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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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Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2024年 186卷

作者： Wang, Wenlong Wang, Yujia Tian, Yuhe Wu, Zhe Natl Univ Singapore Dept Chem & Biomol Engn Singapore 117585 Singapore West Virginia Univ Dept Chem & Biomed Engn Morgantown WV 26506 USA

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi- parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state-space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor- first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

关键词： Machine learning Explicit model predictive control multi-parametric programming Nonlinear processes Chemical process control

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Online probabilistic energy flow for hydrogen-power-heat system based on multi-parametric programming

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APPLIED ENERGY 2024年 372卷

作者： Zhou, Yijia Peng, Hongyi Yan, Mingyu Huazhong Univ Sci & Technol State Key Lab Adv Electromagnet Technol Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 430074 Peoples R China

The introduction of renewable energy introduces operational challenges for the modern multi-energy system. To accommodate the uncertainty, this paper proposes an online probabilistic energy flow for the hydrogen-powerheat system. First, a hydrogen-power-heat system model is established to depict the interdependency of multiple energy, in which hydrogen fuel cells interconnect hydrogen, power, and heat systems by converting the hydrogen into power and heat. The probabilistic energy flow is further built considering the uncertain wind power. An efficient algorithm based on multi-parametric programming (MPP) is proposed to enhance the computational performance of probabilistic multi-energy flow for online applications. The parameter region of the probabilistic multi-energy flow in MPP model is divided into multiple critical regions (CR). Each CR reveals a unique mapping relationship from uncertain wind power to system optimal solutions. Probabilistic energy flow could be quickly calculated based on mapping relationship rather than solving optimization problem. Therefore, the proposed method could be applied in online energy flow calculation. Numerical results tested on a 6-6-8 system and an improved 40-118 - 13 system validate the accuracy and efficiency of the proposed method in probabilistic energy flow calculation.

关键词： multi-parametric programming Hydrogen-power-heat system Probabilistic energy flow Critical region

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Process Design and Control Optimization: A Simultaneous Approach by multi-parametric programming

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AICHE JOURNAL 2017年第11期63卷 4827-4846页

作者： Diangelakis, Nikolaos A. Burnak, Baris Katz, Justin Pistikopoulos, Efstratios N. Imperial Coll London Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77845 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77845 USA

We present a framework for the application of design and control optimization via multi-parametric programming through four case studies. We develop design dependent multi-parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115-138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. (c) 2017 American Institute of Chemical Engineers

关键词： multi-parametric programming design and control integration model predictive control

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On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory

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JOURNAL OF GLOBAL OPTIMIZATION 2017年第3期69卷 587-606页

作者： Oberdieck, Richard Diangelakis, Nikolaos A. Avraamidou, Styliani Pistikopoulos, Efstratios N. Imperial Coll London Ctr Proc Syst Engn Dept Chem Engn London England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA

In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-parametric quadratic programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the parametric solution of the dual of a convex problem.

关键词： Unbounded problems Binary parameters multi-parametric programming Mixed-integer bilevel programming

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An Improved multi-parametric programming Algorithm for Flux Balance Analysis of Metabolic Networks

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2018年第2期178卷 502-537页

作者： Akbari, Amir Barton, Paul I. MIT Proc Syst Engn Lab 77 Massachusetts Ave Cambridge MA 02139 USA

Flux balance analysis has proven an effective tool for analyzing metabolic networks. In flux balance analysis, reaction rates and optimal pathways are ascertained by solving a linear program, in which the growth rate is maximized subject to mass-balance constraints. A variety of cell functions in response to environmental stimuli can be quantified using flux balance analysis by parameterizing the linear program with respect to extracellular conditions. However, for most large, genome-scale metabolic networks of practical interest, the resulting parametric problem has multiple and highly degenerate optimal solutions, which are computationally challenging to handle. An improved multi-parametric programming algorithm based on active-set methods is introduced in this paper to overcome these computational difficulties. Degeneracy and multiplicity are handled, respectively, by introducing generalized inverses and auxiliary objective functions into the formulation of the optimality conditions. These improvements are especially effective for metabolic networks because their stoichiometry matrices are generally sparse;thus, fast and efficient algorithms from sparse linear algebra can be leveraged to compute generalized inverses and null-space bases. We illustrate the application of our algorithm to flux balance analysis of metabolic networks by studying a reduced metabolic model of Corynebacterium glutamicum and a genome-scale model of Escherichia coli. We then demonstrate how the critical regions resulting from these studies can be associated with optimal metabolic modes and discuss the physical relevance of optimal pathways arising from various auxiliary objective functions. Achieving more than fivefold improvement in computational speed over existing multi-parametric programming tools, the proposed algorithm proves promising in handling genome-scale metabolic models.

关键词： multi-parametric programming Flux balance analysis Metabolic networks

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multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach

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COMPUTERS & CHEMICAL ENGINEERING 2016年 85卷 36-39页

作者： Oberdieck, Richard Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX USA

In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： multi-objective optimization multi-parametric programming Explicit Pareto front calculation

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Improved Unit Commitment with Accurate Dynamic Scenarios Clustering Based on multi-parametric programming and Benders Decomposition

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Energy Engineering 2024年第6期121卷 1557-1576页

作者： Zhang Zhi Haiyu Huang Wei Xiong Yijia Zhou Mingyu Yan Shaolian Xia Baofeng Jiang Renbin Su Xichen Tian State Grid Corporation of China Beijing100031China Central China Branch State Grid Corporation of ChinaWuhan430077China School of Electric and Electronic Engineering Huazhong University of Science and TechnologyWuhan430074China China Electric Power Research Institute Co. Ltd.Beijing100192China

Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus *** results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.

关键词： Stochastic programming unit commitment scenarios clustering Benders decomposition multi-parametric programming

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A framework for multi-parametric programming and control - An overview

A framework for multi-parametric programming and control - A...

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IEEE International Engineering Management Conference, Europe

作者： Narciso, Diogo A. C. Faisca, Nuno P. Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2AZ England

In this paper we present an overview of the recent developments in multi-parametric programming and its specific use for control. An unifying optimisation framework to solve general multi-parametric programming proble... 详细信息

ISBN: (纸本)9781424422883

关键词： multi-parametric programming MPC bilevel programming balanced truncation

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Theoretical and algorithmic advances in multi-parametric programming and control

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COMPUTATIONAL MANAGEMENT SCIENCE 2012年第2期9卷 183-203页

作者： Pistikopoulos, Efstratios N. Dominguez, Luis Panos, Christos Kouramas, Konstantinos Chinchuluun, Altannar Ctr Proc Syst Engn London England

This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system.

关键词： multi-parametric programming Bi-level programming Dynamic programming Control

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