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Global mixed-integer dynamic optimization

AICHE JOURNAL 2005年第8期51卷 2235-2253页

作者： Chachuat, B Singer, AB Barton, PI MIT Dept Chem Engn Proc Syst Engn Lab Cambridge MA 02139 USA

Recent advances in process synthesis, design, operations, and control have created an increasing demand for efficient numerical algorithms for optimizing a dynamic system coupled with discrete decisions;these problems are termed mixed-integer dynamic optimization (MIDO). In this communication, we develop a decomposition approach for a quite general class of MIDO problems that is capable of guaranteeing finding a global solution despite the nonconvexities inherent in the dynamic optimization subproblems. Two distinct algorithms are considered. On finite termination, the first algorithm guarantees finding a global solution of the MIDO within nonzero tolerance;the second algorithm finds rigorous bounds bracketing the global solution value, with a substantial reduction in computational expense relative to the first algorithm. A case study is presented in connection with the optimal design and operation of a batch process consisting of a series reaction followed by a separation with no intermediate storage. The developed algorithms demonstrate efficiency and applicability in solving this problem. Several heuristics are tested to enhance convergence of the algorithms;in particular, the use of bounds tightening techniques and the addition of cuts resulting from a screening model of the batch process are considered. (c) 2005 American Institute of Chemical Engineers

关键词： mixed-integer dynamic optimization nonconvex problems global optimization decomposition algorithms outer-approximation batch process design

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An adaptive wavelet method for solving mixed-integer dynamic optimization problems with discontinuous controls and application to alkali-surfactant-polymer flooding

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ENGINEERING optimization 2019年第6期51卷 1028-1048页

作者： Ge, Yulei Li, Shurong Shi, Yuhuan Han, Lu China Univ Petr East China Coll Informat & Control Engn Qingdao Shandong Peoples R China Beijing Univ Posts & Telecommun Automat Sch Beijing Peoples R China CNPC EastChina Design Inst Co Ltd Qingdao Shandong Peoples R China

This article presents an adaptive rationalized Haar function approximation method to solve dynamic optimization with mixed-integer and discontinuous controls. Three measures are taken to deal with the discontinuity. First, the problem is converted into a multi-stage optimization problem by non-uniform control vector parameterization. Secondly, an adaptive strategy is proposed to regulate the interval division and the order of Haar function vectors. Thirdly, a structure detection method is presented to refine the subintervals, in which adjacent arcs with the same input type are merged into one to modify redundant subintervals. During this approximation solution, the mixed-integer restriction is realized by the integer truncation strategy. Combined with the Hamiltonian function, a validation principle is shown to verify the optimality of the solution. Finally, the proposed method is applied to solve the enhanced oil recovery for alkali-surfactant-polymer flooding. The effectiveness of the method is illustrated through simulation.

关键词： mixed-integer dynamic optimization discontinuous control adaptive rationalized Harr function approximation structure detection with optimality validation ASP flooding

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Optimal Scheduling of Active Distribution Networks With Limited Switching Operations Using mixed-integer dynamic optimization

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IEEE TRANSACTIONS ON SMART GRID 2019年第4期10卷 4221-4234页

作者： Deng, Zhuoming Liu, Mingbo Chen, Honglin Lu, Wentian Dong, Ping South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Guangdong Peoples R China

The optimal scheduling of active distribution networks (ADNs) significantly enhances voltage security and reduces costs, particularly as the numbers of distributed generation sources and energy storage devices increase. Therefore, this paper proposes a mixed-integer dynamic optimization (MIDO) model for the optimal scheduling of ADNs. This model incorporates loads and distributed generation outputs with continuous trajectories and aims to provide optimal continuous-trajectory schemes for ADNs. The optimization is conducted with the objective of minimizing the daily costs of electricity purchased from distribution substations. However, in practice, discrete control devices are required to adopt a limited number of switching operations, which increase the computational complexity of the MIDO model. Hence, a reduced convex relaxation method is utilized to achieve reduced convex transformation and tight relaxation of the MIDO model with respect to integer variables. This converts the MIDO model into a continuous dynamic optimization model, which is then further approximated as a nonlinear programming model using the Radau collocation method. Meanwhile, the absolute-value constraints limiting the number of switching operations are eliminated by an equivalent conversion to a series of linear inequalities. Numerical simulations on IEEE 33-bus, PG&E 69-bus, and real-world 110-bus ADNs demonstrate the effectiveness and efficiency of the proposed methodology.

关键词： Active distribution networks continuous trajectory convex relaxation method discrete control devices mixed-integer dynamic optimization optimal scheduling

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dynamic optimization of the PyNP/PNP Phosphorolytic Enzymatic Process Using MOSAICmodeling

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CHEMIE INGENIEUR TECHNIK 2017年第11期89卷 1523-1533页

作者： Wilms, Terrance Rischawy, Daniel Federico Barz, Tilman Esche, Erik Repke, Jens-Uwe Wagner, Anke Neubauer, Peter Bournazou, Mariano Nicolas Cruz TU Berlin Bioproc Engn Ackerstr 76 D-13355 Berlin Germany AIT Austrian Inst Technol GmbH Donau City Str 1 A-1220 Vienna Austria TU Berlin Proc Dynam & Operat Grp Str 17 Juni 135 D-10623 Berlin Germany BioNukleo GmbH Ackerstr 76 D-13355 Berlin Germany

Pyrimidine and purine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage and formation of the glycosidic bond of purine and pyrimidine nucleosides, respectively, and are thus, key catalysts for the synthesis of new compounds. The selection of the best combination of enzyme and reaction conditions is not trivial, as each of the two enzymes can perform the reaction in two directions and thus, also competes with the other one for the reaction intermediates. A generic approach to the solution of this problem based on the formulation of a mixed integer dynamic optimization program using MOSAICmodeling is presented.

关键词： Global optimality mixed-integer dynamic optimization Modified nucleosides Orthogonal collocation Process optimization Transglycosylation

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dynamic ramping for demand response of processes and energy systems based on exact linearization

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JOURNAL OF PROCESS CONTROL 2022年第0期118卷 218-230页

作者： Baader, Florian Joseph Althaus, Philipp Bardow, Andre Dahmen, Manuel Forschungszentrum Julich Inst Energy & Climate Res Energy Syst Engn IEK 10 D-52425 Julich Germany Rhein Westfal TH Aachen D-52062 Aachen Germany Swiss Fed Inst Technol Energy & Proc Syst Engn CH-8092 Zurich Switzerland

The increasing share of volatile renewable electricity production motivates demand response. Substan-tial potential for demand response is offered by flexible processes and their local multi-energy supply systems. Simultaneous optimization of their schedules can exploit the demand response potential, but leads to numerically challenging problems for nonlinear dynamic processes. In this paper, we propose to capture process dynamics using dynamic ramping constraints. In contrast to traditional static ramping constraints, dynamic ramping constraints are a function of the process state and can capture high-order dynamics. We derive dynamic ramping constraints rigorously for the case of single-input single-output processes that are exactly input-state linearizable. The resulting scheduling problem can be efficiently solved as a mixed-integer linear program. In a case study, we study two flexible reactors and a multi-energy system. The proper representation of process dynamics by dynamic ramping allows for faster transitions compared to static ramping constraints and thus higher economic benefits of demand response. The proposed dynamic ramping approach is sufficiently fast for application in online optimization.(c) 2022 Elsevier Ltd. All rights reserved.

关键词： Demand response Exact linearization Scheduling optimization mixed-integer dynamic optimization

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Dimensionality reduction applied to the simultaneous optimization of the economic and life cycle environmental performance of supply chains

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2015年 159卷 223-232页

作者： Kostin, Andrei Guillen-Gosalbez, Gonzalo Jimenez, Laureano Univ Rovira & Virgili Dept Engn Quim Escola Tecn Super Engn Quim E-43007 Tarragona Spain Univ Manchester Sch Chem Engn & Analyt Sci Ctr Proc Integrat Manchester M13 9PL Lancs England

The design and planning of more sustainable supply chains should take into account several impacts for a proper assessment of the environmental performance of the logistic activities. Unfortunately, minimizing several environmental objectives simultaneously leads to hard optimization problems. This paper presents a rigorous computational framework for solving complex multi-objective optimization (MOO) problems encountered in the optimization of logistic tasks under economic and environmental indicators. The key ingredient of our method is the use of an objective reduction algorithm that allows identifying redundant objectives that can be omitted while still preserving the problem structure to the extent possible. The advantages of our method are illustrated by means of two case studies that address the multi-objective optimization of supply chains that produce bioethanol and hydrogen for vehicle use. (C) 2014 Published by Elsevier B.V.

关键词： Hybrid simulation-optimization mixed-integer dynamic optimization Biotechnological processes L-lysine

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Inferential Control of Reactive Destillation Columns - An Algorithmic Approach

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CHEMICAL ENGINEERING & TECHNOLOGY 2011年第8期34卷 1235-1244页

作者： Paramasivan, Ganesh Kienle, Achim Max Planck Inst Dynam Komplexer Tech Syst D-39106 Magdeburg Germany Otto von Guericke Univ Lehrstuhl Automatisierungstech Modellbildung Magdeburg Germany

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed-integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed-integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.

关键词： Control structure selection Decentralized control system mixed-integer dynamic optimization Reactive distillation control

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dynamic predictive scheduling of operational strategies for continuous processes using mixed-logic dynamic optimization

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COMPUTERS & CHEMICAL ENGINEERING 2007年第5-6期31卷 574-587页

作者： Busch, Jan Oldenburg, Jan Santos, Marcella Cruse, Andreas Marquardt, Wolfgang Univ Aachen Rhein Westfal TH Aachen Lehrstuhl Prozesstech D-52064 Aachen Germany

Industrial processes are usually operated in a highly dynamic environment, e.g. with time-varying market prizes, customer demand, technological development or up- and downstream processes. Due to these disturbances, the operational strategies comprising objectives and constraints are regularly adjusted to reflect a change in the environment in order to achieve or maintain optimal process performance. The related operational objectives need not only be of an economical nature, but can also include flexibility, risk or ecological objectives. In this paper, a novel methodology is presented for the modeling and dynamic predictive scheduling of operational strategies for continuous processes. Optimal control actions are computed on a moving horizon employing discrete-continuous modeling and mixed-logic dynamic optimization as introduced by Oldenburg et al. (2003). The approach is successfully demonstrated considering the operation of a wastewater treatment plant. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： dynamic predictive scheduling plant scheduling mixed-logic dynamic optimization mixed-integer dynamic optimization wastewater treatment

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dynamic optimization for the planning of a waste management system involving multiple cities

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JOURNAL OF CLEANER PRODUCTION 2017年 165卷 190-203页

作者： Ezequiel Santibanez-Aguilar, Jose Flores-Tlacuahuac, Antonio Rivera-Toledo, Martin Maria Ponce-Ortega, Jose Tecnol Monterrey Escuela Ingn & Ciencias Campus Monterrey Monterrey 64849 NL Mexico Univ Iberoamer Engn & Chem Sci Dept Mexico City 01210 DF Mexico Univ Michoacana Chem Engn Dept Morelia 58060 Michoacan Mexico

Consumption habits and population growth have drastically increased the waste production around the world. However, several developing countries do not have an adequate waste management system. This way, a mathematical model for the optimal planning of a waste management system could be a useful tool to make decisions about the design of a waste processing system to promote sustainable public polices and cooperation among multiple cities. Therefore, this work proposes a mathematical formulation for the optimal planning of a waste management system considering waste from different neighboring cities divided in several sites, as well as the dependence over time for the variables and parameters through a set of differential equations for properly capturing the associated dynamic behavior. Results show that given the data of potential locations for sites, landfills, processing plants and consumers, as well as prices of useful products, availability of waste, upper and lower limits, unitary costs for the different activities carried out in the waste management system and initial values for inventory and order levels, it is possible to obtain the optimal selection and location of the entities of the waste management system as well as the plant capacities and material flows to be transported, processed, stored and sold. The proposed mathematical formulation is general and it can be applied to any waste type, involving different landfills, sites, cities, processing routes and processing plants. Although the CPU time increases for considering the dynamic behavior, it is proved that the associated costs decrease significantly. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Waste management system mixed-integer dynamic optimization Strategic planning Municipal solid waste

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State-of-the-art and progress in the optimization-based simultaneous design and control for chemical processes

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AICHE JOURNAL 2012年第6期58卷 1640-1659页

作者： Yuan, Zhihong Chen, Bingzhen Sin, Gurkan Gani, Rafiqul Tsinghua Univ Dept Chem Engn Inst Proc Syst Engn Beijing 100084 Peoples R China Tech Univ Denmark Dept Chem & Biochem Engn CAPEC DK-2800 Lyngby Denmark

Significant progress in the area of simultaneous design and control for chemical processes has been achieved and various methodologies have been put forward to address this issue over the last several decades. These methods can be classified in two categories (1) controllability indicator-based frameworks that are capable of screening alternative designs, and (2) optimization-based frameworks that integrate the process design and control system design. The major objective is to give an up-to-date review of the state-of-the-art and progress in the challenging area of optimization-based simultaneous design and control. First, motivations and significances of simultaneous design and control are illustrated. Second, a general classification of existing methodologies of optimization-based simultaneous design and control is outlined. Subsequently, the mathematical formulations and relevant theoretical solution algorithms, their merits, strengths and shortcomings are highlighted. Last, based on the recent advances in this field, challenges and future research directions are discussed briefly. An attempt is made with the help of this review article to stimulate further research and disseminate the simultaneous design methods to challenging problem areas. In particular, the application of optimization-based simultaneous design and control methods to large-scale systems with highly inherent nonlinear dynamics often the case in industrial chemical processes remains a challenging task and yet to be solved. (C) 2012 American Institute of Chemical Engineers AIChE J, 58: 16401659, 2012

关键词： simultaneous design and control controllability index mixed-integer dynamic optimization robust theory black-box optimization

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