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A strategy to tighten the relaxation of bilinear terms towards petrochemical scheduling problem

JOURNAL OF GLOBAL OPTIMIZATION 2025年 1-27页

作者： Zhang, Lifeng Ge, Congqin Zhang, Yanfeng Yang, Wenhui Chen, Bingzhen Yuan, Zhihong Tsinghua Univ Dept Chem Engn State Key Lab Chem Engn Beijing 100084 Peoples R China Sichuan Univ Software Engn Chengdu 610065 Sichuan Peoples R China

This paper proposes a strategy to improve the relaxation of the normalized multiparametric disaggregation technique. By introducing additional partitions to continuous variables, a bivariate relaxation scheme, piece-wise normalized disaggregation technique (PNMDT) is developed. The proposed approach is first tested over numerical nonlinear programming examples. Based on such a strategy, a global optimization algorithm is then proposed to handle nonconvex optimization problems which involve plentiful bilinear terms. This proposed algorithm is evaluated through solving common scheduling problems in the petrochemical industry, the multi-period blending problem, and the multi-period crude oil scheduling problem. The computational results show that the proposed method can efficiently improve the quality of relaxation and speed up the convergence by reducing the required iterations within the algorithm procedure.

关键词： Normalized multiparametric disaggregation technique Nonconvex piece-wise linearization McCormick envelope Scheduling

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∞/∞-Analysis of homogeneous distillation processes

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CHEMICAL ENGINEERING SCIENCE 2012年 84卷 315-332页

作者： Ryll, O. Blagov, S. Hasse, H. Univ Kaiserslautern Lab Engn Thermodynam D-67663 Kaiserslautern Germany BASF SE D-67056 Ludwigshafen Germany

A method for the analysis of flowsheets consisting of an arbitrary number of distillation columns and mixers in conceptual process design is presented in this work. The required information on the process is reduced to a minimum: besides the fluid property model, only information on the flow sheet structure, the overall feed streams and a suitable set of desired product specifications is needed. The method is based on the study of thermodynamic limiting cases by applying infinity/infinity-analysis to distillation columns. Thus, the attainable distillate and bottom compositions are described by the invariant manifolds of the singular points of the respective vapor-liquid equilibria. The approach based on residue curve maps or distillation line diagrams is general and not limited to the number of components or azeotropes. Only homogeneous azeotropes are discussed in the present work. The nonlinearity in the resulting short-cut model is only introduced by the fluid properties. By applying a suitable linearization to the separatrices of the vapor-liquid equilibria the invariant manifolds of the singular points are represented by linear elements. This results in piece-wise linear sub-models for the attainable product compositions. Brute force enumeration of the combined linear sub-models allows finding of all solutions reliably and robustly. Hence, comprehensive feasibility and multiplicity analysis are possible. An overview of the method is given followed by some examples for its application to a number of azeotropic distillation processes. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Separations Distillation Phase equilibria Design infinity/infinity-Analysis piece-wise linearization

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∞/∞-Analysis of heterogeneous distillation processes

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CHEMICAL ENGINEERING SCIENCE 2013年 104卷 374-388页

作者： Ryll, O. Blagov, S. Hasse, H. BASF SE D-67056 Ludwigshafen Germany Univ Kaiserslautern Lab Engn Thermodynam D-67663 Kaiserslautern Germany

A short-cut method for the conceptual design of processes consisting of distillation columns and decanters is presented. It extends the previous work on homogeneous distillation columns and processes (Ryll et. al., 2012b) to heterogeneous distillation processes. The approach is based on the consideration of thermodynamic limiting cases, e.g., for distillation columns infinity/infinity-analysis is used. The decanters are modeled using the respective liquid multi-phase equilibria. By applying an appropriate piece-wise linearization to the separatrices of the vapor-liquid(-liquid) equilibria as well as to the liquid multi-phase equilibria, the original nonlinear process model is replaced by a piece-wise linear model (Feng et al., 2003). The algorithm for the simulation of the decanters is based on a recent publication (Ryll et al., 2012a). The new short-cut method enables the analysis of flow sheets consisting of an arbitrary number of distillation columns and decanters and yields to the stream table of feasible processes. The application range of the method is further enhanced by including the units mixer, component split and split. Two examples are discussed in detail to demonstrate the application of the new method. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Separations Distillation Phase equilibria Design infinity/infinity-Analysis piece-wise linearization

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Energy-Saving Cross-Layer Optimization for Multihop Cognitive Networks 8

Energy-Saving Cross-Layer Optimization for Multihop Cognitiv...

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8th International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Tian, Feng Cui, Qi Xing, Pengchao Zhu, Wenjun Li, Dapeng Yang, Zhen Nanjing Univ Posts & Telecommun Key Lab Broadband Wireless Commun & Sensor Networ Nanjing 210003 Jiangsu Peoples R China

ISBN: (纸本)9781509028603

Energy consumption reducing in wireless communications has attracted increasing attention recently. Power control is a key technology for cognitive networks, which can affect energy saving of cognitive network and interfere with primary networks. In this paper, we jointly consider power control in physical layer, scheduling in link layer and routing in network layer to present a cross-layer optimization for power control in multi-hop cognitive network and formulate a mixed integer nonlinear program (MINLP) problem. To solve it, we develop a piece-wise linearization technique to transform the nonlinear term in constraints into the linear one and finally obtain the approximate optimal solution. Simulation results demonstrate the efficacy of the solution procedure and the optimal power control can achieve energy saving.

关键词： Multi-hop cognitive network Power control Energy saving piece-wise linearization Cross-Layer optimization

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A Linearized Mathematical Formulation for Combined Centralized and Distributed Waste Water Treatment Network Design

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Operations Research Forum 2022年第3期3卷 36页

作者： Broukos, Pantelis Fragkogios, Antonios Shah, Nilay Imperial College London Department of Chemical Engineering Urban Energy Systems London United Kingdom BATI Energie Sarl Luxembourg Luxembourg Department of Mechanical Engineering University of Thessaly Volos Greece

Waste water treatment (WWT) is a very important issue affecting both the environment and public health in the twenty-first century. The increasing earth’s population together with the growing urbanism leads to the need of redesigning effective WWT. In this paper, the problem of optimal Waste Water Treatment Network Design (WWTND) is addressed. To this end, various parameters affecting the problem have been taken into consideration, such as the distance between the residential areas and the treatment plants, estimations for future population of towns and costs of expanding existing network or building a new one. The last parameter of cost has a lot of components (pipeline cost, treatment plant cost, etc.), all of which are non-linear functions depending on the amount of waste water produced and treated within the network. The authors have developed a mathematical model for the solution of WWTND problem and have applied piecewise linearization in order to deal with the non-linear terms. The developed model has been implemented on an area in Luxemburg, for which data were collected. The results prove the model’s validity and usefulness, while its solution is computationally affordable. © 2022, The Author(s).

关键词： Network design Non-linear programming piece-wise linearization Waste water treatment

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Modeling and Online Parameter Identification of Li-Polymer Battery Cells for SOC estimation

Modeling and Online Parameter Identification of Li-Polymer B...

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21st IEEE International Symposium on Industrial Electronics (ISIE)

作者： Rahimi-Eichi, H. Baronti, F. Chow, M. -Y. North Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA Univ Pisa Dept Informat Engn I-56100 Pisa Italy

ISBN: (纸本)9781467301589

Finding an accurate and easily to implement model of batteries is an essential step in properly estimating the state of charge (SOC) of the battery in real-time. In this paper, an equivalent circuit based battery model with nonlinear relationship between the open circuit voltage (V-OC) and the SOC is projected into several piece-wise linear functions. Moving window Least Squares (LS) parameter identification technique is then utilized to estimate and update the parameters of the battery model in each sampling time. The continuously updated parameters are fed to a linear observer to estimate the SOC of the battery. The effectiveness of the proposed modeling and estimation approach are verified experimentally on Lithium Polymer batteries.

关键词： Battery modeling piece-wise linearization parameter identification state observer design State-of-Charge estimation PHEV/PEV

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Planejamento dos sistemas de distribuição de energia elétrica integrando a confiabilidade do serviço

Planejamento dos sistemas de distribuição de energia elét...

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作者： Tabares Pozos, Alejandra Universidade Estadual Paulista

O planejamento bem-sucedido de redes de distribuição requer uma metodologia que inclua um modelo de rede preciso que considere não apenas os custos econômicos, mas também os custos associados à confiabilidade do sistema. Considerando estas duas características essenciais, esta tese propõe modelos matemáticos que permitam incluir a avaliação da confiabilidade dentro do problema do planejamento de expansão de sistemas de distribuição com múltiplos estágios, visando expandir os ativos de rede (ramos e subestações) e minimizar os custos de confiabilidade do sistema. Em relação às características da rede, o modelo de planejamento proposto utiliza um fluxo de potência AC não-linear e não convexo, que é convertido em um problema convexo usando reformulação cônica, técnicas de linearização por partes, com o intuito de obter tratabilidade computacional usando técnicas clássicas de otimização. Além disso, a avaliação de confiabilidade convencional baseada em simulação é implementada de forma equivalente por meio de expressões algébricas dentro do modelo matemático. Vários casos de estudo são usados para demostrar a eficácia da metodologia de planejamento *** planning of distribution networks requires a methodology that includes an accurate network model that considers not only the economic costs but also the costs associated with system reliability. Considering these two essential characteristics, this thesis proposes mathematical models that include reliability assessment within multi-stage expansion planning problem of distribution systems, aiming at expanding network assets (branches and substations) and minimizing reliability costs of the system. In relation to the network characteristics, the proposed planning model uses a non-convex nonlinear AC power flow, which is converted into a convex problem using conic reformulation and piece-wise linearization, to obtain the computational treatability using classical optimization techniques. In addition, conven

关键词： Confiabilidade Fluxo de potência AC Linearização por parte Otimização Planejamento de expansão AC power flow Expansion planning Optimization piece-wise linearization Reliability Tese de doutorado

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Adapting a Dehazing System to Haze Conditions by piece-wisely Linearizing a Depth Estimator

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SENSORS 2022年第5期22卷 1957-1957页

作者： Ngo, Dat Lee, Seungmin Kang, Ui-Jean Ngo, Tri Minh Lee, Gi-Dong Kang, Bongsoon Dong A Univ Dept Elect Engn Busan 49315 South Korea Univ Danang Univ Sci & Technol Fac Elect & Telecommun Engn Danang 550000 Vietnam

Haze is the most frequently encountered weather condition on the road, and it accounts for a considerable number of car crashes occurring every year. Accordingly, image dehazing has garnered strong interest in recent decades. However, although various algorithms have been developed, a robust dehazing method that can operate reliably in different haze conditions is still in great demand. Therefore, this paper presents a method to adapt a dehazing system to various haze conditions. Under this approach, the proposed method discriminates haze conditions based on the haze density estimate. The discrimination result is then leveraged to form a piece-wise linear weight to modify the depth estimator. Consequently, the proposed method can effectively handle arbitrary input images regardless of their haze condition. This paper also presents a corresponding real-time hardware implementation to facilitate the integration into existing embedded systems. Finally, a comparative assessment against benchmark designs demonstrates the efficacy of the proposed dehazing method and its hardware counterpart.

关键词： image dehazing haze condition piece-wise linearization hardware implementation

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