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Routing in grid graphs by cutting planes

ZOR Zeitschrift für Operations Research Mathematical Methods of Operations Research 1995年第3期41卷 255-275页

作者： Grötschel, Martin Martin, Alexander Weismantel, Robert Konrad-Zuse-Zentrum Berlin-Wilmersdorf 10711 Heilbronner Str. 10 Germany

In this paper we study the following problem, which we call the weighted routing problem. Let be given a graph G = (V, E) with non-negative edge weights we ∈ ℝ+ and let N, N ≥ 1, be a list of node sets. The weighted... 详细信息

In this paper we study the following problem, which we call the weighted routing problem. Let be given a graph G = (V, E) with non-negative edge weights w_e ∈ ℝ₊ and let N, N ≥ 1, be a list of node sets. The weighted routing problem consists in finding mutually disjoint edge sets S₁,..., S_N such that, for each k ∈ {1, ..., N}, the subgraph (V(S_k), S_k) contains an [s, t]-path for all s, t ∈ T_k and the sum of the weights of the edge sets is minimal. Our motivation for studying this problem arises from the routing problem in VLSI-design, where given sets of points have to be connected by wires. We consider the weighted routing problem from a polyhedral point of view. We define an appropriate polyhedron and try to (partially) describe this polyhedron by means of inequalities. We describe our separation algorithms for some of the presented classes of inequalities. Based on these separation routines we have implemented a branch and cut algorithm. Our algorithm is applicable to an important subclass of routing problems arising in VLSI-design, namely to switchbox routing problems where the underlying graph is a grid graph and the list of node sets is located on the outer face of the grid. We report on our computational experience with this class of problem instances. © 1995 Physica-Verlag.

关键词： cutting plane algorithm Routing in VLSI-design Steiner Tree Steiner Tree Packing Switchbox Routing

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Numerical Analysis of Metal Powders in Uniaxial Compaction

Numerical Analysis of Metal Powders in Uniaxial Compaction

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6th International Latin American Conference on Power Technology

作者： Schaerer, Magna Monteiro Roehl, Deane Silveira, Jose Luis Univ Fed Rio de Janeiro DEM COPPE POB 68503 BR-21945970 Rio de Janeiro Brazil PUC Rio Rua Marques Sao Vicente BR-22453900 Rio De Janeiro Brazil

ISBN: (纸本)9780878493609

Powder consolidation constitutes an important step in the manufacture of products of high quality and precision. To obtain these components, with desired forms and final mechanical properties, it is of extreme importance to have knowledge about the processes to obtain powders, compacting and sintering. The objective of this work is to verify which model, obtained from the literature, better describes the compaction densification behavior of iron powder in closed-die. Doraivelu's criterion was carried through the method of the finite elements with the implementation of an elastoplastic model with hardening. The influence of the yield function coefficient against the relative density was evaluated, as well as, the yield function in the hydrostatic space.

关键词： Metal powder Compaction Plasticity cutting plane algorithm Friction Finite Element Method

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Statistical Power Optimization of Deep-Submicron Digital CMOS Circuits Based on Structured Perceptron 14

Statistical Power Optimization of Deep-Submicron Digital CMO...

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14 International Symposium on Integrated Circuits (ISIC)

作者： Zjajo, Amir van der Meijs, Nick van Leuken, Rene Delft Univ Technol Circuits & Syst Grp Mekelweg 4 NL-2628 CD Delft Netherlands

ISBN: (纸本)9781479948338

The effect of process variability on power and performance of integrated circuits can only be reduced with statistical optimization techniques. In this paper, we examine optimum V-DD-V-T design for minimizing power in deep-submicron CMOS circuits and introduce highly-efficient algorithm for yield constrained optimum power operation to include the impact of process variability and avoid the limitations of commonly employed deterministic optimization techniques. The yield constraint becomes active as the optimization concludes, eliminating the problem of overdesign in worst-case approach. The experimental results, obtained with ISCAS'85 circuits implemented in UMC 1P8M 65nm technology, demonstrate feasibility of the method.

关键词： statistical yield constrained optimization minimum power operation cutting plane algorithm

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An exact algorithm for identical parallel machine scheduling under scenarios 3

An exact algorithm for identical parallel machine scheduling...

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3rd World Conference on Mechanical Engineering and Intelligent Manufacturing (WCMEIM)

作者： Xie Han-Xin Wang Bing Shanghai Univ Sch Mechatron Engn & Automat Shanghai Peoples R China

ISBN: (纸本)9781665441094

This paper discusses an uncertain identical parallel machine scheduling problem. Discrete scenario set is used to describe the uncertain processing times in actual production conditions. Objective of this problem is to minimize the mean makespan among all scenarios, which reflects solution optimality in uncertain environment. The concept of mean scenario is defined in this paper and is used to transform the model of mean makespan under scenarios into traditional deterministic identical parallel machine problem. The cutting plane algorithm is used on the basis of the mean scenario to solve the problem. The developed algorithm was applied in extensive test cases, involving different sizes and parameters. The computational results show that this proposed algorithm can solve this parallel machine model in reasonable time and can be applied in practical problems.

关键词： manufacturing discrete scenarios identical parallel machine scheduling cutting plane algorithm exact algorithm

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Robust Unit Commitment Problem with Demand Response and Wind Energy

Robust Unit Commitment Problem with Demand Response and Wind...

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General Meeting of the IEEE-Power-and-Energy-Society

作者： Zhao, Long Zeng, Bo Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA

ISBN: (纸本)9781467327299

Currently, both demand response (DR) strategy and renewable energy have been adopted to improve power generation efficiency and reduce greenhouse gas emission. However, the uncertainty and intermittent generation pattern in wind farms and the complexity of demand side management pose huge challenges. In this paper, we analytically investigate how to integrate DR and wind energy with fossil fuel generators to (i) minimize power generation cost;and (2) fully take advantage of the wind energy with the managed demand to reduce greenhouse emission. We first build a two-stage robust unit commitment (UC) model to obtain day-ahead generator schedules where wind uncertainty is captured by a polytopic uncertainty set. Then, we extend our model to include DR strategy such that both price levels and generator schedules will be derived for the next day. For these two challenging models, we derive their mathematical properties and develop a novel solution method. Our computational study on an IEEE 118-bus system with 36 units shows that robust UC models can fully make use of wind generation with less generation cost. Also, the developed algorithm is computationally superior to classical Benders decomposition method.

关键词： unit commitment problem robust optimization cutting plane algorithm

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Adaptive Robust Optimal Reactive Power Dispatch in Distribution Networks

Adaptive Robust Optimal Reactive Power Dispatch in Distribut...

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2017 IEEE Power & Energy Society General Meeting

作者： Li, Peishuai Wu, Zaijun Hu, Minqiang Dou, Xiaobo Wang, Yang Southeast Univ Sch Elect Engn Nanjing Jiangsu Peoples R China State Grid Jiangsu Econ Res Inst Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781538622124

It is increasing popular to integrate distributed generation (DG) into distribution systems, the traditional optimal reactive power dispatch approach is no longer able to cope with it. The robust optimization (RO) theory is introduced to deal with the uncertainty of large-scale DGs. Adaptive robust optimal reactive power dispatch (AR-OPRD) is proposed to reduce the conservation of RO. An adaptive function is constructed to derive the relationship between the optimal reactive power output and active power output of an arbitrary DG. A new cutting plane algorithm is introduced to solve AR-ORPD mathematical model efficiently. In this paper, examples have been used to demonstrate the validity and effectiveness of the method.

关键词： Adaptive robust optimization optimal reactive power dispatch uncertainty cutting plane algorithm

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Advanced feasibility cuts in decoupled cooperative optimization of power flow

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COMPUTERS & CHEMICAL ENGINEERING 2022年 157卷 107635-107635页

作者： Varelmann, Tim Lipow, Adrian W. Baldea, Michael Mitsos, Alexander Rhein Westfal TH Aachen Proc Syst Engn AVT SVT D-52074 Aachen Germany Univ Texas Austin McKetta Dept Chem Engn Austin TX 78712 USA Univ Texas Austin Oden Inst Computat Engn & Sci Austin TX 78712 USA JARA CSD D-52056 Aachen Germany Forschungszentrum Julich Inst Energy & Climate Res Energy Syst Engn IEK 10 D-52425 Julich Germany

Solving the optimal power flow problem in a cooperative way between power generators and industrial users can reduce electricity costs more effectively than price-based demand side management. In previous work, we recently developed a decomposition-based algorithm based on Benders-type cuts to solve cooperative optimal power flow problems, which allows to protect sensitive load information. However, the algorithm suffers from unfavorable scaling behavior when the number of cooperating load entities increases. Herein, we improve the quality of the cutting planes that cooperating electricity users generate for the grid in lieu of sharing their dynamic process models. After comparing different cutting strategies and combinations thereof, we develop a tailored cutting strategy. This strategy improves the scaling behavior of our decomposition-based algorithm with multiple cooperating electricity user locations drastically. We obtain speedups factors up to almost 60 compared to our algorithm with the initial cutting strategy. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Demand-side management Cooperative optimal power flow Congestion management cutting plane algorithm

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Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes

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RAIRO-OPERATIONS RESEARCH 2021年第1-Sup期55卷 S1747-S1765页

作者： Berghman, Lotte Spieksma, Frits C. R. T'kindt, Vincent TBS Business Sch 20 BD Lascrosses BP 7010 F-31068 Toulouse 7 France TU Eindhoven Dept Math & Comp Sci NL-5600 MB Eindhoven Netherlands Univ Tours Lab Informat Fondamentale & Appl EA 6300 ERL CNRS 7002 ROOT 64 Ave Jean Portalis F-37200 Tours France

We consider a time-indexed formulation for the unrelated parallel machine scheduling problem. We show that all polyhedral knowledge known from the single machine problem (in particular, valid inequalities) is applicable to this formulation. We present new facet-inducing valid inequalities and a preprocessing technique involving fixing variables based on reduced costs. We combine both techniques in a basic cutting-plane algorithm and test the performance of the resulting algorithm by running it on randomly generated instances.

关键词： Unrelated machine scheduling time-indexed formulation valid inequalities cutting plane algorithm variable fixing

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Extracting maximal objects from three-dimensional solid materials

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COMPUTERS & OPERATIONS RESEARCH 2021年 132卷 105290-105290页

作者： Silva, Everton Fernandes Calik, Hatice Vancroonenburg, Wim Leao, Aline Aparecida Souza Wauters, Tony Katholieke Univ Leuven Dept Comp Sci CODeS Gebroeders Smetstr B-9000 Ghent Belgium

In the problem of extracting maximal items/objects from three-dimensional materials, we are given a piece of solid material and an object with predefined ratios. The goal is to extract the largest possible convex or nonconvex object from the solid material. There are two variants of the problem: the general case where the solid material is non-convex and its special case consisting of a convex solid material. We propose a matheuristic approach for solving both problems. For the special case, the problem is also modeled as a non-linear programming formulation. Meanwhile, for the general case a mixed integer linear programming formulation is provided based on the decomposition of the non-convex material into a finite number of convex regions. Computational experiments evaluate the performance of both models for small-scale instances considering objects with at most 1400 and 370 vertices for the special and general case, respectively. We observe that the required computational effort increases with the number of vertices of the objects, therefore, it is also evaluated the efficiency of the proposed matheuristic approach for more complicated instances, considering objects with a higher number of vertices. In order to establish benchmark instances for future research, all instances used are publicly available.

关键词： Maximal packing cutting plane algorithm Matheuristic

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LMI CONSTRAINT FOR PHASE CONTROL OF BENDING MODES: APPLICATION TO THE ATTITUDE CONTROL OF A SATELLITE

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IFAC Proceedings Volumes 2007年第7期40卷 341-346页

作者： Mohamed ABBAS-TURKI Gilles DUC Massimiliano MAINI école Normale Supérieure de Cachan Laboratory SATIE 61 av du Président Wilson 94235 CACHAN Cedex France Ecole Supérieure d'électricité Automatic Control Department 3 rue Joliot-Curie 91192 Gif-sur-Yvette Cedex France Alcatel Space 100 bd du Midi BP99 06156 Cannes la Bocca Cedex France

When designing a controller, the conflict between various specifications can become very hard so that the feasibility of the control problem becomes an important question. One of the main dilemmas in satellite control is the conflict between the need to increase the bandwidth (in order to improve the time domain performances) and the instability brought by flexible modes (which are located more and more in low frequencies). To solve this problem the bending modes should be controlled in phase, by guaranteeing a sufficient phase margin for the controlled plant. Although there are different works giving a solution of the phase margin specification, the use of other classical criterion leads to poles-zeros compensations, resulting in a high sensibility to uncertainties. In this context, this paper presents a procedure based on convex constraints to control the phase of flexible modes together with handling other robust and performance objectives. The approach proposed in this work associates LMI formulations, the Youla parameterization and a cutting plane algorithm; it enables to decide on the feasibility of the problem and gives a corresponding controller.

关键词： Mutiobjective control LMI cutting plane algorithm Youla parameterization flexible satellite

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