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Initialising distillation column models

COMPUTERS & CHEMICAL ENGINEERING 2000年第11-12期23卷 1811-1824页

作者： Fletcher, R Morton, W Univ Edinburgh Sch Chem Engn Edinburgh EH9 3JL Midlothian Scotland Univ Dundee Dept Math Dundee DD1 4HN Scotland

Difficulties associated with the optimisation of distillation column models by non-linear programming are considered. The paper presents a systematic procedure to enable these difficulties to be overcome and proposes a particular formulation of the distillation column model. A certain limiting case of the column model is examined, that of infinite reflux or zero feed. This limiting case considerably simplifies the model and provides a system of non-linear equations that is readily solved. The solution of this problem gives useful information about the purity that can be achieved in the general case and the number of plates needed to attain a given level of purity. The limiting problem provides starting values for the solution of the general column and suggests a homotopy that can be followed if difficulties arise in obtaining convergence. To obtain a stable form of the limiting case requires the general column model to be formulated in a certain way, which to our knowledge has not previously been considered. The ideas have been successfully tested on various multi-column flowsheets involving distillation columns with heat integration. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： distillation column mathematical model zero-feed column non-linear programming AMPL

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Purchasing from multiple capital-constrained suppliers using order financing

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第22期62卷 8157-8172页

作者： Wu, Andy Natl Chung Hsing Univ Dept Mkt 145 Xingda Rd Taichung 402 Taiwan

Small and medium enterprises (SMEs) play a critical role in supply chains and social stability. Unfortunately, SMEs often lack access to traditional bank financing. To develop SME suppliers, some creditworthy companies have built platforms to coordinate banks and suppliers by employing purchase order financing (POF). After noting that SMEs differ in terms of their operational flexibility and uncertainty, this research examines optimal purchasing portfolios on such platforms. Specifically, we construct a Stackelberg model involving one buyer and two suppliers and analyse the Karush-Kuhn-Tucker necessary conditions for a buyer's strategy upon which the optimal portfolio can be achieved. According to the experiments that we design to simulate about 200,000 various scenarios, the large buyer only needs to consider the top five strategies. The choice of strategy mainly depends on cost differences of suppliers, and flexibility can be used as an identifier of the purchase quantity.

关键词： Purchasing supply chain management OM-finance interface Stackelberg model non-linear programming purchase order financing

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Adaptive firefly algorithm with chaos for mechanical design optimization problems

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APPLIED SOFT COMPUTING 2015年 36卷 152-164页

作者： Baykasoglu, Adil Ozsoydan, Fehmi Burcin Dokuz Eylul Univ Fac Engn Dept Ind Engn TR-35397 Izmir Turkey

Firefly algorithm (FA) is a newer member of bio-inspired meta-heuristics, which was originally proposed to find solutions to continuous optimization problems. Popularity of FA has increased recently due to its effectiveness in handling various optimization problems. To enhance the performance of the FA even further, an adaptive FA is proposed in this paper to solve mechanical design optimization problems, and the adaptivity is focused on the search mechanism and adaptive parameter settings. Moreover, chaotic maps are also embedded into AFA for performance improvement. It is shown through experimental tests that some of the best known results are improved by the proposed algorithm. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Firefly algorithm Chaotic maps Design optimization non-linear programming

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A pixel-based regularization approach to inverse lithography

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MICROELECTRONIC ENGINEERING 2007年第12期84卷 2837-2852页

作者： Poonawala, Amyn Milanfar, Peyman Univ Calif Santa Cruz Dept Comp Engn Santa Cruz CA 95064 USA Univ Calif Santa Cruz Dept Elect Engn Santa Cruz CA 95064 USA

Inverse lithography attempts to synthesize the input mask which leads to the desired output wafer pattern by inverting the forward model from mask to wafer. In this article, we extend our earlier framework for image prewarping to solve the mask design problem for coherent, incoherent, and partially coherent imaging systems. We also discuss the synthesis of three variants of phase shift masks (PSM);namely, attenuated (or weak) PSM, 100% transmission PSM, and strong PSM with chrome. A new two-step optimization strategy is introduced to promote the generation and placement of assist bar features. The regularization framework is extended to guarantee that the estimated PSM have only two or three (allowable) transmission values, and the aerial-image penalty term is introduced to boost the aerial image contrast and keep the side-lobes under control. Our approach uses the pixel-based mask representation, a continuous function formulation, and gradient-based iterative optimization techniques to solve the inverse problem. The continuous function formulation allows analytic calculation of the gradient in O(MNlog(MN)) operations for an M x N pattern making it practically feasible. We also present some results for coherent and incoherent imaging systems with very low k(1) values to demonstrate the effectiveness of our approach.(C) 2007 Elsevier B.V. All rights reserved.

关键词： inverse lithography OPC PSM pixel-based approach non-linear programming optimization regularization low-complexity

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Optimal control problems with multiple characteristic time points in the objective and constraints

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AUTOMATICA 2008年第11期44卷 2923-2929页

作者： Loxton, R. C. Teo, K. L. Rehbock, V. Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia

In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Control parametrization Optimal control computation non-linear optimal control Constrained optimal control non-linear programming

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Weighted Multiple Predictor-corrector Interior Point Method for Optimal Power Flow

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2011年第2期39卷 99-112页

作者： Xie, Liang Chiang, Hsiao-Dong Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Dept Elect Engn Shanghai 200240 Peoples R China Cornell Univ Sch Elect & Comp Engn Ithaca NY USA

The interior point method is considered one of the most efficient methods for solving different types of optimal power flow problems. In this article, a weighted multiple predictor-corrector interior point method is proposed and applied to solve two non-linear optimal power flow problems, which include the generation cost minimization problem and the active power loss minimization problem. A two-stage line-search strategy is employed to obtain the optimal composite direction in order to improve the convergence property of the predictor-corrector interior point method. The proposed method is evaluated on three IEEE test systems and three large-scale systems ranging in size from 57 to 2790 buses. Numerical results demonstrate that, compared with the original multiple predictor-corrector interior point method, the proposed method can converge to an optimal power flow solution with a fewer iterations and faster computational time. Moreover, comparison numerical studies show that the proposed method can be faster and more robust than that traditional predictor-corrector interior point method and its variants.

关键词： interior point method line search non-linear programming optimal power flow weight corrector

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Opportunities and challenges: Landfill gas to biomethane injection into natural gas distribution grid through pipeline

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JOURNAL OF CLEANER PRODUCTION 2018年 175卷 409-419页

作者： Hoo, Poh Ying Hashim, Haslenda Ho, Wai Shin Univ Teknol Malaysia Fac Chem & Energy Engn Proc Syst Engn Malaysia PROSPECT Skudai 81310 Johor Malaysia

Biomethane, a renewable gas (RG), is gaining popularity globally since the advocacy for greenhouse gas (GHG) emission reductions. Biomethane includes upgraded biogas and upgraded landfill gas. Upgraded biogas is generated and upgraded from biomass, for example, energy crops or agricultural waste through anaerobic digestion, while upgraded landfill gas is collected and upgraded directly from gas released from a landfill site. In Malaysia, biogas and landfill gas are usually used on site. The potential for transporting upgraded biogas for off-site utilisation through pipeline injection is yet to be explored. This paper presents economic models, spatial analysis and scenario analysis to identify an appropriate biogas supply chain to different demand: industrial area, commercial area and residential area at different pressures: 20 psig, 4.3 psig and 0.43 psig through injection into the natural gas grid. The trade-off between the compression pressure and the distance of transportation is assessed and the results reveal that injection of biogas into the natural gas gate for industrial usage at 20 psig is the best option, with associated costs of 2.07 x 10(9) MYR/y. The cost is higher than supplying the demand with natural gas, which has an annual cost of MYR 985.87 M. Therefore, incentives for sales of biogas and turning the environmental liability of methane gas emitted from the landfill into an economic opportunity is essential so that the biogas can be sold at a competitive price as natural gas. The methodology can be applied at regional and country level to support policy makers to define and implement a strategy for future landfill gas to be injected into the natural gas grid in order achieve the country's renewable energy target of 30% in 2025. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Landfill gas Biomethane Injection Malaysia non-linear programming

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Optimal control of HVAC systems using DDP and NLP techniques

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OPTIMAL CONTROL APPLICATIONS & METHODS 1996年第1期17卷 71-78页

作者： Kota, NN House, JM Arora, JS Smith, TF UNIV IOWA DEPT CIVIL & ENVIRONM ENGNIOWA CITYIA 52242 UNIV IOWA DEPT MECH ENGNIOWA CITYIA 52242

The objective of this study is to apply the differential dynamic programming (DDP) technique of optimal control to heating, ventilating and air-conditioning (HVAC) systems and to compare its performance with a non-linear programming (NLP) technique using the sequential quadratic programming method. The DDP technique is briefly described and studied. Limitations of the technique are noted. Three cases of a system that has been treated previously in the literature are optimized by the two techniques and the computational times compared, The study shows DDP to be efficient compared with NLP for the example problems. NLP is, however, more robust and general and can treat constraints on the state variables directly. Further investigation is needed for larger-scale problems to fully explore the features of the two methods.

关键词： optimal control HVAC systems non-linear programming differential dynamic programming

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ALLOCATING NODES TO HUBS FOR MINIMIZING THE HUBS PROCESSING RESOURCES: A CASE STUDY

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RAIRO-OPERATIONS RESEARCH 2019年第3期53卷 807-827页

作者： Balma, Ali Mrad, Mehdi Univ Tunis Ecole Natl Super Ingenieurs Tunis 5 Av Taha Hussein Tunis 1008 Tunisia Univ Tunis Tunis Business Sch BADEM POB 65 Bir El Kassaa 2059 Tunisia King Saud Univ Dept Ind Engn Coll Engn POB 800 Riyadh 11421 Saudi Arabia

This paper addresses the problem of allocating the terminal nodes to the hub nodes in a telecommunication network. Since the flow processing induces some undesirable delay, the objective is to minimize the total flow processed by the hubs. This study focuses on a real life network of the tunisian operator Tunisie Telecom whose operations managers are concerned by the quality of service. We provide three compact formulations that give optimal solutions for networks of large size. In particular, the last two are obtained by applying the Reformulation-linearization Technique to a nonlinear formulation of the problem. The latter formulation derived within this approach is the most computationally effective, as pointed out by the computational experiments conducted on the real life network of Tunisie Telecom with 110 nodes and 5 hubs. Finally, we discuss and compare between the single allocation and double allocation configurations.

关键词： Hub allocation non-linear programming Combinatorial optimization Graphs and Networks Reformulation-linearization Technique Telecommunications

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ON VERIFICATION OF FUEL-OPTIMAL SPACE TRAJECTORIES

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OPTIMAL CONTROL APPLICATIONS & METHODS 1988年第3期9卷 285-302页

作者： VASUDEVAN, G LUTZE, FH Department of Aerospace Engineering Virginia Polytechnic Institute and State University Blacksburg Virginia 24061 U.S.A.

Candidate fuel-optimal trajectories for rendezvous in space are obtained with a parameter optimization method. These trajectories, which may include a minimum radius constraint, are verified against necessary conditions for optimality. Necessary conditions are presented in the form of requirements on a primer vector and in terms of requirements on the jumps in the costates when the constraint is encountered. In addition, criteria due to Lion and Handelsmann indicate how to improve candidate trajectories which prove non-optimal so that they become locally optimal. Numerical results are presented which show that the candidate solutions must be obtained to a high level of accuracy before primer vector tests are valid.

关键词： Fuel-optimal rendezvous trajectories Impulsive orbital transfer Primer vector theory non-linear programming Minimum radius trajectory constraint

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