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Constrained dynamic programming of mixed-integer linear problems by multi-parametric programming

COMPUTERS & CHEMICAL ENGINEERING 2014年第0期70卷 172-179页

作者： Rivotti, Pedro Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

This work addresses the topic of constrained dynamic programming for problems involving multi-stage mixed-integer linear formulations with a linear objective function. It is shown that such problems may be decomposed into a series of multi-parametric mixed-integer linear problems, of lower dimensionality, that are sequentially solved to obtain the globally optimal solution of the original problem. At each stage, the dynamic programming recursion is reformulated as a convex multi-parametric programming problem, therefore avoiding the need for global optimisation that usually arises in hard constrained problems. The proposed methodology is applied to a problem of mixed-integer linear nature that arises in the context of inventory scheduling. The example also highlights how the complexity of the original problem is reduced by using dynamic programming and multi-parametric programming. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Dynamic programming Multi-parametric programming mixed-integer linear programming

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Assessment of Energy Storage Operation in Vertically Integrated Utility and Electricity Market

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ENERGIES 2017年第5期10卷 683页

作者： Luburic, Zora Pandzic, Hrvoje Plavsic, Tomislav Univ Zagreb Fac Elect Engn & Comp Unska 3 Zagreb 10000 Croatia Croatian Transmiss Syst Operator Ltd Kupska 4 Zagreb 10000 Croatia

The aim of this paper is to compare the operational pattern of an energy storage system (ESS) in a vertically-integrated utility and in a deregulated market environment for different levels of wind integration. As the main feature of a vertically-integrated utility is a centralized decision-making process, all of the investment and operating decisions are made with a single goal of minimizing the overall system operating costs. As a result, an ESS in such an environment is operated in a way that is optimal for the overall system economics. On the other hand, the system operator in a deregulated market has less power over the system resources, and commitment and dispatch decisions are a result of the market clearing procedure. In this setting, the ESS owner aims at maximizing its profit, which might not be in line with minimizing overall system operating costs or maximizing social welfare. To compare the ESS operation in these two environments, we analyze the storage operation in two different settings. The first one is a standard unit commitment model with the addition of centrally-controlled storage. The second one is a bilevel model, where the upper level is a coordinated ESS profit maximization problem, while the lower level a simulated market clearing. The case study is performed on a standardized IEEE RTS-96 system. The results show a reduction in the generation dispatch cost, online generation capacity and wind curtailment for both models. Moreover, ESS significantly increases social welfare in the market-based environment.

关键词： energy storage unit commitment mixed-integer linear programming day-ahead electricity market

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Tracking Multiple Maneuvering Targets Using integer programming and Spline Interpolation

Tracking Multiple Maneuvering Targets Using Integer Programm...

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International Conference on Information Fusion

作者： Ketan Date Rakesh Nagi Department of Industrial and Enterprise Systems Engineering University of Illinois at Urbana-Champaign Urbana Illinois USA

In this paper, we propose an integer programming based model for tracking multiple maneuverable targets in a planar region. The objective function of this model uses both pairs and triplets of observations, which offer more accurate representation for constant velocity targets. Triplet scores in this model are calculated using a novel approach based on cubic spline interpolation, while the data association problem is solved using a specialized multi-dimensional assignment formulation. We show that the spline interpolation based scoring model provides more accurate reconstruction of trajectories, when compared to a naive model based on linear interpolation, on various randomly generated trajectories, at the expense of modest increase in computation time. The proposed multi-dimensional assignment formulation has nice structural properties and tight linear programming relaxation bound, which results in small computation times.

关键词： Multi-target tracking Maneuvering targets mixed-integer linear programming Data association Spline interpolation

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Operation of Flexible Multiproduct Modular Continuous Polymerization Plants

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MACROMOLECULAR REACTION ENGINEERING 2016年第4期10卷 435-457页

作者： Schoppmeyer, Christian Vermue, Henry Subbiah, Subanatarajan Kohlmann, Daniel Ferlin, Patrick Engell, Sebastian Materna GmbH D-44141 Dortmund Germany Tebodin Netherlands BV NL-9727 KB Groningen Netherlands ABB Corp Res Ctr D-68526 Ladenburg Germany BASF Personal Case & Nutr GmbH D-40589 Dusseldorf Germany Rhodia SOLVAY Grp CRTA F-93306 Aubervilliers France TU Dortmund Univ Proc Dynam & Operat Grp Dept Biochem & Chem Engn D-44227 Dortmund Germany

In this work, the operation of modular flexible continuous polymerization plants is investigated. For a benchmark problem (six products with an overall yearly demand of 20,000 t, two continuous production lines with modules that can be moved between the lines) that is defined by industrial speciality polymer producers, the optimal campaign planning problem is solved, minimizing the cost of cleaning and waste production. The results are compared to the production of the same portfolio of products in a batch plant. The results show that the changeovers between different products and production parameters lead to a loss of production capacity and additional costs. For long production campaigns (demand satisfaction on a monthly basis), these costs and losses are comparatively small, whereas for short demand satisfaction periods (one week) they are significant. On the other hand, longer demand satisfaction periods require a significant amount of product inventory and hence storage facilities.

关键词： F3 Factory mixed-integer linear programming modular continuous plants process operations scheduling

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Controlling Floods by Optimization Methods

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WATER RESOURCES MANAGEMENT 2016年第12期30卷 4053-4062页

作者： Soleimani-Alyar, Maryam Ghaffari-Hadigheh, Alireza Sadeghi, Fatemeh Azarbaijan Shahid Madani Univ Dept Appl Math Tabriz Iran Payame Noor Univ Illkhchi Branch Tehran Tehran Province Iran

Floods as natural phenomena exist and will continue to occur. No manmade project can stop a flood from happening, but there are several effective methods to reduce its risk, aftermath and consequences. This paper considers a novel formulation of the network interdiction problem with application on controlling floods. The aim of this work is to identify those arcs prone for flood, and implementing flood-control projects on these arcs, while required budget for deriving all these operations is bounded. the model is tested on a real-world case in Tabriz-Iran, and results are visualized.

关键词： Network interdiction Flood-control mixed-integer linear programming

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Multi-Objective Reconfiguration of Radial Distribution Systems Using Reliability Indices

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第2期31卷 1048-1062页

作者： Paterakis, Nikolaos G. Mazza, Andrea Santos, Sergio F. Erdinc, Ozan Chicco, Gianfranco Bakirtzis, Anastasios G. Catalao, Joao P. S. Univ Beira Interior Covilha Portugal Univ Lisbon IST INESC ID P-1699 Lisbon Portugal Politecn Torino Dept Energy Power & Energy Syst Unit I-10129 Turin Italy Yildiz Tech Univ Dept Elect Engn Istanbul Turkey Aristotle Univ Thessaloniki GR-54006 Thessaloniki Greece

This paper deals with the distribution network reconfiguration problem in a multi-objective scope, aiming to determine the optimal radial configuration by means of minimizing the active power losses and a set of commonly used reliability indices formulated with reference to the number of customers. The indices are developed in a way consistent with a mixed-integer linear programming (MILP) approach. A key contribution of the paper is the efficient implementation of the epsilon-constraint method using lexicographic optimization in order to solve the multi-objective optimization problem. After the Pareto efficient solution set is generated, the resulting configurations are evaluated using a backward/forward sweep load-flow algorithm to verify that the solutions obtained are both non-dominated and feasible. Since the epsilon-constraint method generates the Pareto front but does not incorporate decision maker (DM) preferences, a multi-attribute decision making procedure, namely, the technique for order preference by similarity to ideal solution (TOPSIS) method, is used in order to rank the obtained solutions according to the DM preferences, facilitating the final selection. The applicability of the proposed method is assessed on a classical test system and on a practical distribution system.

关键词： Distribution system reconfiguration epsilon-constraint method loss minimization mixed-integer linear programming multi-objective optimization reliability

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An exact approach for the prioritization process of industrial influents in wastewater systems

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2016年第1期18卷 339-346页

作者： Verdaguer, M. Suy, J. Villaret, M. Clara, N. Bofill, M. Poch, M. Univ Girona Inst Environm Lab Chem & Environm Engn LEQUIA Girona 17071 Spain Univ Girona Dept Comp Sci Appl Math & Stat Girona 17071 Spain

In wastewater systems, the efficiency of the treatment process is strongly related to the composition of its influent. When the treatment is overloaded (in volume and/or pollutants), its efficiency decreases and the effluent cannot attain the quality required by the receiving waters. This work considers the problem of mixing multiple wastewater streams, with multiple contaminants, into a single stream (the influent) on which various specifications are imposed. The problem has recently been solved by probabilistic methods that can achieve a nearly optimal solution. In this paper, an exact technique is proposed to find the optimal solution with a mixed-integer linear programming solver for the first time. The procedure is applied to a case study with different industrial effluents whose discharges will compose the influent to a treatment plant with constrained capacity (both in volume and pollutant loads). The optimal utility solution achieved describes the discharges that satisfy all constraints. This proposal constitutes an efficient way to manage treatment influents while reducing the computational time required by two orders of magnitude compared to probabilistic methods.

关键词： Wastewater management Industrial influents Wastewater systems mixed-integer linear programming Exact methods

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Rigorous approach to scheduling of sterile drug product manufacturing

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COMPUTERS & CHEMICAL ENGINEERING 2016年 94卷 221-234页

作者： Eberle, Lukas Capon-Garcia, Elisabet Sugiyama, Hirokazu Graser, Andreas Schmidt, Rainer Hungerbuhler, Konrad ETH Vladimir Prelog Weg 1 CH-8093 Zurich Switzerland F Hoffmann La Roche Ltd Grenzacherstr 124 CH-4070 Basel Switzerland Univ Tokyo Bunkyo Ku 7-3-1 Hongo Tokyo 1138656 Japan

Optimizing the scheduling of liquid drug product manufacturing is paramount for pharmaceutical companies in their increasingly competitive environment and requires the modelling of industry-specific constraints. Such constraints include: (i) changing sequence-dependent setup times;(ii) maintaining a sterile production environment (e.g., through sterile holding times);(iii) periods with limited or no plant activity (e.g., no workforce during weekends);and (iv) demand timing (i.e., delivery deadline and release date constraints). In this work, an immediate precedence model is formulated to optimize the scheduling of liquid drug product manufacturing, considering the industry-specific constraints. The primary objective is to minimize the production makespan. Four case studies comprising up to 38 batches from a real multi-product facility illustrate the performance of the rigorous optimization approach. The makespan could be reduced by up to 7.9% compared to expert schedules. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Mathematical optimization mixed-integer linear programming Scheduling Batch production Industrial application Campaigning

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Strengthened MILP Formulation for Certain Gas Turbine Unit Commitment Problems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第2期31卷 1440-1448页

作者： Pan, Kai Guan, Yongpei Watson, Jean-Paul Wang, Jianhui Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA Sandia Natl Labs Discrete Math & Complex Syst Dept POB 5800 Albuquerque NM 87185 USA Argonne Natl Lab Div Energy Syst Lemont IL 60439 USA

In this paper, we derive a strengthened MILP formulation for certain gas turbine unit commitment problems, in which the ramping rates are no smaller than the minimum generation amounts. This type of gas turbines can usually start-up faster and have a larger ramping rate, as compared to the traditional coalfired power plants. Recently, the number of this type of gas turbines increases significantly due to affordable gas prices and their scheduling flexibilities to accommodate intermittent renewable energy generation. In this study, several new families of strong valid inequalities are developed to help reduce the computational time to solve these types of problems. Meanwhile, the validity and facet-defining proofs are provided for certain inequalities. Finally, numerical experiments on a modified IEEE 118-bus system and the power system data based on recent studies verify the effectiveness of applying our formulation to model and solve this type of gas turbine unit commitment problems, including reducing the computational time to obtain an optimal solution or obtaining a much smaller optimality gap, as compared to the default CPLEX, when the time limit is reached with no optimal solutions obtained.

关键词： Gas turbines mixed-integer linear programming unit commitment

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Exploiting symmetry in unit commitment solutions for a large-scale electricity market

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ELECTRIC POWER SYSTEMS RESEARCH 2016年第0期140卷 363-377页

作者： Alemany, Juan Komarnicki, Przemyslaw Lin, Jeremy Magnago, Fernando Fraunhofer Inst Factory Operat & Automat Magdeburg Germany Univ Nacl Rio Cuarto GASEP Cordoba Argentina Fraunhofer Inst Factory Operat & Automat Magdeburg Germany PJM Interconnect Audubon PA USA Nexant Inc Chandler AZ USA

Symmetry is a natural phenomenon that appears when an electric system has identical generating units. As a core function in any electricity market, the unit commitment algorithm solves a very large-scale mixed-integer based optimization problem. In this work, the symmetric properties that exist in a competitive electricity market are exploited in improving the performance of its unit commitment solutions. A static symmetry removal strategy based on hierarchical constraints is proposed. They establish priorities for the unit status variables. Extensive numerical examples are illustrated using a real-world, large-scale electricity market. Two available commercial solvers are used to compare the performance of each solver with and without our proposed method. Results show that there are opportunities to improve the unit commitment solutions if the symmetric properties of the market system are properly exploited. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Large-scale electricity market mixed-integer linear programming Symmetry Unit commitment Units with identical costs

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