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Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems

JOURNAL OF GLOBAL OPTIMIZATION 2016年第4期64卷 765-784页

作者： Castro, Pedro M. Univ Lisbon Fac Ciencias CMAF CIO P-1749016 Lisbon Portugal

A key element for the global optimization of non-convex mixed-integer bilinear problems is the computation of a tight lower bound for the objective function being minimized. Multiparametric disaggregation is a technique for generating a mixed-integer linear relaxation of a bilinear problem that works by discretizing the domain of one of the variables in every bilinear term according to a numeric representation system. This can be done up to a certain accuracy level that can be different for each discretized variable so as to adjust the number of significant digits to their range of values and give all variables the same importance. We now propose a normalized formulation (NMDT) that achieves the same goal using a common setting for all variables, which is equivalent to the number of uniform partitions in a closely related, piecewise McCormick (PCM) approach. Through the solution of several benchmark problems from the literature involving four distinct problem classes, we show that the computational performance of NMDT is already better than PCM for ten partitions, with the difference rising quickly due to the logarithmic versus linear growth in the number of binary variables with the number of partitions. The results also show that a global optimization solver based on the proposed relaxation compares favorably with commercial solvers BARON and GloMIQO.

关键词： mixed-integer nonlinear programming Quadratic optimization Disjunctive programming Algorithm Process networks

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Optimizing the supply chain configuration and production-sales policies for new products over multiple planning horizons

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 196卷 150-162页

作者： Negahban, Ashkan Dehghanimohammadabadi, Mohammad Penn State Univ Sch Grad Profess Studies Malvern PA 19355 USA Northeastern Univ Dept Mech & Ind Engn Boston MA 02115 USA

The objective of this paper is to jointly optimize supplier selection, pipeline and safety stock inventories, and production-sales policies for new products over multiple planning horizons such that the total" profit over the product's life-cycle is maximized. A mixed-integer nonlinear programming model is proposed that not only allows for adjusting the level of pipeline and safety stocks at different supply chain stages, but also for switching suppliers and/or modifying their demand allocations in different planning horizons in response to changes in the new product's demand. A representative supply chain network for computer assembly is then used to illustrate the applicability of the model. The findings from our numerical experiments with the model can potentially have important implications for future research and practice. In contrast to the traditional understanding of flexibility, the results indicate that the total profit may not necessarily be an increasing function of the number of planning horizons. The performance of commonly used heuristic policies for supplier selection as well as different myopic and build-up production-sales policies are also compared with the model's prescribed solutions in order to provide insight on when such heuristic policies and combinations thereof can be effective. The interdependency between supplier switching cost and the number of build-up periods is also illustrated.

关键词： mixed-integer nonlinear programming Innovation diffusion Production and sales plans Multi-echelon inventory system Supplier selection Supplier switching cost

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An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach

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AIN SHAMS ENGINEERING JOURNAL 2020年第2期11卷 409-418页

作者： Danilo Montoya, Oscar Gil-Gonzalez, Walter Grisales-Norena, L. F. Univ Tecnol Bolivar Programa Ingn Elect & Ingn Elect Km 1 Via Turbaco Cartagena Colombia Univ Tecnol Pereira AA 97 Pereira 660003 Colombia Inst Tecnol Metropolitano Medellin 050012 Colombia

This paper addresses the classical problem of optimal location and sizing of distributed generators (DGs) in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To solve such model, we employ the General Algebraic Modeling System (GAMS) in conjunction with the BONMIN solver, presenting its characteristics in a tutorial style. To operate all the DGs, we assume they are dispatched with a unity power factor. Test systems with 33 and 69 buses are employed to validate the proposed solution methodology by comparing its results with multiple approaches previously reported in the specialized literature. A 27-node test system is also used for locating photovoltaic (PV) sources considering the power capacity of the Caribbean region in Colombia during a typical sunny day. Numerical results confirm the efficiency and accuracy of the MINLP model and its solution is validated through the GAMS package. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.

关键词： Distributed generation Distribution systems General algebraic modeling system mixed-integer nonlinear programming Optimal location and sizing of distributed generation

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Heat integration and heat recovery steam cycle optimization for a low carbon lignite/biomass-to-jet fuel demonstration project

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APPLIED ENERGY 2019年 239卷 1322-1342页

作者： Elsido, Cristina Martelli, Emanuele Kreutz, Thomas Politecn Milan Dept Energy Via Lambruschini 4 I-20156 Milan Italy Princeton Univ Andlinger Ctr Energy & Environm 86 Olden St Princeton NJ 08544 USA

This paper reports the heat integration study for a demonstration plant to co-process lignite and woody biomass into jet fuel with CO2 capture and storage. Since all the main process reactions are exothermic and convert approximately 65% of the feedstock chemical energy into heat, designing an efficient heat recovery steam cycle and heat exchanger network is essential for the overall thermo-economic performance. Different integration options for the plant's heat recovery steam cycle are analyzed and compared, considering costs and the key technical limitations. The design of the heat recovery steam cycle and heat exchanger network is optimized with an energy targeting methodology, a sequential synthesis method and a recently proposed simultaneous methodology. Given the high specific costs of the units caused by the novelty and small size and of the demonstration plant, the techno-economic optimization returns solutions with considerably lower efficiency (up to -5% percentage points) and power output (up to -18%) compared to the energy targeting methodology. The difference in optimal HRSC designs and performance are minor (less than -2% power output) for full-scale plants based on mature technologies.

关键词： Heat recovery steam cycle Heat exchanger network Polygeneration mixed-integer nonlinear programming Utility Fischer-Tropsch

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Material and energy coupling systems optimization for large-scale industrial refinery with sustainable energy penetration under multiple uncertainties using two-stage stochastic programming

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APPLIED ENERGY 2024年 371卷

作者： Xu, Tiantian Long, Jian Zhao, Liang Du, Wenli East China Univ Sci & Technol Minist Educ Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China Qingyuan Innovat Lab Quanzhou 362801 Peoples R China

The coupling of multimedia materials and energy with sustainable energy penetration in large-scale industrial refineries significantly lowers energy consumption and greenhouse gas (GHG) emissions. This paper presents a sustainable retrofitting framework for coupled production materials and steam systems (CPMSS) utilising twostage stochastic programming (TSSP). A novel sustainable energy-integrated CPMSS (SEICPMSS) model that includes wind, solar, and hydrogen energy and considers multiple operating modes and hydrogen consumption of the process units was established. First-principles models of wind turbines, solar thermal collectors, and proton exchange membrane electrolysers were adopted to sustainably retrofit the CPMSS. Latin hypercube sampling and Gaussian mixture model methods were applied to classify high volumes of uncertain wind speed and solar radiation data. A SEICPMSS optimisation model formulated as a mixed-integer nonlinear programming problem was developed by considering the investment costs, carbon taxes, and operational costs. Finally, a series of case studies from the industrial refinery's CPMSS were conducted to illustrate the effectiveness of the proposed method. The optimisation results indicate that the TSSP method can reduce operating costs by 5.3355 x 108 CNY/year and decrease GHG emissions by 7.4104 x 106 t/year compared to the traditional CPMSS without the integration of sustainable energy systems.

关键词： Refinery Integrated sustainable energy system mixed-integer nonlinear programming Two-stage stochastic programming Uncertainty Greenhouse gas emission

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Application of an advanced real options approach for renewable energy generation projects planning

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2011年第4期15卷 2087-2094页

作者： Martinez-Cesena, E. A. Mutale, J. Univ Manchester Sch Elect & Elect Engn Manchester M60 1QD Lancs England

Nowadays, there is growing interest in renewable energy (RE) generation projects due to environmental and sustainability concerns. However, initial costs and uncertainties caused by RE source variability, changes in support schemes, and other factors can render RE projects unattractive when subject to conventional financial assessment. Initial research suggests that the value of RE projects can be enhanced by the application of real options (RO) theory in the planning and evaluation of such projects. Literature on application of RO planning in RE generation projects is limited, and typically focuses solely on flexible investment decisions and neglects flexible design A more comprehensive approach should address flexibility in designs. This paper proposes an advanced RO methodology for RE generation projects planning, and illustrates the methodology using variations of a hydropower case study. The fundamental differences between advanced RO approaches and other techniques are illustrated on a simple case study. The complete version of the proposed advanced methodology is then compared against other available tools. The results show higher expected profits for projects planned with the advanced RO methodology. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Real options (RO) Uncertainty Optimization mixed-integer nonlinear programming Hydropower

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Dynamic Multi-Bus Dispatching Strategy With Boarding and Holding Control for Passenger Delay Alleviation and Schedule Reliability: A Combined Dispatching-Operation System

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2022年第8期23卷 12846-12860页

作者： Zhang, Yi Su, Rong Zhang, Yicheng Wang, Bohui ASTAR Inst Infocomm Res I2R Singapore 138632 Singapore Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

The continuing increase of the on-road private cars is contributing to a deterioration of the urban traffic system. Public transportation is widely used to tackle this issue due to its large ridership. In this paper, we propose a multi-bus dispatching strategy combined with the boarding and holding control (MBDBH) to improve bus utilization and further decrease the passenger excess delay. Dispatching adjustments and operation control are taken into account in the system. At the dispatching level, on the one hand, either a bus platoon or a single bus can be dispatched for each trip to provide adaptive bus capacity to match the highly-fluctuated stop demands, on the other hand, we adjust the bus dispatching time based on the existing timetable to minimize passenger excess waiting time to a large extent. Meanwhile, the operation level incorporates both holding strategy and boarding limit strategy to bring more flexible adjustments in improving bus service. Besides the efficiency, we also minimize the headway variation in order to maintain a high system reliability. The problem is formulated as a mixed integer nonlinear programming (MINP) problem, which is solved by the commercial solver Gurobi. With the computational complexity as a concern, we propose a distributed algorithm to implement dual decomposition based on the partial Lagrangian relaxation. Finally, numerical examples are investigated to illustrate the significant time reduction of distributed algorithm and the efficiency of our proposed strategy: The proposed MBDBH model can reduce roughly 50% and 30% of remaining passenger volumes when compared with the timetable-based fixed schedule and the optimized single-bus dispatching schedule, respectively.

关键词： Dispatching Optimization Delays Mathematical models Schedules Reliability Costs Public transport systems multi-bus dispatching boarding limit holding control mixed-integer nonlinear programming Lagrangian relaxation

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Equipment Selection for Coupling a Microgrid with a Power-to-Gas System in the Context of Optimal Design and Operation

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COMPUTERS & CHEMICAL ENGINEERING 2024年 181卷

作者： Akulker, Handan Aydin, Erdal Bogazici Univ Dept Chem Engn TR-34342 Istanbul Turkiye Ondokuz Mayis Univ Dept Chem Engn TR-55139 Samsun Turkiye Koc Univ Dept Chem & Biol Engn TR-34457 Istanbul Turkiye Koc Univ TUPRAS Energy Ctr KUTEM TR-34450 Istanbul Turkiye

This study proposes a one-layer deterministic mixed-integer nonlinear programming to design and schedule a PTG-integrated microgrid. The key contribution is that optimal equipment selection, design, and scheduling, considering the PTG system at the core of the problem, are determined just in a single formulation. Scenarios based on different carbon dioxide taxes and natural gas prices are investigated. Only one wind turbine farm is chosen when the carbon dioxide tax is increased from 50 $/ton to 100 $/ton. On the other hand, when the natural gas price is increased from 1.548 $/m3 to 1.72 $/m3, two wind turbine farms are selected. Solar panel arrays are not chosen in all the scenarios. Generated power by solar panels is not enough for installation despite their much lower carbon dioxide emissions and negligible operational costs. Consequently, the optimal equipment selections may change linked to the natural gas price and carbon dioxide tax.

关键词： mixed-integer nonlinear programming Carbon dioxide emission taxing Multi-energy microgrid Optimal design Power-to-gas system Optimal scheduling

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Green supply chain planning considering consumer's transportation process

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2018年 109卷 311-330页

作者： Gao, Jingzhe Xiao, Zhongdong Cao, Binbin Chai, Qiangfei Xi An Jiao Tong Univ Sch Management 28 Xianning Rd Xian 710049 Shaanxi Peoples R China

This article addresses a product delivery and store network layout strategy problem considering not only firms' but also consumers' cost. The study presents several mathematical programming models to minimize the cost or maximize the profit. Then, we design a two-step solution method for exact solutions and present an implementation. The results show that a carbon cap will do more good than harm for the environment. Trying to minimize the cost from both sides will not only improve the efficiency of social resource use but also enable stores to attract more consumers. Limiting emissions for firms will result in significant emissions reduction without an excessive cost increase.

关键词： Carbon cap mixed-integer nonlinear programming Supply chain network design Green supply chain planning

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A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第1期65卷 47-71页

作者： Fampa, Marcia Lee, Jon Melo, Wendel Univ Fed Rio de Janeiro Inst Matemt Rio De Janeiro Brazil Univ Fed Rio de Janeiro COPPE PESC Rio De Janeiro Brazil Univ Michigan Ann Arbor MI 48109 USA

We present a specialized branch-and-bound (b&b) algorithm for the Euclidean Steiner tree problem (ESTP) in and apply it to a convex mixed-integer nonlinear programming (MINLP) formulation of the problem, presented by Fampa and Maculan. The algorithm contains procedures to avoid difficulties observed when applying a b&b algorithm for general MINLP problems to solve the ESTP. Our main emphasis is on isomorphism pruning, in order to prevent solving several equivalent subproblems corresponding to isomorphic Steiner trees. We introduce the concept of representative Steiner trees, which allows the pruning of these subproblems, as well as the implementation of procedures to fix variables and add valid inequalities. We also propose more general procedures to improve the efficiency of the b&b algorithm, which may be extended to the solution of other MINLP problems. Computational results demonstrate substantial gains compared to the standard b&b for convex MINLP.

关键词： Euclidean Steiner tree problem mixed-integer nonlinear programming Branch-and-bound Isomorphism pruning

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