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A guarantee rate optimization model for wastewater treatment system design under uncertainty

NAVAL RESEARCH LOGISTICS 2020年第6期67卷 420-437页

作者： Zhao, Kena Ng, Tsan Sheng Adam Liu, Xiao Natl Univ Singapore Dept Ind Syst Engn & Management Singapore 117576 Singapore Shanghai Jiao Tong Univ Dept Ind Engn & Management Shanghai Peoples R China

We consider a design problem for wastewater treatment systems that considers uncertainty in pollutant concentration levels at water sources. The goal is to optimize the selection of treatment technologies and pipeline connections, so that treated wastewater can achieve specified effluents discharge limits as well as possible. We propose a new two-stage model to optimize a set ofguarantee levels, that is, the maximum concentration level of source pollutants for which treated wastewater can be compliant with discharge limits. In the first stage, treatment technologies and pipeline connections are selected. In the second stage, when pollutant concentration levels are revealed, wastewater distribution and mixing are determined. A key attractiveness of the proposedguarantee rateoptimization model is that it can be simplified into a single-stage mixed-integer linear program. In our numerical experiments based on real-world pollutants data, theguarantee ratemodel demonstrates its advantages in terms of computational efficiency, scalability and solution quality, compared with the standard probability maximization model. Finally, the methodology proposed in this paper can also be applied to other two-stage problems under uncertainty with similar uncertainty characteristics.

关键词： data uncertainty mixed-integer linear program stochastic programming two-stage optimization wastewater treatment

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Power System Restoration With Renewable Participation

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2023年第2期14卷 1112-1121页

作者： Qiu, Feng Zhang, Yichen Yao, Rui Du, Pengwei Argonne Natl Lab Energy Syst Div Lemont 60439 IL USA Univ Texas Arlington Dept Elect Engn Arlington TX 76019 USA Google Mountain View CA 94043 USA Elect Regulat Council Texas ERCOT Austin TX 78744 USA

Power system restoration requires initial power sources to restart generators, energizing transmissions, and pick up critical loads. Sufficient initial power capacity is critical for restoration success and reducing outage duration. Due to the reliability requirement and high standby costs, black-start resources are scarce and expensive in areas where hydro power is not available. Variable renewable energy (VRE), whose fast-ramping capability and economical standby costs are suitable for black-start, is traditionally excluded from participation in system restoration because its uncertainty and variability could cause severe disturbance to the system that is already fragile during restoration. Recently, VRE is becoming a potential participant in system restoration as auxiliary black-start resources. This work will explore the potential benefits of renewable energy in restoration and potential ways for VRE to participate in system restoration. We propose two dispatch models for wind participation. The uncertainty of wind generation is handled by probabilistic constraints to guarantee a feasible restoration plan with a high probability. We perform computational experiments to demonstrate the effectiveness of proposed models and benefits of renewable participation in restoration with the two approaches.

关键词： Chance constraint data driven mixed-integer linear program wind dispatchability

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Online rescheduling of physicians in hospitals

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FLEXIBLE SERVICES AND MANUFACTURING JOURNAL 2018年第1-2期30卷 296-328页

作者： Gross, Christopher N. Fuegener, Andreas Brunner, Jens O. Univ Augsburg Fac Business & Econ Dept Hlth Care Operat Hlth Informat Management Univ Ctr Hlth SciKlinikum Augsburg UNIKA T Univ Str 16 D-86159 Augsburg Germany Univ Cologne Fac Management Econ & Social Sci Dept Supply Chain Management & Management Sci Albertus Magnus Pl D-50923 Cologne Germany

Scheduling physicians is a complex task. Legal requirements, different levels of qualification, and preferences for different working hours increase the difficulty of determining a solution that simultaneously fulfills all requirements. Unplanned absences, e.g., due to illness, additionally drive the complexity. In this study, we discuss an approach to deal with the following trade-off. Changes to the existing plan should be kept as small as possible. However, an updated plan should still meet the requirements regarding work regulation, qualifications needed, and physician preferences. We present a mixed-integer linear programming model to create updated duty and workstation rosters simultaneously following absences of scheduled personnel. To enable a comparison with previous sequential approaches, we separate our model into two models for the duty and workstation roster which generate plans sequentially. In a case study, we apply our integrated and sequential models to real-life data from a German university hospital with 133 physicians, 17 duties, and 20 workstations. We consider a planning horizon of 4 weeks and reschedule physicians on each day for three different cost settings for the trade-off between plan quality (in terms of preferences, fairness, coverage and training) and plan stability, resulting in a total of 4201 model runs. We demonstrate that our integrated model can achieve near-optimal results with reasonable computational efforts. In each of these runs our model reschedules physicians within 1-21 s. We run the sequential models on the same data, but for only one cost setting, resulting in 1401 runs. The results indicate that our integrated model manages to respect interdependencies between duty and workstation roster whereas the sequential models will always optimize for the plan which is created first. Overall, results indicate that our integrated model parameters allow managing the trade-off between plan quality goals and plan stability.

关键词： OR in health services Physician rescheduling Online planning mixed-integer linear program

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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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Network design and analysis for multi-enzyme biocatalysis

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BMC BIOINFORMATICS 2017年第1期18卷 1-12页

作者： Blass, Lisa Katharina Weyler, Christian Heinzle, Elmar Saarland Univ Biochem Engn Inst Campus A1-5 D-66123 Saarbrucken Germany

Background: As more and more biological reaction data become available, the full exploration of the enzymatic potential for the synthesis of valuable products opens up exciting new opportunities but is becoming increasingly complex. The manual design of multi-step biosynthesis routes involving enzymes from different organisms is very challenging. To harness the full enzymatic potential, we developed a computational tool for the directed design of biosynthetic production pathways for multi-step catalysis with in vitro enzyme cascades, cell hydrolysates and permeabilized cells. Results: We present a method which encompasses the reconstruction of a genome-scale pan-organism metabolic network, path-finding and the ranking of the resulting pathway candidates for proposing suitable synthesis pathways. The network is based on reaction and reaction pair data from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and the thermodynamics calculator eQuilibrator. The pan-organism network is especially useful for finding the most suitable pathway to a target metabolite from a thermodynamic or economic standpoint. However, our method can be used with any network reconstruction, e.g. for a specific organism. We implemented a path-finding algorithm based on a mixed-integer linear program (MILP) which takes into account both topology and stoichiometry of the underlying network. Unlike other methods we do not specify a single starting metabolite, but our algorithm searches for pathways starting from arbitrary start metabolites to a target product of interest. Using a set of biochemical ranking criteria including pathway length, thermodynamics and other biological characteristics such as number of heterologous enzymes or cofactor requirement, it is possible to obtain well-designed meaningful pathway alternatives. In addition, a thermodynamic profile, the overall reactant balance and potential side reactions as well as an SBML file for visualization are generated for each pathway alte

关键词： Network design Network analysis Pathway Biocatalysis Multi-enzyme catalysis mixed-integer linear program Path-finding Side reactions Thermodynamics Synthetic biology

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

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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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Cooperative Routing for an Air-Ground Vehicle Team-Exact Algorithm, Transformation Method, and Heuristics

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2020年第1期17卷 537-547页

作者： Manyam, Satyanarayana G. Sundar, Kaarthik Casbeer, David W. Infoscitex Corp Dayton OH 45431 USA Ctr Nonlinear Studies Los Alamos NM 87544 USA US Air Force Res Lab Control Sci Ctr Excellence Wright Patterson AFB OH 45433 USA

This paper considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and an unmanned aerial vehicle (UAV) that travel cooperatively and visit a set of targets while satisfying the communication constraints. The problem is formulated as a mixed-integer linear program, and a branch-and-cut algorithm is developed to solve the problem to optimality. Furthermore, a transformation method and a heuristic are also developed for the problem. The effectiveness of all the algorithms is corroborated through extensive computational experiments on several randomly generated instances. Note to Practitioners-This paper is motivated by an intelligence, surveillance, and reconnaissance mission involving a single unmanned aerial vehicle (UAV) and a ground vehicle, where the vehicles must coordinate their activity in the presence of communication constraints. The combination of a small UAV and a ground vehicle is an ideal platform for such missions, since small UAVs can fly at low altitudes and can avoid obstacles or threats that would be problematic for the ground vehicle alone. This paper addresses the coordinated routing problem involving these two vehicles and presents an algorithm to obtain an optimal solution for this problem, fast heuristics to obtain good feasible solutions, and also a transformation method to transform any instance of this cooperative vehicle routing problem to an instance of the one-in-a-set traveling salesman problem.

关键词： Branch-and-cut communication constraints cooperative vehicle routing heuristics mixed-integer linear program path planning unmanned aerial vehicles (UAVs)

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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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