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On the properties of general dual-feasible functions

On the properties of general dual-feasible functions

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14th international conference on Computational Science and Its Applications, ICCSA 2014

作者： Rietz, Jürgen Alves, Cláudio De Carvalho, José Manuel Valério Clautiaux, François Escola de Engenharia Universidade Do Minho 4710-057 Braga Portugal Institut de Mathématiques de Bordeaux Université de Bordeaux 33405 Talence Cedex France

ISBN: (纸本)9783319091280

Dual-feasible functions have been used to compute fast lower bounds and valid inequalities for integer linear optimization problems. However, almost all the functions proposed in the literature are defined only for positive arguments, which restricts considerably their applicability. the characteristics and properties of dual-feasible functions with general domains remain mostly unknown. In this paper, we show that extending these functions to negative arguments raises many issues. We explore these functions in depth with a focus on maximal functions, i.e. the family of non-dominated functions. the knowledge of these properties is fundamental to derive good families of general maximal dual-feasible functions that might lead to strong cuts for integer linear optimization problems and strong lower bounds for combinatorial optimization problems with knapsack constraints. © 2014 Springer international Publishing.

关键词： integer programming

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A mixed integer programming model for multi-period dyeing and batching problem in a yarn plant 44

A mixed integer programming model for multi-period dyeing an...

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Joint international Symposium on "the Social Impacts of Developments in Information, Manufacturing and Service Systems" 44th international conference on Computers and Industrial Engineering, CIE 2014 and 9th international Symposium on Intelligent Manufacturing and Service Systems, IMSS 2014

作者： Ozturk, C. Ornek, A. Insight Centre for Data Analytics University College Cork Cork Ireland Department of Industrial Engineering Izmir University of Economics Turkey

In a so-called multi-period yarn dyeing and batching problem, we try to determine the optimal batching of customer orders to be dyed in dye machines in each shift to minimize total lateness and earliness costs. In addition to weight, production quantity and volume capacity of the machines, there is a set of technical dyeing interaction constraints such as flotte, colour types, colour percentages and chemical recipe of customer orders when yarns are immersed in a large vat of coloured water known as the dye-liquor that includes dyestuffs, plus a range of chemicals to assist the dyeing process in the same shift. Furthermore, because of multi-period multi-shift nature of the problem, there is a setup carryover restriction which enforces that from shift to shift the colours must be processed in the increasing degree of darkness, i.e., in technical terms, the colour percentage of the batch increases. To the best of our knowledge, there is no study in the literature to solve this combinatorial optimization problem. Hence, in this paper, we first develop a novel mixed integer programming (MIP) formulation and then, we present a case study in a worldwide known yarn manufacturing company.

关键词： Yarn

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Linear programming hierarchies suffice for directed steiner tree

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17th international conference on integer programming and combinatorial optimization, IPCO 2014

作者： Friggstad, Zachary Könemann, Jochen Kun-Ko, Young Louis, Anand Shadravan, Mohammad Tulsiani, Madhur Department of Computing Science University of Alberta Canada Department of Combinatorics and Optimization University of Waterloo Canada Department of Computer Science Princeton University United States College of Computing Georgia Tech. United States Toyota Technical Institute at Chicago United States

ISBN: (纸本)9783319075563

We demonstrate that rounds of the Sherali-Adams hierarchy and 2 rounds of the Lovász-Schrijver hierarchy suffice to reduce the integrality gap of a natural LP relaxation for Directed Steiner Tree in -layered graphs from ω (√k) to O(·logk) where k is the number of terminals. this is an improvement over Rothvoss' result that 2 rounds of the considerably stronger Lasserre SDP hierarchy reduce the integrality gap of a similar formulation to O(·logk). We also observe that Directed Steiner Tree instances with 3 layers of edges have only an O(logk) integrality gap in the standard LP relaxation, complementing the known fact that the gap can be as large as ω (√k) in graphs with 4 layers. © 2014 Springer international Publishing Switzerland.

关键词： Linear programming

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Efficient image and video co-localization with Frank-Wolfe algorithm

Efficient image and video co-localization with Frank-Wolfe a...

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13th European conference on Computer Vision, ECCV 2014

作者： Joulin, Armand Tang, Kevin Fei-Fei, Li Computer Science Department Stanford University United States

ISBN: (纸本)9783319105987

In this paper, we tackle the problem of performing efficient co-localization in images and videos. Co-localization is the problem of simultaneously localizing (with bounding boxes) objects of the same class across a set of distinct images or videos. Building upon recent state-of-the-art methods, we show how we are able to naturally incorporate temporal terms and constraints for video co-localization into a quadratic programming framework. Furthermore, by leveraging the Frank-Wolfe algorithm (or conditional gradient), we show how our optimization formulations for both images and videos can be reduced to solving a succession of simple integer programs, leading to increased efficiency in both memory and speed. To validate our method, we present experimental results on the PASCAL VOC 2007 dataset for images and the YouTube-Objects dataset for videos, as well as a joint combination of the two. © 2014 Springer international Publishing.

关键词： Quadratic programming

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Optimal Control Formulations for the Unit Commitment Problem 1

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5th international conference on the Dynamics of Information Systems

作者： Fontes, Dalila B. M. M. Fontes, Fernando A. C. C. Roque, Luis A. C. Univ Porto LIAAD INESC TEC Rua Dr Roberto Frias P-4200464 Oporto Portugal Univ Porto Rua Dr Roberto Frias Inst Sistemas Robot Porto Fac Engn P-4200465 Porto Portugal Inst Super Engenharia Porto Dept Matemat Porto Portugal

ISBN: (数字)9783319100463

ISBN: (纸本)9783319100456

the unit commitment (UC) problem is a well-known combinatorial optimization problem arising in operations planning of power systems. It involves deciding both the scheduling of power units, when each unit should be turned on or off, and the economic dispatch problem, how much power each of the on units should produce, in order to meet power demand at minimum cost while satisfying a set of operational and technological constraints. this problem is typically formulated as nonlinear mixed-integer programming problem and has been solved in the literature by a huge variety of optimization methods, ranging from exact methods (such as dynamic programming and branch-and-bound) to heuristic methods (genetic algorithms, simulated annealing, and particle swarm). Here, we discuss how the UC problem can be formulated with an optimal control model, describe previous discrete-time optimal control models, and propose a continuous-time optimal control model. the continuous-time optimal control formulation proposed has the advantage of involving only real-valued decision variables (controls) and enables extra degrees of freedom as well as more accuracy, since it allows to consider sets of demand data that are not sampled hourly.

关键词： Unit commitment problem Power systems planning Nonlinear optimization Mixed-integer programming Optimal control

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On the unique-lifting property

引用

17th international conference on integer programming and combinatorial optimization, IPCO 2014

作者： Averkov, Gennadiy Basu, Amitabh Institute of Mathematical Optimization Faculty of Mathematics University of Magdeburg Germany Department of Applied Mathematics and Statistics Johns Hopkins University United States

ISBN: (纸本)9783319075563

We study the uniqueness of minimal liftings of cut generating functions obtained from maximal lattice-free polytopes. We prove a basic invariance property of unique minimal liftings for general maximal lattice-free polytopes. this generalizes a previous result by Basu, Cornuéjols and Köppe [3] for simplicial maximal lattice-free polytopes, thus completely settling this fundamental question about lifting. We also extend results from [3] for minimal liftings in maximal lattice-free simplices to more general polytopes. these nontrivial generalizations require the use of deep theorems from discrete geometry and geometry of numbers, such as the Venkov-Alexandrov-McMullen theorem on translative tilings, and McMullen's characterization of zonotopes. © 2014 Springer international Publishing Switzerland.

关键词： Topology

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Box-constrained mixed-integer polynomial optimization using separable underestimators

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17th international conference on integer programming and combinatorial optimization, IPCO 2014

作者： Buchheim, Christoph D'Ambrosio, Claudia Fakultät für Mathematik Technische Universität Dortmund Vogelpothsweg 87 44227 Dortmund Germany École Polytechnique 91128 Palaiseau Cedex France

ISBN: (纸本)9783319075563

We propose a novel approach to computing lower bounds for box-constrained mixed-integer polynomial minimization problems. Instead of considering convex relaxations, as in most common approaches, we determine a separable underestimator of the polynomial objective function, which can then be minimized easily over the feasible set even without relaxing integrality. the main feature of our approach is the fast computation of a good separable underestimator;this is achieved by computing tight underestimators monomialwise after an appropriate shifting of the entire polynomial. If the total degree of the polynomial objective function is bounded, it suffices to consider finitely many monomials, the optimal underestimators can then be computed offline and hardcoded. For the quartic case, we determine all optimal monomial underestimators analytically. In the case of pure integer problems, we perform an extensive experimental evaluation of our approach. It turns out that the proposed branch-and-bound algorithm clearly outperforms all standard software for mixed-integer optimization when variable domains contain more than two values, while still being competitive in the binary case. Compared to approaches based on linearization, our algorithm suffers significantly less from large numbers of monomials. It could minimize complete random polynomials on ten variables with domain { - 10,10} in less than a minute on average, while no other approach was able to solve any such instance within one hour of running time. © 2014 Springer international Publishing Switzerland.

关键词： Branch and bound method

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How good are sparse cutting-planes?

引用

17th international conference on integer programming and combinatorial optimization, IPCO 2014

作者： Dey, Santanu S. Molinaro, Marco Wang, Qianyi School of Industrial and Systems Engineering Georgia Institute of Technology United States

ISBN: (纸本)9783319075563

Sparse cutting-planes are often the ones used in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch-&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In order to understand this question better, given a polyope P (e.g. the integer hull of a MIP), let P k be its best approximation using cuts with at most k non-zero coefficients. We consider d(P, P k ) = as a measure of the quality of sparse cuts. In our first result, we present general upper bounds on d(P, P k ) which depend on the number of vertices in the polytope and exhibits three phases as k increases. Our bounds imply that if P has polynomially many vertices, using half sparsity already approximates it very well. Second, we present a lower bound on d(P, P k ) for random polytopes that show that the upper bounds are quite tight. third, we show that for a class of hard packing IPs, sparse cutting-planes do not approximate the integer hull well. Finally, we show that using sparse cutting-planes in extended formulations is at least as good as using them in the original polyhedron, and give an example where the former is actually much better. © 2014 Springer international Publishing Switzerland.

关键词： integer programming

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A hybrid heuristic based on column generation for two- and three- stage bin packing problems

A hybrid heuristic based on column generation for two- and t...

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14th international conference on Computational Science and Its Applications, ICCSA 2014

作者： Alvelos, Filipe Silva, Elsa De Carvalho, José Manuel Valério Centro Algoritmi Departamento de Produção e Sistemas Universidade Do Minho 4710-057 Braga Portugal INESC TEC Campus Da FEUP Rua Dr. Roberto Frias 378 4200-465 Porto Portugal

ISBN: (纸本)9783319091280

We address two two-dimensional bin packing problems where the bins are rectangular and have the same size. the items are also rectangular and all of them must be packed with the objective of minimizing the number of bins. In the first problem, the two-stage problem, the items must be packed in levels. In the second problem, the restricted 3-stage problem, items can be grouped in stacks which are packed in levels. We propose a new decomposition model where subproblems are associated with the item that initializes a bin. the decomposition is solved by a heuristic which combines (perturbed) column generation, local search, beam branch-and-price, and the use of a general purpose mixed integer programming solver. this approach is closely related with SearchCol, a framework for solving integer programming / combinatorial optimization decomposition models. Computational results with 500 instances from the literature show that the proposed hybrid heuristic is efficient in obtaining high quality solutions. It uses more 8 and 17 bins than the 7364 and 7340 bins of a compact model from the literature for the 2 and 3-stage problems, respectively, while the sum of the time spent for all instances is 35% and 58% of the time spent by the compact model. © 2014 Springer international Publishing.

关键词： integer programming

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Adaptive embedded systems: New composed technical solutions for feasible low-power and real-time flexible OS tasks 11

Adaptive embedded systems: New composed technical solutions ...

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11th international conference on Informatics in Control, Automation and Robotics, ICINCO 2014

作者： Chniter, Hamza Khalgui, Mohamed Jarray, Fethi INSAT Institute University of Carthage T-Carthage Tunisia FST Faculty University of Elmanar Elmanar Tunisia ISI Institute Mednine Tunisia Laboratoire CEDRIC CNAM 292 rue St-Martin Paris Cedex 0375141 France

ISBN: (纸本)9789897580390

the paper deals with low-power adaptive scheduling of synchronous and flexible real-time OS tasks. A software reconfiguration scenario is assumed to be any run-time operation allowing the addition-removal-update of OS tasks to adapt the system to its environment under well-defined conditions. the problem is that any reconfiguration can push the system to an unfeasible behavior where temporal properties are violated or the energy consumption is possibly high and unacceptable. A task in the system can change its characteristics at any time when a reconfiguration scenario is applied, it can also be stopped or replaced by another one. the difficulty is how to find the new temporal parameters of the systems tasks after any reconfiguration. We use a DVS processor which is with a variable speed to support run-time solutions that re-obtain the system's feasibility. the challenge is how to compute the best combinations between available processor speeds for a good compromise between execution time and energy consumption. We propose a combinatorial optimization method based on integer programming and heuristics. We propose also a solution when the available speeds do not allow the feasibility of the system. Both approaches include a mechanism to adjust the deadlines of tasks to satisfy the feasibility conditions and overcome the problem of rejected tasks. this mechanism makes the scheduling more flexible and able to react in accordance with its environment.

关键词： integer programming

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