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Lagrangian Cardinality Cuts and Variable Fixing for Capacitated Network Design [chapter]

Meinolf Sellmann, Georg Kliewe, Achim Kobe stein
2002 Lecture Notes in Computer Science  
Different variable fixing algorithms based on Lagrangian relaxations are evaluated solitarily and in combined versions.  ...  We present a branch-and-bound approach for the Capacitated Network Design Problem. We focus on tightening strategies such as variable fixing and local cuts that can be applied in every search node.  ...  In accordance to the results reported in [11] , we found that the knapsack relaxation is clearly superior both with respect to the number of subgradient iterations needed to solve the Lagrangian dual  ... 
doi:10.1007/3-540-45749-6_73 fatcat:5yqytyn6czapbaemorrddgr2qy

Decomposition Methods for Network Design

Bernard Gendron
2011 Procedia - Social and Behavioral Sciences  
and operational costs, the multicommodity aspect, and the presence of capacity constraints.  ...  We focus on mathematical programming approaches for the MCND and present three classes of methods that have been used to solve large-scale instances of the MCND: a cutting-plane method, a Benders decomposition  ...  The combinatorial explosion observed when increasing the number of arcs also limits the size of the problems that can be solved.  ... 
doi:10.1016/j.sbspro.2011.08.006 fatcat:nl52757ejbaelamj6noa4i6aoe

A Capacitated Location-Inventory Model with Demand Selection

Zhengyi Li, Jiangtao Hai
2019 Journal of Advanced Transportation  
We develop an efficient algorithm to solve the subproblem that arises from the Lagrangian relaxation procedure.  ...  We formulate the problem as a nonlinear integer programming model and solve the model via a Lagrangian relaxation based approach.  ...  Acknowledgments This research is supported by Humanity and Social Science Youth Foundation of the Ministry of Education of China (No. 14YJC630078).  ... 
doi:10.1155/2019/2143042 fatcat:f36xwwfqq5dlblqi2oxtrcxdha

A Lagrangian-Based Branch-and-Bound Algorithm for the Two-Level Uncapacitated Facility Location Problem with Single-Assignment Constraints

Bernard Gendron, Paul-Virak Khuong, Frédéric Semet
2016 Transportation Science  
and Technology, the French Ministry of Higher Education and Research, and the National Center for Scientific Research.  ...  Acknowledgments Financial support for this project was provided by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Fonds de recherche du Québec en nature et technologies  ...  The Lagrangian dual is solved with a fast two-step heuristic; in the first step, the LP relaxation is solved, while the second step solves a single Lagrangian subproblem with Lagrange multipliers initialized  ... 
doi:10.1287/trsc.2016.0692 fatcat:a4j55v44yzcabooadn46idwtv4

About Lagrangian Methods in Integer Optimization

Antonio Frangioni
2005 Annals of Operations Research  
It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal solution of the "convexified  ...  It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian  ...  of work from which some of the results presented herein are taken.  ... 
doi:10.1007/s10479-005-3447-9 fatcat:jt4m35zdovdx5c4fdbslzvyl3y

Transmitter Optimization for the Multi-Antenna Downlink With Per-Antenna Power Constraints

Wei Yu, Tian Lan
2007 IEEE Transactions on Signal Processing  
Further, it is shown that various notions of uplink-downlink duality may be unified under a Lagrangian duality framework.  ...  with its own power amplifier and is limited individually by the linearity of the amplifier.  ...  The idea is to solve its Lagrangian dual problem (20) directly using an interior-point method.  ... 
doi:10.1109/tsp.2006.890905 fatcat:ianwssvmrjfa5pvpnug5yy5aze

Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design

Bernard Gendron, Mathieu Larose
2014 EURO Journal on Computational Optimization  
The pricing subproblem corresponds to a Lagrangian relaxation of the flow conservation and capacity constraints, leaving in the Lagrangian subproblem only the strong inequalities.  ...  We present a branch-and-price-and-cut algorithm for solving large-scale instances of the multicommodity capacitated fixed-charge network design problem.  ...  Acknowledgments Funding for this project has been provided by the Natural Sciences and Engineering Council of Canada (NSERC). This support is gratefully acknowledged.  ... 
doi:10.1007/s13675-014-0020-9 fatcat:kskxrjfmk5drnmqektl3crspde

Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem

Lucas Létocart, Anass Nagih, Gérard Plateau
2012 Computers & Operations Research  
It appears that the computation of these Lagrangian dual bounds involves the resolution of numerous 0-1 linear knapsack subproblems.  ...  Thus, taking this huge number of solvings into account, we propose to embed reoptimization techniques for improving the efficiency of the preprocessing phase of the 0-1 quadratic knapsack resolution.  ...  and iter the number of iterations of the subgradient procedure for solving the Lagrangian dual (we denote by p the number of knapsack problems solved at each iteration).  ... 
doi:10.1016/j.cor.2010.10.027 fatcat:hzssrwywprex5pupa57f7absk4

An Improved Subgradiend Optimization Technique for Solving IPs with Lagrangean Relaxation

M Babul Hasan, Md Toha
2013 Dhaka University Journal of Science  
The objective of this paper is to improve the subgradient optimization method which is used to solve non-differentiable optimization problems in the Lagrangian dual problem.  ...  It is well known that the dual function is a concave function over its domain (regardless of the structure of the cost and constraints of the primal problem), but not necessarily differentiable.  ...  It may be noted that when m constraints that have been dualized are equality constraints of the form , the corresponding Lagrangian multipliers are unrestricted in sign and the Lagrangian dual becomes  ... 
doi:10.3329/dujs.v61i2.17059 fatcat:vdkfh3o45nfjvmbgkhbrp5qlk4

Lagrangian relaxation for the time-dependent combined network design and routing problem

Dimitri Papadimitriou, Bernard Fortz, Enrico Gorgone
2015 2015 IEEE International Conference on Communications (ICC)  
Though this approach yields one subproblem per network node, solving the Lagrangian dual by means of the bundle method remains a complex computational tasks.  ...  As an alternative, we propose a Lagrangian approach for computing a lower bound by relaxing the flow conservation constraints such that the Lagrangian subproblem itself decomposes by node.  ...  ACKNOWLEDGMENT The work of B. Fortz is supported by the Interuniversity Attraction Poles Program of the Belgian Science Policy Office.  ... 
doi:10.1109/icc.2015.7249283 dblp:conf/icc/PapadimitriouFG15 fatcat:5tplmiw66rfdxinqhj6vsq3a6u

Design of a Distribution Network Using Primal-Dual Decomposition

J. A. Marmolejo, R. Rodríguez, O. Cruz-Mejia, J. Saucedo
2016 Mathematical Problems in Engineering  
A method to solve the design of a distribution network for bottled drinks company is introduced.  ...  This approach allows exploring simultaneously the primal and dual subproblems of the original problem.  ...  To generate the dual subproblem we relax the cross-dock balance constraint (4) . is the Lagrangian multiplier of dualized constraint (4).  ... 
doi:10.1155/2016/7851625 fatcat:ilxaewcthjckjn7utk4wpkype4


Junyoung Kwak, Taeyoung Chun, Haeseong Cho, Sangjoon Shin, Olivier A. Bauchau
2014 Journal of the Korea Society for Industrial and Applied Mathematics  
For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition.  ...  It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.  ...  It is found that when the number of the sub-domains is fixed, the proposed FETI-local algorithm is advantageous in terms of computation.  ... 
doi:10.12941/jksiam.2014.18.017 fatcat:ykajaignpnehfl3ti2w2f6hghe

An efficient heuristic approach to solve the unate covering problem

R. Cordone, F. Ferrandi, D. Sciuto, R.W. Calvo
2001 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
We adopt this approach, but we propose a constructive heuristic algorithm that combines the use of Binary Decision Diagrams with the lagrangian relaxation.  ...  On the problems whose optimum is actually unknown, the best known result is strongly improved.  ...  In addition, we wish to thank the anonymous DATE-2000 reviewers for their useful comments on an earlier draft of this paper.  ... 
doi:10.1109/43.969431 fatcat:2qelrekw5vcejjobkvkfqnoyna

An efficient heuristic approach to solve the unate covering problem

Roberto Cordone, Fabrizio Ferrandi, Donatella Sciuto, Roberto Wolfler Calvo
2000 Proceedings of the conference on Design, automation and test in Europe - DATE '00  
We adopt this approach, but we propose a constructive heuristic algorithm that combines the use of Binary Decision Diagrams with the lagrangian relaxation.  ...  On the problems whose optimum is actually unknown, the best known result is strongly improved.  ...  In addition, we wish to thank the anonymous DATE-2000 reviewers for their useful comments on an earlier draft of this paper.  ... 
doi:10.1145/343647.343799 fatcat:ppvo66odkvectpshnke5vadmnm

An Applications Oriented Guide to Lagrangian Relaxation

Marshall L. Fisher
1985 Interfaces  
In this tutorial, Marshall Fisher provides a practical guide to the use of the approach with many examples and illustrations.  ...  Lagrangian relaxation is a tool that is increasingly being used in large-scale mathematical programming applications, such as last year's CPMS/TIMS Management Achievement Award winner (Bell et al. 1983  ...  The paper has also benefited from a careful reading by the referee, Terry Harrison, and was supported in part by NSF Grant ECS 82-05 438 to the University of Pennsylvania.  ... 
doi:10.1287/inte.15.2.10 fatcat:w23jvut3w5hgpmamm6qmiryo3u
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