mappings, ensuring that the system is ultimately bounded within a set with adjustable size and convergence rate. Then, we develop an offline, mixed-integer optimization-based method that allows us to compute that quantity exactly.

关键词： mixed-integer linear optimization neural networks robust control uncertain systems

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A mixed-integer optimization model for the economic and environmental analysis of biomass production

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BIOMASS & BIOENERGY 2014年 67卷 8-23页

作者： Cobuloglu, Halil Ibrahim Bueyuektahtakin, I. Esra Wichita State Univ Dept Ind & Mfg Engn Wichita KS 67260 USA

Biofuel production from second-generation feedstock has become critical due to environmental concerns and the need for sustainable energy supply. This paper provides a unique optimization approach of quantifying and formulating the economic and environmental benefits of switchgrass production at the farm level. In particular, we propose a multi-objective mixed-integer programming model, which maximizes the revenue from harvested switchgrass biomass and the economic value obtained from the positive environmental impacts of switchgrass yield during a ten-year planning horizon. Environmental impacts include soil erosion prevention, sustainability of bird populations, carbon sequestration, and carbon emissions, while economic impacts are analyzed under various budget, yield, and sustainability scenarios. The proposed model is then applied to a case study in the state of Kansas. Results show that given the current market prices, switchgrass cultivation on grassland and cropland is highly profitable. The model results also suggest that if utilized by the government, conservation reserve program (CRP) incentives could make marginal land more favorable over cropland. We perform sensitivity analysis to address the uncertainty in budget, yield, and utilization of cropland, and present insights into the economic and environmental impacts of switchgrass production. This model can also be extended to biomass production from any other types of energy crops to identify the most efficient production planning strategies under various management scenarios. Published by Elsevier Ltd.

关键词： Switchgrass Biofuel and biomass production mixed-integer linear optimization Sustainability and biodiversity Carbon emissions and sequestration Soil erosion prevention

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Minimizing delays of patient transports with incomplete information: A modeling approach based on the vehicle routing problem

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OR SPECTRUM 2024年 1-40页

作者： Adelhuette, Dennis Braun, Kristin Liers, Frauke Tschuppik, Sebastian Friedrich Alexander Univ Erlangen Nurnberg Dept Data Sci Cauerstr 11 D-91058 Erlangen Germany Fraunhofer Inst Integrated Circuits IIS Nordostpk 84 D-90411 Nurnberg Germany

We investigate a challenging task in ambulatory care, the minimizing of delays of patient transports. In practice, a limited number of vehicles is available for non-rescue transports. Furthermore, the dispatcher rarely has access to complete information when establishing a transport plan for dispatching the vehicles. If additional transport is requested on demand then schedules need to be updated, which can lead to long delays. We model the scheduling of patient transports as a vehicle routing problem with general time windows and solve it as a mixed-integer linear problem that is modified whenever additional transport information becomes available. We propose a modeling approach that is designed to determine fair and stable plans. Furthermore, we show that the model can easily be modified when transports need to satisfy additional requirements, e.g., during pandemics, exemplarily the Covid-19 pandemic. To show the applicability and efficiency of our modeling approach, we conduct a numerical study using historical data from the region of Middle Franconia. The results reveal and show that, by applying mathematical optimization-or, to be more precise by solving mixed-integer linear problem formulations-one can significantly decrease delays and have considerable potential for optimized patient transports.

关键词： OR in health services Vehicle routing Heuristics mixed-integer linear optimization Patient transport

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