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Lift-and-Project Cuts for mixed integer Convex Programs

15th International Conference on integer programming and Combinatorial Optimization (IPCO)

作者： Bonami, Pierre Aix Marseille Univ LIF CNRS 163 Ave Luminy Case 901 F-13288 Marseille 9 France

ISBN: (纸本)9783642208072

This paper addresses the problem of generating cuts for mixed integer nonlinear programs where the objective is linear and the relations between the decision variables are described by convex functions defining a convex feasible region. We propose a new method for strengthening the continuous relaxations of such problems using cutting planes. Our method can be seen as a practical implementation of the lift-and-project technique in the nonlinear case. To derive each cut we use a combination of a nonlinear programming subproblem and a linear outer approximation. One of the main features of the approach is that the subproblems solved to generate cuts are typically not more complicated than the original continuous relaxation. In particular they do not require the introduction of additional variables or nonlinearities. We propose several strategies for using the technique and present preliminary computational evidence of its practical interest. In particular, the cuts allow us to improve over the state of the art branch-and-bound of the solver Bonmin, solving more problems in faster computing times on average.

关键词： mixed integer nonlinear programming Disjunctive programming Lift-and-Project Cutting Planes

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Multicast in Femtocell Networks: A Successive Interference Cancellation Approach

Multicast in Femtocell Networks: A Successive Interference C...

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54th Annual IEEE Global Telecommunications Conference (GLOBECOM)

作者： Hu, Donglin Mao, Shiwen Auburn Univ Dept Elect & Comp Engn Auburn AL 36849 USA

ISBN: (纸本)9781424492688

A femtocell is a small cellular base station (BS), typically used for serving approved users within a small coverage. In this paper, we investigate the problem of data multicast in femtocell networks that incorporates superposition coding (SC) and successive interference cancellation (SIC). The problem is to decide the transmission schedule for each BS, as well as the power allocation for the SC layers, to achieve a sufficiently large SNR for each layer to be decodable with SIC. The objective is to minimize the total BS power consumption. We formulate a mixed integer nonlinear programming (MINLP) problem, which is NP-hard in general. We then reformulate the problem into a simpler form, and derive upper and lower performance bounds. Finally, we consider three typical connection scenarios in the femtocell network, and develop optimal and near-optimal algorithms for the three scenarios. The proposed algorithms have low computational complexity, and outperform a heuristic scheme with considerable gains in our simulation study.

关键词： BS power consumption Bandwidth Base stations Femtocell networks Heuristic algorithms MINLP problem NP-hard problem Power demand Resource management Silicon carbide computational complexity data multicast femtocellular networks femtocellular radio heuristic programming heuristic scheme integer programming interference suppression low computational complexity lower performance bounds mixed integer nonlinear programming multicast communication near-optimal algorithms network coding nonlinear programming power allocation scheduling small cellular base station successive interference cancellation approach superposition coding transmission scheduling upper performance bounds

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A complete software package for transformer design optimization and economic evaluation analysis

A complete software package for transformer design optimizat...

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6th Japanese-Mediterranean Workshop on Applied Electromagnetic Engineering for Magnetic Superconducting and Nanomaterials

作者： Amoiralis, Eleftherios I. Georgilakis, Pavlos S. Tsili, Marina A. Kladas, Antonios G. Souflaris, Athanassios T. Tech Univ Crete Dept Prod Engn & Management GR-73100 Khania Greece Natl Tech Univ Athens Fac Elect & Comp Engn GR-15780 Athens Greece Schneider Elect AE GR-32011 Viotia Greece

ISBN: (纸本)9780878492152

In the present paper, a Transformer Design Optimization (TDO) software package is developed providing a user-friendly transformer design and visualization environment. This software consists of a collection of design optimization, visualization and verification tools, able to provide transformer designers all the proper interactive capabilities required for the enhancement of the automated design process of a manufacturing industry.

关键词： Distribution Transformer Transformer Design Optimization mixed integer nonlinear programming Software Package Transformer Specifications Manufacturing Cost Total Owning Cost Finite Element Method Visualization Tools Graphical User Interface

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Network Power Management: models and heuristic approaches

Network Power Management: models and heuristic approaches

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54th Annual IEEE Global Telecommunications Conference (GLOBECOM)

作者： Garroppo, Rosario G. Giordano, Stefano Nencioni, Gianfranco Scutella, Maria Grazia Univ Pisa Dip Ingn Informaz I-56100 Pisa Italy Univ Pisa Dipartimento Informat Pisa Italy

ISBN: (纸本)9781424492688

The paper describes and compares different approaches that can be used to design Network Power Management methods, with the aim of reducing the power consumption of telecommunication networks. The approaches are based on the solution of optimization problems that have, in general, a mixed integer nonlinear programming (MINLP) formulation. Given that the problems are NP-hard, exact methods for finding optimal solutions can be used only for scenarios of limited size. In this framework, the paper proposes a heuristic for finding a suboptimal solution of the Power Aware Routing and Network Design (PARND) problem, which is one of the more general design problems in Network Power Management. The simulation study highlights the capability of the proposed heuristic to obtain solutions near the optimum and to outperform the other approaches in terms of energy savings, while satisfying the constraints of the traffic demands.

关键词： Equations Green products NP-hard problems Network topology PARND problem Peer to peer computing Power demand Routing Switches heuristic approach integer programming mixed integer nonlinear programming network power management nonlinear programming optimization power aware routing and network design power consumption telecommunication network management telecommunication network routing

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Modeling and Multi-objective Optimization of Refinery Hydrogen Network

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Chinese Journal of Chemical Engineering 2011年第6期19卷 990-998页

作者：焦云强苏宏业廖祖维侯卫锋 State Key Laboratory of Industrial Control Technology Institute of Cyber-Systems and Control Zhejiang University Hangzhou 310027 China State Key Laboratory of Chemical Engineering Department of Chemical and Biological Engineering Zhejiang University Hangzhou 310027 China Zhejiang ＂Supcon Software Co. Ltd. Hangzhou 310053 China

The demand of hydrogen in oil refinery is increasing as market forces and environmental legislation, so hydrogen network management is becoming increasingly important in refineries. Most studies focused on single-objective optimization problem for the hydrogen network, but few account for the multi-objective optimization problem. This paper presents a novel approach for modeling and multi-objective optimization for hydrogen network in refineries. An improved multi-objective optimization model is proposed based on the concept of superstructure. The optimization includes minimization of operating cost and minimization of investment cost of equipment. The proposed methodology for the multi-objective optimization of hydrogen network takes into account flow rate constraints, pressure constraints, purity constraints, impurity constraints, payback period, etc. The method considers all the feasible connections and subjects this to mixed-integer nonlinear programming （MINLP）. A deterministic optimization method is applied to solve this multi-objective optimization problem. Finally, a real case study is intro-duced to illustrate the applicability of the approach.

关键词： refinery multi-objective optimization hydrogen network mixed integer nonlinear programming

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OPTIMIZATION STRATEGIES FOR THE VULNERABILITY ANALYSIS OF THE ELECTRIC POWER GRID

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SIAM JOURNAL ON OPTIMIZATION 2010年第4期20卷 1786-1810页

作者： Pinar, Ali Meza, Juan Donde, Vaibhav Lesieutre, Bernard Sandia Natl Labs Dept Informat & Decis Sci Livermore CA 94550 USA Univ Calif Berkeley Lawrence Berkeley Lab High Performance Comp Res Dept Berkeley CA 94720 USA ABB Inc Corp Res Ctr Raleigh NC 27606 USA Univ Calif Berkeley Lawrence Berkeley Lab Environm Energy Technol Div Berkeley CA 94720 USA Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA

Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a bilevel mixed integer nonlinear programming problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) and the Laplacian matrix in spectral graph theory (a representation of the graph of the power grid). The reduced combinatorial problem is known as the network inhibition problem, for which we present a mixed integer linear programming formulation. Our experiments on benchmark power grids show that the reduced combinatorial model provides an accurate approximation, to enable vulnerability analyses of real-sized problems with more than 16,520 power lines.

关键词： mixed integer nonlinear programming network inhibition network flow mixed integer linear programming electric power flow network vulnerability graph theory

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Global optimization of mass and property integration networks with in-plant property interceptors

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CHEMICAL ENGINEERING SCIENCE 2010年第15期65卷 4363-4377页

作者： Napoles-Rivera, Fabricio Maria Ponce-Ortega, Jose El-Halwagi, Mahmoud M. Jimenez-Gutierrez, Arturo Inst Tecnol Celaya Dept Chem Engn Celaya Gto Mexico Univ Michoacana Dept Chem Engn Morelia Mich Mexico Texas A&M Univ Dept Chem Engn College Stn TX 77843 USA

This paper presents a mathematical programming model for the optimal design of mass and property integration networks that include property interceptors with in the structure of the network, as opposed to the end-of-pipe use of such interceptors. The model is based on are cycle and reuse scheme that simultaneously satisfies process and environmental constraints. The properties considered in this work are composition, toxicity, theoretical oxygen demand, pH, density and viscosity. The property mixing rules included in the model give rise to bilinear terms for the property operators, and a global optimization algorithm is used for the solution of the model. The model minimizes the total annual cost of the network, which includes the fresh sources cost and the annualized property treatment system and the piping costs. Three examples are included to show the applicability and advantages of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Mass integration Property integration mixed integer nonlinear programming Mathematical modeling Optimization Chemical processes Design

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The multi-product newsboy problem with supplier quantity discounts and a budget constraint

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期206卷 350-360页

作者： Zhang, Guoqing Univ Windsor Dept Ind & Mfg Syst Engn Windsor ON N9B 3P4 Canada

This paper considers the multi-product newsboy problem with both supplier quantity discounts and a budget constraint, while each feature has been addressed separately in the literature. Different from most previous nonlinear optimization models on the topic, the problem is formulated as a mixed integer nonlinear programming model due to price discounts. A Lagrangian relaxation approach is presented to solve the problem. Computational results on both small and large-scale test instances indicate that the proposed algorithm is extremely effective for the problem. An extension to multiple constraints and preliminary computational results are also reported. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Inventory Newsboy model Quantity discount Budget constraint Lagrangian relaxation mixed integer nonlinear programming

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Modeling without categorical variables: a mixed-integer nonlinear program for the optimization of thermal insulation systems

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OPTIMIZATION AND ENGINEERING 2010年第2期11卷 185-212页

作者： Abhishek, Kumar Leyffer, Sven Linderoth, Jeffrey T. Argonne Natl Lab Div Math & Comp Sci Argonne IL 60439 USA United Airlines Enterprise Optimizat Elk Grove Village IL 60007 USA Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA

Optimal design applications are often modeled by using categorical variables to express discrete design decisions, such as material types. A disadvantage of using categorical variables is the lack of continuous relaxations, which precludes the use of modern integer programming techniques. We show how to express categorical variables with standard integer modeling techniques, and we illustrate this approach on a load-bearing thermal insulation system. The system consists of a number of insulators of different materials and intercepts that minimize the heat flow from a hot surface to a cold surface. Our new model allows us to employ black-box modeling languages and solvers and illustrates the interplay between integer and nonlinear modeling techniques. We present numerical experience that illustrates the advantage of the standard integer model.

关键词： mixed integer nonlinear programming Modeling with binary variables Thermal insulation systems Categorical variables

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Aggregate models based on improved group methods for simulation and optimization of distillation systems

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COMPUTERS & CHEMICAL ENGINEERING 2010年第8期34卷 1312-1319页

作者： Kamath, Ravindra S. Grossmann, Ignacio E. Biegler, Lorenz T. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

This note deals with aggregate models for complex distillation systems in large-scale flowsheets. Group methods were originally devised for simple absorber and stripper calculations with no major extensions for handling distillation. In this work, group methods are systematically analyzed and further improved by modifying some of the previously proposed approximations. As a result, the improved group method exhibits accurate predictions and this is demonstrated using simulation and optimization case studies for a variety of chemical systems and operating conditions. It is observed that the prediction of output variables is in close agreement with that of the rigorous equilibrium stage model. In case of optimization problems, the optimal number of trays and feed locations differ by only one or two trays. The aggregate model can be applied in a sequence of steps in order to improve the reliability and robustness of the solution procedure. A rounding heuristic is also proposed which can provide near-optimal solutions with a significant reduction in computational time. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Optimal distillation design Aggregate design models nonlinear programming mixed integer nonlinear programming

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