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Distributed Optimization and Coordination Algorithms for Dynamic Traffic Metering in Urban Street Networks

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2019年第5期20卷 1930-1941页

作者： Mohebifard, Rasool Hajbabaie, Ali Washington State Univ Dept Civil & Environm Engn Pullman WA 99164 USA

Previous research has shown that proper metering of entry traffic to urban street networks, similar to metering traffic on on-ramps in freeway facilities, reduces traffic congestion, especially in oversaturated flow conditions. Building on the previous research, this paper presents a real-time and scalable methodology for finding near-optimal metering rates dynamically in urban street networks. The problem is formulated into a mixed-integer linear program (MILP) based on the cell transmission model. We propose a distributed optimization scheme that decomposes the network level MILP into several link-level MILPs to reduce the complexity of the problem. We convert the link-level MILPs to linear programs to reduce the computational complexity further. Moreover, we create distributed coordination between the link-level linear programs to push the solutions toward optimality. The distributed optimization and coordination solution algorithm is incorporated into a rolling horizon technique to account for the time-varying demand and capacity and to reduce the computational complexity further. We applied the proposed solution technique to a number of case studies and observed that it was scalable and real time and found solutions that were at most 2.2% different from the optimal solution of the problem. Like the previous studies, we found significant improvements in network operations as a result of traffic metering.

关键词： Dynamic traffic metering perimeter control distributed optimization distributed coordination model predictive control mixed-integer linear program

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Coordinated scheme for expansion planning of distribution networks: a bilevel game approach

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第14期14卷 2839-2846页

作者： Akbari, Tohid Moghaddam, Saeed Zolfaghari Pooyesh Inst Higher Educ Fac Elect Engn Qom Iran Urmia Univ Technol Fac Elect Engn Orumiyeh Iran

The expansion planning of a distribution network (DN) is studied separately and independently from the behaviour of the transmission network (TN) as well as other DNs. However, DNs are being converted from passive to active mode by extensively integrating distributed generations (DGs) into them. Hence, an uncoordinated expansion planning may lead to redundant investment cost and suboptimal solutions. Accordingly, the main motivation of this study is to propose a coordinated expansion scheme among distribution companies (DISCOs). In doing so, a novel bilevel game-based framework is presented to coordinate the decisions of DISCOs for distribution expansion planning problem. Primal-dual formulation is used to convert the bilevel problem into a single level one resulting in a discretely-constrained generalised Nash equilibrium problem. The generalised Nash equilibrium problem is further formulated as a mixed-integer linear program using Karush-Kuhn-Tucker conditions. The methodology proposed is applied to the IEEE 24-bus RTS with several 24-bus DNs. The results show that ignoring the action of other DISCOs may lead to the over- or under-investment in DG sector which consequently decreases the DISCOs' profit. The results also show that congestion in transmission lines can considerably affect the strategic decisions of DISCOs on DG investment.

关键词： game theory power markets linear programming integer programming power distribution planning power distribution economics bilevel game approach transmission network distributed generations uncoordinated expansion planning redundant investment cost coordinated expansion scheme distribution companies distribution expansion planning Nash equilibrium DISCO profit bilevel game-based framework distribution network planning mixed-integer linear program Karush-Kuhn-Tucker conditions IEEE 24-bus RTS transmission lines

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Price-Taker Offering Strategy in Electricity Pay-as-Bid Markets

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IEEE TRANSACTIONS ON POWER SYSTEMS 2018年第2期33卷 2175-2183页

作者： Mazzi, Nicolo Kazempour, Jalal Pinson, Pierre Univ Padua Dept Ind Engn I-35122 Padua Italy Tech Univ Denmark Dept Elect Engn DK-2800 Lyngby Denmark

The recent increase in the deployment of renewable energy sources may affect the offering strategy of conventional producers, mainly in the balancing market. The topics of optimal offering strategy and self-scheduling of thermal units have been extensively addressed in the literature. The feasible operating region of such units can be modeled using a mixed-integer linear programming approach, and the trading problem as a linear programming problem. However, the existing models mostly assume a uniform pricing scheme in all market stages, while several European balancing markets (e.g., in Germany and Italy) are settled under a pay-as-bid pricing scheme. The existing tools for solving the trading problem in pay-as-bid electricity markets rely on nonlinear optimization models, which, combined with the unit commitment constraints, result in a mixed-integer nonlinear programming problem. In contrast, we provide a linear formulation for that trading problem. Then, we extend the proposed approach by formulating a two-stage stochastic problem for optimal offering in a two-settlement electricity market with a pay-as-bid pricing scheme at the balancing stage. The resulting model is mixed-integer and linear. The proposed model is tested on a realistic case study against a sequential offering approach, showing the capability of increasing profits in expectation.

关键词： mixed-integer linear program offering strategy pay-as-bid stochastic programming thermal unit

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How tight is the corner relaxation?

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DISCRETE OPTIMIZATION 2008年第2期5卷 262-269页

作者： Fischetti, Matteo Monaci, Michele Univ Padua DEI I-35131 Padua Italy

Given a mixed-integer linear programming (MILP) model and an optimal basis of the associated linear programming relaxation, the Gomory's corner relaxation is obtained by dropping nonnegativity constraints on the basic variables. Although this relaxation received a considerable attention in the literature in the last 40 years, the crucial issue of evaluating the practical quality of the corner-relaxation bound was not addressed so far. In the present paper we report, for the first time, the optimal value of the corner relaxation (in two possible variants) for a very large set of MILP instances from the literature, thus providing a missing yet very important piece of information about the practical relevance of this relaxation. The outcome of our experiments is that the corner relaxation often gives a tight approximation of the integer hull, the main so for MILPs with general-integer variables-the approximation tends to be less satisfactory when a consistent number of binary variables exists. (c) 2007 Elsevier B.V. All rights reserved.

关键词： mixed-integer linear program Gomory's corner polyhedron computational analysis

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Machine scheduling in underground mining: an application in the potash industry

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OR SPECTRUM 2016年第2期38卷 365-403页

作者： Schulze, Marco Rieck, Julia Seifi, Cinna Zimmermann, Jurgen Tech Univ Clausthal Inst Management & Econ Operat Res Grp D-38678 Clausthal Zellerfeld Germany

In this paper, a scheduling problem that occurs in potash mining is introduced, where a block excavation sequence has to be found taking into account a limited number of underground machines as well as safety-related restrictions. The aim is to minimize the maximum completion time of excavations, i.e., the makespan. The resulting problem can be transformed into a hybrid flow shop scheduling problem with reentry, unrelated machines, and job-precedences. A mixed-integer linear model is presented and small-scale instances are solved with CPLEX. In order to tackle medium- and large-scale instances heuristically, a basic and an advanced multi-start algorithm are developed, based on a specific priority rule-based construction procedure. In addition, a modified version of the Giffler and Thompson procedure is applied. Computational experiments are conducted on problem instances derived from real-world data in order to evaluate the performances of the proposed solution procedures.

关键词： Underground mining Hybrid flow shop Reentrant flows mixed-integer linear program Priority rule-based procedure Multi-start

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Network design for a decarbonised supply chain considering cap-and-trade policy of carbon emissions

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ANNALS OF OPERATIONS RESEARCH 2023年 1-35页

作者： Majumdar, Abhijit Singh, Surya Prakash Jessica, Jessica Agarwal, Aashi Indian Inst Technol Dept Text & Fibre Engn New Delhi 110016 Delhi India Indian Inst Technol Dept Management Studies New Delhi 110016 Delhi India

Decarbonisation of the supply chain necessitates the control of carbon emissions along with the minimisation of cost. This is quite challenging in a multi-echelon supply chain involving multiple suppliers, multiple products, multiple time periods and multimodal transportation. This research deals with the design of a decarbonised supply chain network, under a dynamic environment, considering carbon emissions at various stages of the supply chain. A mixed-integer linear program (MILP) has been developed for a four-echelon supply chain. The problem is solved by using two approaches. The integrated approach, which considers the entire supply chain network as a single entity, yields better results in terms of profitability and more so, when the selling price is lower. Scenario analysis reveals that as the carbon cap reduces, the gross profit shows concomitant reduction and when the former goes below a threshold value, carbon procurement becomes necessary lowering the gross profit further. As the carbon price per unit increases, the gross profit initially decreases and then stabilises. This study contributes by developing an integrated dynamic supply chain network model incorporating carbon emissions at different stages.

关键词： Carbon emissions Decarbonisation mixed-integer linear program Network design Supply chain

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Optimal design of a distributed energy resource system that economically reduces carbon emissions

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APPLIED ENERGY 2018年 232卷 119-138页

作者： Flores, Robert J. Brouwer, Jacob Univ Calif Irvine Adv Power & Energy Program Irvine CA 92617 USA

Distributed energy resources (DER) are commonly associated with reduced CO2e emissions. The decision to design such a system that reduces emissions typically results in increased costs. In order to economically select and operate a DER system that also reduces CO2e emissions, a mixed integer linear program for sizing and dispatching a DER system was developed and used with real data to determine the optimal DER design that reduces emissions at the lowest cost. The optimization program includes a novel formulation of constraints that govern utility natural gas, generator operation, and interaction with fleet vehicles. The results show that the least expensive way of reducing CO2e is through the use of renewable gas in a conventional combined heat and power engine (i.e., a gas turbine), resulting in a cost to reduce emissions of between $120 and $150 per CO2e tonne. Reducing emissions further requires the adoption of higher efficiency generators, or renewable generators, increasing cost of CO2e by up to $475 per tonne. Allowing for electrical export and the offset of grid operations results in the purchase of less energy storage, reducing the cost of CO2e to $190 per tonne under retail electricity rates, or $230 per tonne when the DER operator sends excess renewables back to the utility grid for free. Finally optimization results for this particular case indicate that changes to the transportation system occur last since the marginal costs of changing fleet vehicles is highest versus the CO2e reduction benefit.

关键词： mixed-integer linear program Distributed energy optimization Greenhouse gas reduction Solar export rates

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Designing drone delivery networks for vaccine supply chain: a case study of Niger

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IISE TRANSACTIONS ON HEALTHCARE SYSTEMS ENGINEERING 2024年第3期14卷 193-213页

作者： Eksioglu, Sandra D. Proano, Ruben A. Kolter, Maximilian Nurre Pinkley, Sarah Univ Arkansas Dept Ind Engn Fayetteville AR 72701 USA Rochester Inst Technol Dept Ind & Syst Engn Rochester NY USA

This research aims to evaluate the use of drones to deliver pediatric vaccines in remote areas of low-income and low-middle-income countries. Delivering vaccines in these regions is challenging because of the inadequate road networks and long transportation distances that make it difficult to maintain the cold chain's integrity during delivery. We propose a mixed-integer linear program to determine the location of drone hubs to facilitate vaccine delivery. The model considers the operational attributes of drones, vaccine wastage in the supply chain, cold storage, and transportation capacities. We develop a case study using data from Niger to determine the impact of drone deliveries in improving vaccine availability. Based on our numerical analysis, regional centers should be considered potential locations for drone hubs. We demonstrate that outreach sessions supported by drone deliveries of vaccines can improve vaccine availability. These improvements depend on the available budget to build drone hubs and purchase drones, available cold storage capacity, and the population density in the study region.

关键词： Drone delivery network vaccine supply chain in low-income and low-middle-income countries mixed-integer linear program Niger's vaccine supply chain

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Approximate Closed-Loop Minimax Model Predictive Operation Control of Microgrids

Approximate Closed-Loop Minimax Model Predictive Operation C...

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European Control Conference (ECC)

作者： Hans, Christian A. Nenchev, Vladislav Raisch, Joerg Reincke-Collon, Carsten Tech Univ Berlin Berlin Germany Max Planck Inst Dynami Komplexer Tech Syst Magdeburg Germany Younicos AG Berlin Germany

ISBN: (纸本)9783952426937

We address an optimal control problem for a microgrid in islanded operation with bounded uncertain load and renewable infeed. While model predictive control (MPC) with worst-case cost evaluation is often employed to obtain robust optimal control laws in the presence of bounded disturbances, it suffers from an inherent conservativeness. To counteract this phenomenon, we propose an approximate closed-loop minimax MPC scheme, where the renewable energy sources output can be curtailed. The MPC is formulated as a mixed-integer linear program, solved online and applied in a receding horizon fashion. In the case study, the approximate closed-loop approach yields a better prediction accuracy and performance than the corresponding open-loop scheme.

关键词： closed loop systems distributed power generation integer programming linear programming minimax techniques optimal control power system control predictive control renewable energy sources robust control approximate closed-loop minimax model predictive operation control islanded operation microgrids mixed-integer linear program robust optimal control laws Generators Load modeling Optimal control Optimization Robustness Thermal loading Yttrium

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An Application of Distributed Optimisation to Energy Communities in Italy 116

An Application of Distributed Optimisation to Energy Communi...

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2024 International Annual Conference of the Italian Association of Electrotechnics

作者： Saguatti, Lorenzo Bovera, Filippo Gabba, Marco Martoriello, Gaia Zatti, Matteo LEAP scarl Piacenza Italy Politecn Milan Dept Energy Milan Italy

ISBN: (纸本)9798350378498;9788887237627

The development of energy communities would benefit from the use of optimisation tools to improve their economic performance. However, collecting members' data, forecasts and contracts in a single centralised optimisation problem endangers their privacy and autonomy. To tackle this issue, it is possible to leverage distributed optimisation techniques. The paper first presents a deterministic scheduling optimisation model for an energy community under the Italian regulatory framework;then, the alternating direction method of multipliers (ADMM) is used to separate it in one distinct optimisation problem for each member, and a master problem that provides coordination. Since the original centralised problem is nonconvex, ADMM can achieve only local optima;thus, global optimal solutions of the centralised model are used as a benchmark for ADMM performance. Results show that ADMM, with a constant penalty parameter, converges only when the parameter is set sufficiently large, and reaches local solutions far from the global optimum. Conversely, starting with a small penalty parameter and increasing it iteratively ensures convergence for any starting value and yields solutions closer to the global optimum.

关键词： Energy communities Shared energy mixed-integer linear program Distributed optimisation Alternating Direction Method of Multipliers

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