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Sufficient pruning conditions for MINLP in gas network design

EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION 2017年第1-2期5卷 239-261页

作者： Humpola, Jesco Serrano, Felipe Zuse Inst Berlin Takustr 7 D-14195 Berlin Germany

One-quarter of Europe's energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi-billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology optimization problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by fixing all integral variables. We offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex continuous nonlinear program (NLP) can be certified by solving an MILP. This result provides an efficient pruning procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speedup for the necessary computations.

关键词： Network design mixed-integer nonlinear programming Infeasibility detection

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A mathematical model for assessing the effects of a lot splitting feature on a dynamic cellular manufacturing system

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PRODUCTION ENGINEERING-RESEARCH AND DEVELOPMENT 2017年第4-5期11卷 557-573页

作者： Kazemi, Mohammad Gol, Shima Shafiee Tavakkoli-Moghaddam, Reza Kia, Reza Khorrami, Javad Birjand Univ Technol Dept Ind Engn Birjand Iran Univ Tehran Sch Ind Engn Coll Engn Tehran Iran Islamic Azad Univ Firoozkooh Branch Dept Ind Engn Firoozkooh Iran Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran

Numerous studies have been carried out in the field of cellular manufacturing systems (CMS) by considering different types of production costs. In all the presented models, it has been assumed that either the production lot of a part type should be processed by only one machine or it can be split among several machines. To the best of our knowledge, there is no research considering the advantages and disadvantages of the lot splitting feature in designing a CMS under a dynamic environment. In this paper, a mixed-integer nonlinear programming model is formulated to design a dynamic CMS by considering the burdened costs of processing part operations, idleness of cells and machines, inter-cell movements, installation/uninstallation of machines, machine overhead, production lost, splitting production lots and dispersing machines among cells. Furthermore, the advantages and disadvantages of the lot splitting feature are investigated by regarding its effect on the burdened costs. After linearization, an illustrative numerical example is solved by GAMS software (CPLEX solver) to illustrate the model performance and analyze the effect of the lot splitting feature. Since the given problem is NP-hard, an efficient simulated annealing algorithm is developed and tested using several test problems.

关键词： Facilities planning and design Dynamic cellular manufacturing systems mixed-integer nonlinear programming Lot splitting effects Simulated annealing

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Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

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MATHEMATICAL programming COMPUTATION 2017年第3期9卷 321-367页

作者： Hijazi, Hassan Coffrin, Carleton Van Hentenryck, Pascal Australian Natl Univ NICTA CSIRO Data61 Decis Sci 7 London Circuit Canberra ACT 2601 Australia Los Alamos Natl Lab POB 1663 Los Alamos NM 87545 USA Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.

关键词： mixed-integer nonlinear programming Global optimization Convex relaxation Optimal power flow Optimal transmission switching Capacitor placement

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A note on representations of linear inequalities in non-convex mixed-integer quadratic programs

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OPERATIONS RESEARCH LETTERS 2017年第6期45卷 631-634页

作者： Letchford, Adam N. Grainger, Daniel J. Univ Lancaster Dept Management Sci Lancaster LA1 4YW England Univ Lancaster Lancaster England

In the literature on the quadratic 0-1 knapsack problem, several alternative ways have been given to represent the knapsack constraint in the quadratic space. We extend this work by constructing analogous representations for arbitrary linear inequalities for arbitrary non-convex mixed-integer quadratic programs with bounded variables. (C) 2017 Elsevier B.V. All rights reserved.

关键词： mixed-integer nonlinear programming Global optimisation Semidefinite programming

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Convex probabilistic allocation of wind generation in smart distribution networks

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IET RENEWABLE POWER GENERATION 2017年第9期11卷 1211-1218页

作者： Akbari, Mohammad-Amin Aghaei, Jamshid Barani, Mostafa Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran

This study introduces a probabilistic optimisation model for allocation of renewable distributed generations (DGs) in radial distribution networks. The methodology is based on a probabilistic generation - load model that combines all possible operating conditions of the wind-based DG units as well as load levels with their probabilities. A multiobjective performance index is extracted that is formulated as a combination of two indices, namely energy losses reduction and voltage improvement. Besides, a probabilistic AC optimal power flow is used to determine the optimal allocation of wind DG and maximise the multiobjective performance index. Two alternative control approaches of the future smart grids, i.e. area based under load tap changer control and adaptive power factor control, are assessed to maximise potential benefits and expand the penetration level of DGs. At first, this problem is formulated as a mixed-integer non-linear programming (MINLP) which leads to a computationally NP-hard problem. Accordingly, the obtained MINLP problem is relaxed and reformulated in the form of a well-suited second-order cone programming problem which is computationally efficient scheme to be solved. The implementation of the proposed framework on 4-bus and IEEE 33-bus radial distribution systems shows the performance of the proposed optimisation mechanism.

关键词： distribution networks wind power load flow smart power grids power factor nonlinear programming integer programming computational complexity optimisation distributed power generation on load tap changers smart distribution networks wind generation convex probabilistic allocation probabilistic optimisation model renewable distributed generation allocation radial distribution networks probabilistic generation wind-based DG units multiobjective performance index energy losses reduction voltage improvement probabilistic AC optimal power flow optimal allocation smart grids load tap changer control adaptive power factor control mixed-integer nonlinear programming MINLP computationally NP-hard problem second-order cone programming problem IEEE 4-bus radial distribution systems IEEE 33-bus radial distribution systems

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A Branch and Bound Algorithm to Solve Nonconvex MINLP Problems via Novel Division Strategy: An Electric Power System Case Study 17

A Branch and Bound Algorithm to Solve Nonconvex MINLP Proble...

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17th IEEE International Conference on Environment and Electrical Engineering (IEEE EEEIC) / 1st IEEE Industrial and Commercial Power Systems Europe Conference (IEEE I and CPS Europe)

作者： de Jesus Delgado, Marcos Andre Pourakbari-Kasmaei, Mahdi Rider, Marcos Julio UFMT Dept Math Rondonopolis MT Brazil UNESP Dept Elect Engn Ilha Solteira SP Brazil Univ Estadual Campinas Dept Syst & Energy Campinas SP Brazil

ISBN: (纸本)9781538639177

This paper presents two Branch and Bound algorithms (B&B) for solving mixed-integer nonlinear programming (MINLP) problems with nonconvex search space. The main advantage of the proposed algorithms, comparing with the commonly used B&B algorithms, is using an innovative way of variables' separation and subproblems' division while, if necessary, one more variable is used in the separation process. This approach allows circumventing the probable difficulties caused by nonlinearity and nonconvexity. This paper aims at addressing the following issues of how to: 1) deal with nonlinear programming problems, 2) detect the infeasibility of the resulted NLP problems, and 3) deal with the nonconvexity of the problem. In order to show the applicability, the proposed algorithms are applied to one of the most complicated problems in power system, the long-term static transmission expansion planning, which is modeled as an MINLP problem. Several case studies such as Garver 6-bus, IEEE 24-bus, South Brazilian 46-bus, Bolivian 57-bus, and the Colombian 93-bus are conducted to reveal the effectiveness and shortcoming of the proposed algorithms. Results show that the proposed algorithms can find the best-known solutions for most of the aforementioned systems with a significant reduction in the number of subproblems.

关键词： branch and bound algorithm mixed-integer nonlinear programming transmission expansion planning

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Review of mixed-integer nonlinear and Generalized Disjunctive programming Methods

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CHEMIE INGENIEUR TECHNIK 2014年第7期86卷 991-1012页

作者： Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

This work presents a review of the main deterministic mixed-integer nonlinear programming (MINLP) solution methods for problems with convex and nonconvex functions. An overview for deriving MINLP formulations through generalized disjunctive programming (GDP), which is an alternative higher-level representation of MINLP problems, is also presented. A review of solution methods for GDP problems is provided. Some relevant applications of MINLP and GDP in process systems engineering are described in this work.

关键词： Generalized disjunctive programming mixed-integer nonlinear programming nonlinear programming Optimization

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Heuristic Optimization Model for the Optimal Layout and Pipe Design of Sewer Systems

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WATER RESOURCES MANAGEMENT 2016年第5期30卷 1605-1620页

作者： Steele, Joshua C. Mahoney, Kurt Karovic, Omer Mays, Larry W. Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85257 USA

The design of urban stormwater systems and sanitary sewer systems consists of solving two problems: generating a layout of the system and the pipe design which includes the crown elevations, slopes and commercial pipe sizes. A heuristic model for determining the optimal (minimum cost) layout and pipe design of a storm sewer network is presented. The hierarchical procedure combines a sewer layout model formulated as a mixed-integer nonlinear programming (MINLP) problem which is solved using the General Algebraic Modeling System (GAMS) and a simulated annealing optimization procedure for the pipe design of a generated layout was developed in Excel. The GAMS and simulated annealing models are interfaced through linkage of Excel and GAMS. The pipe design model is based upon the simulated annealing method to optimize the crown elevations and diameter of pipe segments in a storm sewer network using layouts generated using GAMS. A sample scenario demonstrates that using these methods may allow for significant costs saving while simultaneously reducing the time typically required to design and compare multiple storm sewer networks.

关键词： Sewer systems Optimization Minimum cost design Hierarchical modeling Simulated annealing mixed-integer nonlinear programming

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Optimal Design of Pre-control Plans

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2016年第2期32卷 623-634页

作者： Giner-Bosch, Vicent San Matias, Susana Clemente-Ciscar, Monica Carrion, Andres Univ Politecn Valencia Ctr Qual & Change Management Cami Vera S-N E-46022 Valencia Spain Univ Politecn Valencia Dept Estadist & Invest Operat Aplicadas & Calidad Cami Vera S-N E-46022 Valencia Spain

Pre-control is a quality tool for quick set-up approvals, especially used in short-run processes. It is based on specifications instead of the natural variability of the process and uses cumulative counts in order to yield a conclusion. Its main drawbacks are a high false alarm rate and a low power to detect process deviations, under certain circumstances. These issues can be addressed by making the technique more flexible, as shown in previous works. In this paper, we introduce a Mathematical programming approach in order to optimally determine the value of the pre-control parameters, so that it can meet the user's requirements while minimizing the sample size of the technique as much as possible. We propose and develop a mathematical model for optimal pre-control and perform some numerical experiments in order to show its effectiveness. Copyright (c) 2015John Wiley & Sons, Ltd.

关键词： pre-control set-up approval process capability mixed-integer nonlinear programming optimization

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Integrated Gasoline Blending and Order Delivery Operations: Part I. Short-Term Scheduling and Global Optimization for Single and Multi-Period Operations

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AICHE JOURNAL 2016年第6期62卷 2043-2070页

作者： Li, Jie Xiao, Xin Floudas, Christodoulos A. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77843 USA Chinese Acad Sci Inst Proc Engn State Key Lab Multiphase Complex Syst Beijing 100190 Peoples R China Univ Manchester Sch Chem Engn & Analyt Sci Manchester M13 9PL Lancs England

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60-70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give-aways, reducing costly transitions and slop generation, exploiting low-quality cuts, and reducing inventory costs. In this article, we first introduce a new unit-specific event-based continuous-time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the non-convexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed-integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed-integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156-9174. All examples are solved to be 1%-global optimality with modest computational effort. (C) 2016 American Institute of Chemical Engineers

关键词： scheduling refinery operations gasoline blending mixed-integer nonlinear programming MINLP global optimization multi-period

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