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Quantifying polymer structural component evolution using X-ray scattering and mixed-integer network component analysis

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COMPUTERS & CHEMICAL ENGINEERING 2011年第11期35卷 2564-2578页

作者： Tolle, Ian Martin, Lealon L. Univ Texas Austin Dept Chem Engn Cockrell Sch Engn Austin TX 78712 USA Rensselaer Polytech Inst Dept Chem & Biol Engn Troy NY 12180 USA Rensselaer Polytech Inst Dept Decis Sci & Engn Syst Troy NY 12180 USA

In this work we present a novel computational approach for the extraction of underlying polymer structural component signatures and corresponding structural evolution through decomposition of multivariate X-ray scattering (SAXS/WAXS) datasets. Without assumptions based on structural geometry, this mixed-integer network component analysis (NCA) methodology generates a reduced set of component scattering signatures and component fraction evolution. Structural models are then assigned to each component based on a generalized expression for scattering from multi-phase materials. The methodology is applied systematically to the study of ethylene/alpha-olefin copolymer isothermal crystallization. The decomposition generates component signatures defining structures of varying extent within the sample but with constant average local structure. For WAXS datasets, these components can be correlated to crystalline and amorphous regions, while for SAXS datasets they can be correlated to ordered and disordered crystalline lamellae. These model choices agree with structures observed in the literature and are confirmed by comparison to reference crystallinity data. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Network component analysis mixed-integer nonlinear programming Chemometrics X-ray scattering Ethylene/alpha-olefin copolymers Crystallization

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Optimization of Supply Chain Systems with Price Elasticity of Demand

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INFORMS JOURNAL ON COMPUTING 2011年第4期23卷 557-568页

作者： Kaplan, Ugur Turkay, Metin Karasozen, Bulent Biegler, Lorenz T. Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey Middle E Tech Univ Dept Math TR-06531 Ankara Turkey Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

A centralized multiechelon, multiproduct supply chain network is presented in a multiperiod setting with products that show varying demand against price. An important consideration in such complex supply chains is to maintain system performance at high levels for varying demands that may be sensitive to product price. To examine the price-centric behavior of the customers, the concept of price elasticity of demand is addressed. The proposed approach includes many realistic features of typical supply chain systems such as production planning and scheduling, inventory management, transportation delay, transportation cost, and transportation limits. In addition, the proposed system can be extended to meet unsatisfied demand in future periods by backordering. Effects of the elasticity in price demand in production and inventory decisions are also examined. The supply chain model is formulated as a convex mixed-integer nonlinear programming problem. Reformulations are presented to make the problem tractable. The differential equations are reformulated as difference equations, and unbounded derivatives in the nonlinear objective function are handled with an approximation, with guaranteed bounds on the loss of optimality. The approach is illustrated on a multiechelon, multiproduct supply chain network.

关键词： mixed-integer nonlinear programming supply chain management smoothing price elasticity of demand

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Modern tools for the time-discrete dynamics and optimization of gene-environment networks

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COMMUNICATIONS IN nonlinear SCIENCE AND NUMERICAL SIMULATION 2011年第12期16卷 4768-4779页

作者： Defterli, Ozlem Fuegenschuh, Armin Weber, Gerhard Wilhelm Cankaya Univ Fac Art & Sci Dept Math & Comp Sci TR-06530 Ankara Turkey Zuse Inst Berlin Dept Optimizat D-14195 Berlin Germany Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey

In this study, we discuss the models of genetic regulatory systems, so-called gene-environment networks. The dynamics of such kind of systems are described by a class of time-continuous ordinary differential equations having a general form (E) over dot = M(E)E, where E is a vector of gene-expression levels and environmental factors and M(E) is the matrix having functional entries containing unknown parameters to be optimized. Accordingly, time-discrete versions of that model class are studied and improved by introducing 3rd-order Heun's method and 4th-order classical Runge-Kutta method. The corresponding iteration formulas are derived and their matrix algebras are obtained. After that, we use nonlinear mixed-integer programming for the parameter estimation in the considered model and present the solution of a constrained and regularized given mixed-integer problem as an example. By using this solution and applying both the new and existing discretization schemes, we generate corresponding time-series of gene-expressions for each method. The comparison of the experimental data and the calculated approximate results is additionally done with the help of the figures to exercise the performance of the numerical schemes on this example. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Gene-networks Regulatory systems Dynamical systems Discretization mixed-integer nonlinear programming

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Gap inequalities for non-convex mixed-integer quadratic programs

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OPERATIONS RESEARCH LETTERS 2011年第5期39卷 297-300页

作者： Galli, Laura Kaparis, Konstantinos Letchford, Adam N. Univ Lancaster Dept Management Sci Lancaster LA1 4YW England Univ Bologna DEIS I-40136 Bologna Italy

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general non-convex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Max-cut problem mixed-integer nonlinear programming Polyhedral combinatorics

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Nonconvex Generalized Benders Decomposition for Stochastic Separable mixed-integer nonlinear Programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2011年第3期151卷 425-454页

作者： Li, Xiang Tomasgard, Asgeir Barton, Paul I. MIT Dept Chem Engn Proc Syst Engn Lab Cambridge MA 02139 USA Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management N-7034 Trondheim Norway

This paper considers deterministic global optimization of scenario-based, two-stage stochastic mixed-integer nonlinear programs (MINLPs) in which the participating functions are nonconvex and separable in integer and continuous variables. A novel decomposition method based on generalized Benders decomposition, named nonconvex generalized Benders decomposition (NGBD), is developed to obtain epsilon-optimal solutions of the stochastic MINLPs of interest in finite time. The dramatic computational advantage of NGBD over state-of-the-art global optimizers is demonstrated through the computational study of several engineering problems, where a problem with almost 150,000 variables is solved by NGBD within 80 minutes of solver time.

关键词： Stochastic programming mixed-integer nonlinear programming Decomposition algorithm Global optimization

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AN ASYNCHRONOUS PARALLEL HYBRID OPTIMIZATION APPROACH TO SIMULATION-BASED mixed-integer nonlinear PROBLEMS

AN ASYNCHRONOUS PARALLEL HYBRID OPTIMIZATION APPROACH TO SIM...

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23rd European Modeling and Simulation Symposium / International Mediterranean and Latin American Modeling Multiconference

作者： Fowler, K. R. Kopp, T. Orsini, J. Griffin, J. D. Gray, G. A. Clarkson Univ Dept Math & Comp Sci Potsdam NY 13676 USA SAS New York NY USA Sandia Natl Labs Livermore CA 94550 USA

ISBN: (纸本)9788890372445

To address simulation-based mixed-integer problems, a hybrid algorithm was recently proposed that combines the global search strengths and the natural capability of a genetic algorithm to handle integer variables with a local search on the real variables using an implementation of the generating set search method. Since optimization is guided only by function values, the hybrid is designed to run asynchronously on a parallel platform. The algorithm has already been shown to perform well on a variety of test problems, and this work is a first step in understanding how the parallelism and local search components influence the search phase of the algorithm. We show that the hybridization can improve the capabilities of the genetic algorithm by using less function evaluations to locate the solution and provide a speed-up analysis on a standard mixed-integer test problem with equality and inequality constraints.

关键词： genetic algorithm pattern search asynchronous mixed-integer nonlinear programming

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A discrete competitive facility location model with variable attractiveness

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2011年第9期62卷 1726-1741页

作者： Kucukaydin, H. Aras, N. Altinel, I. K. Bogazici Univ Dept Ind Engn TR-34342 Istanbul Turkey

We consider the discrete version of the competitive facility location problem in which new facilities have to be located by a new market entrant firm to compete against already existing facilities that may belong to one or more competitors. The demand is assumed to be aggregated at certain points in the plane and the new facilities can be located at predetermined candidate sites. We employ Huff's gravity-based rule in modelling the behaviour of the customers where the probability that customers at a demand point patronize a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. The objective of the firm is to determine the locations of the new facilities and their attractiveness levels so as to maximize the profit, which is calculated as the revenue from the customers less the fixed cost of opening the facilities and variable cost of setting their attractiveness levels. We formulate a mixed-integer nonlinear programming model for this problem and propose three methods for its solution: a Lagrangean heuristic, a branch-and-bound method with Lagrangean relaxation, and another branch-and-bound method with nonlinear programming relaxation. Computational results obtained on a set of randomly generated instances show that the last method outperforms the others in terms of accuracy and efficiency and can provide an optimal solution in a reasonable amount of time. Journal of the Operational Research Society (2011) 62, 1726-1741 doi:10.1057/jors.2010.136 Published online 8 September 2010

关键词： competitive facility location variable facility attractiveness mixed-integer nonlinear programming Lagrangean heuristic branch-and-bound

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Confrontation of Different Objectives in the determination of train scheduling

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Procedia - Social and Behavioral Sciences 2011年 20卷 302-312页

作者： David Canca Alejandro Zarzo Encarnación Algaba Eva Barrena E.T.S. Ingenieros Universidad de Sevilla Camino de los Descubrimientos s/n 41092. Seville Spain E.T.S.I.I. Universidad Politécnica de Madrid José Gutiérrez Abascal 2 28006. Madrid Spain

In the railway networks management context, the determination of train schedules is a topic which affects both the level of satisfaction amongst the users and the network performance and profitability. This double influence makes it a widely studied topic in the literature, where nowadays the main lines of research tend to improve the solving methods of the corresponding integer programming problems. However, literature about methods that take both user and service provider point of view jointly into account is sparse. In this work, we tackle the problem of scheduling in middle and long distances networks by means of a non-linear integer programming model which fits the schedules to a dynamic behavior of demand and represents a trade-off between some measures of quality of the service offered and aspects related to the network profitability. The confrontation of different objective selection policies is analyzed in depth in the core part of this study, with the intention of both improving the insight into the proposed model and adding the flexibility of choosing different objectives by knowing in advance their influence on the resulting schedule plan.

关键词： train scheduling quality of service mixed-integer nonlinear programming

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Recipe Determination and Scheduling of Gasoline Blending Operations

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AICHE JOURNAL 2010年第2期56卷 441-465页

作者： Li, Jie Karimi, I. A. Srinivasan, Rajagopalan Natl Univ Singapore Dept Chem & Biomol Engn Singapore 117576 Singapore Inst Chem & Engn Sci Singapore 627833 Singapore

Gasoline is a major contributor to the profit of a refinery. Scheduling gasoline-blending operations is a critical and complex routine task involving tank allocation, component mixing, blending, product storage, and order delivery. Optimized schedules can maximize profit by avoiding ship demurrage, improving order delivery, minimizing quality give-aways, avoiding costly transitions and slop generation, and reducing inventory costs. However, the blending recipe and scheduling decisions make this problem a nonconvex mixed-integer nonlinear program (MINLP). In this article, we develop a slot-based MILP formulation for an integrated treatment of recipe, specifications, blending, and storage and incorporate many real-life features such as multipurpose product tanks, parallel nonidentical blenders, minimum run lengths, changeovers, piecewise constant profiles for blend component qualities and feed rates, etc. To ensure constant blending rates during a run, we develop a novel and efficient procedure that solves successive MILPs instead of a nonconvex MINLP. We use 14 examples with varying sizes and features to illustrate the superiority and effectiveness of our formulation and solution approach. The results show that our solution approach is superior to commercial solvers (BARON and DICOPT). (C) 2009 American Institute of Chemical Engineers AIChE J, 56: 441-465, 2010

关键词： gasoline recipe blending mixed-integer nonlinear programming nonconvex property index

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Perspective reformulations of mixed integer nonlinear programs with indicator variables

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MATHEMATICAL programming 2010年第1-2期124卷 183-205页

作者： Guenluek, Oktay Linderoth, Jeff IBM Corp Thomas J Watson Res Ctr Dept Math Sci Yorktown Hts NY 10598 USA Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA

We study mixed integer nonlinear programs (MINLP)s that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is "turned off", forces some of the decision variables to assume fixed values, and, when it is "turned on", forces them to belong to a convex set. Many practical MINLPs contain integer variables of this type. We first study a mixed integer set defined by a single separable quadratic constraint and a collection of variable upper and lower bound constraints, and a convex hull description of this set is derived. We then extend this result to produce an explicit characterization of the convex hull of the union of a point and a bounded convex set defined by analytic functions. Further, we show that for many classes of problems, the convex hull can be expressed via conic quadratic constraints, and thus relaxations can be solved via second-order cone programming. Our work is closely related with the earlier work of Ceria and Soares (Math Program 86:595-614, 1999) as well as recent work by Frangioni and Gentile (Math Program 106:225-236, 2006) and, Akturk et al. (Oper Res Lett 37:187-191, 2009). Finally, we apply our results to develop tight formulations of mixed integer nonlinear programs in which the nonlinear functions are separable and convex and in which indicator variables play an important role. In particular, we present computational results for three applications quadratic facility location, network design with congestion, and portfolio optimization with buy-in thresholds that show the power of the reformulation technique.

关键词： mixed-integer nonlinear programming Perspective functions

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