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Lagrangian Smoothing Heuristics for Max-Cut
2005
Journal of Heuristics
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This paper presents a smoothing heuristic for an NP-hard combinatorial problem. ...
Furthermore, to the best of our knowledge, this is the first time that a Lagrangian heuristic is combined with pathfollowing techniques. ...
Kiwiel for making NOA 3.0 available, and Stefan Vigerske, who helped us with the C++ coding and Linux scripting. We also like to thank two anonymous referees for their critics to our first draft. ...
doi:10.1007/s10732-005-3603-z
fatcat:j76ixkqsc5f4tjm2ryv7vrwqgq
On greedy construction heuristics for the MAX-CUT problem
2007
International Journal of Computational Science and Engineering (IJCSE)
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This paper compares the performance of several greedy construction heuristics for MAX-CUT problem. ...
Given a graph with non-negative edge weights, the MAX-CUT problem is to partition the set of vertices into two subsets so that the sum of the weights of edges with endpoints in different subsets is maximized ...
Lagrangian Smoothing Heuristics for Max-Cut. Journal of Heuristics, 11: 447-463, 2005. ...
doi:10.1504/ijcse.2007.017827
fatcat:xh4cchrbczcdpcz3hp7trsy5cq
Heuristics for the multi-item capacitated lot-sizing problem with lost sales
2013
Computers & Operations Research
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To find a good lower bound, we use a Lagrangian relaxation of the capacity constraints, when single-item uncapacitated lot-sizing problems with lost sales have to be solved. ...
To find feasible solutions, we propose a non-myopic heuristic based on a probing strategy and a refining procedure. We propose also some metaheuristic principles to improve solutions. ...
Algorithm 2 2 Lagrangian heuristic Let s L be a Lagrangian solution s * ← Cut(s L ) s ← s L ; iter ← 1 while s is not feasible and iter ≤ M axIter do s ← Improved Smooth(s) s ← Cut(s) if cost(s) < cost ...
doi:10.1016/j.cor.2012.06.010
fatcat:qldjqhy6hjg3jagz6ueuy3g4yy
About Lagrangian Methods in Integer Optimization
2005
Annals of Operations Research
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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 ...
Acknowledgments I'm indebted with Giorgio Gallo, Alberto Borghetti, Fabrizio Lacalandra, Carlo Alberto Nucci, Andrea Lodi, and Giovanni Rinaldi for their fundamental contribution in the various pieces ...
doi:10.1007/s10479-005-3447-9
fatcat:jt4m35zdovdx5c4fdbslzvyl3y
Exact makespan minimization of unrelated parallel machines
2021
Open Journal of Mathematical Optimization
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For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. ...
To improve these bounds and to enable the solution of larger instances, we propose a branch-and-bound method based on a Lagrangian relaxation of the assignment constraints. ...
Finally, we would like to thank the anonymous reviewers for their valuable feedback. ...
doi:10.5802/ojmo.4
fatcat:fbovkv3wibgbtmkjboapxhj4ve
An efficient surrogate subgradient method within Lagrangian relaxation for the Payment Cost Minimization problem
2012
2012 IEEE Power and Energy Society General Meeting
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In the presented methodology the problem structure is exploited using Lagrangian relaxation and the relaxation of the integrality constraints is exploited using branch-and-cut. ...
For large Payment Cost Minimization problems, the method can find significantly better feasible solutions within less CPU time than that obtained by standard branch-and-cut methods implemented in commercial ...
These directions are smooth from one iteration to the next, thus the zigzagging is avoided. ...
doi:10.1109/pesgm.2012.6345529
fatcat:uoz2qxjjnbf5rd43c34ahixlme
A Hybrid Approach of Bundle and Benders Applied Large Mixed Linear Integer Problem
2013
Journal of Applied Mathematics
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In this work, we propose the following algorithm; a Lagrangian relaxation is made on the mentioned set of constraints; we presented a process heuristic for the calculation of the multiplier through the ...
According to the methodology proposed, for each iteration of the algorithm, we propose Benders decomposition where quotas are provided for the value function andε-subgradient. ...
heuristics for selecting cuts, given that the accumulations of all inequalities explode the subproblem. ...
doi:10.1155/2013/678783
fatcat:idpzgyqlkvcxbj642lgqtxye2i
A dual ascent heuristic for obtaining a lower bound of the generalized set partitioning problem with convexity constraints
2019
Discrete Optimization
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The proposed dual ascent heuristic is based on a reformulation and it uses Lagrangian relaxation and subgradient method. ...
In this paper we propose a dual ascent heuristic for solving the linear relaxation of the generalized set partitioning problem with convexity constraints, which often models the master problem of a column ...
Acknowledgement The authors would like to thank the anonymous reviewers and associate editor for their helpful suggestions. ...
doi:10.1016/j.disopt.2019.05.001
fatcat:bxswkzph55hp5obnyyl4z3ds64
A Review on the Performance of Linear and Mixed Integer Two-Stage Stochastic Programming Software
2022
Algorithms
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This paper presents a tutorial on the state-of-the-art software for the solution of two-stage (mixed-integer) linear stochastic programs and provides a list of software designed for this purpose. ...
The best lower bound of (PNAC) is computed by solving the following maximization problem, referred to as the Lagrangian dual problem: Z LD = max λ D(λ) (18) The Lagrangian dual is a concave non-smooth ...
Algorithm 2: Cutting-plane dual search 1 Set k ←− 0, z LB ←− −∞ and λ 0 ←− 0 2 repeat 3 SOLVE (17b) to obtain (x k ω , y k ω ) and D ω (λ k ω ) for given λ k ω for each ω ∈ Ω 4 set z LB ←− max{z LB , D ...
doi:10.3390/a15040103
fatcat:veyipe64hjcpbpcnnnpjleihxq
A Bundle Approach for SDPs with Exact Subgraph Constraints
[article]
2019
arXiv
pre-print
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Computational experiments on the Max-Cut, stable set and coloring problem show the efficiency of this approach. ...
We introduce a computational framework for these relaxations designed to cope with these difficulties. ...
We first look at the exact subgraph relaxations for Max-Cut. ...
arXiv:1902.05345v1
fatcat:ra4ckvzbdvaklpulpc5hzxhfdm
Multicommodity Network Flows: A Survey, Part II: Solution Methods
2018
International Journal of Operations Research
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Finally the computational performance of different solution methods in literature is compared and directions for future research are suggested. ...
price-directive, resourcedirective, and basis partitioning methods, then summarizes recent progress in applying approximation algorithms, interior-point algorithms, quadratic programming algorithms, and heuristics ...
Most of them are related to augmented Lagrangian methods which find a saddle point of a smooth min-max function obtained by augmenting the Lagrangian with quadratic terms of both primal and dual variables ...
doi:10.6886/ijor.201812_15(4).0002
doaj:6614b47a60864f25b944b6417a14e054
fatcat:3agaw3ax2jf6jjcikglnlzxrjy
Improving problem reduction for 0–1 Multidimensional Knapsack Problems with valid inequalities
2016
Computers & Operations Research
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Recently a novel core based heuristic [15] is proposed which is based on the Lagrangian Relaxation (LR) method. The Lagrangian relaxation of MKP can ...
Although cuts are commonly used in the branch and cut algorithms for general ILP solvers, our 40 application allows for classes of cuts with more expensive computational costs. ...
LR(λ) provides an upper bound for the MKP problem, and can be further strengthened by solving the Lagrangian dual problem LD = min λ LR(λ) (3) which is a non-smooth convex optimisation problem, and can ...
doi:10.1016/j.cor.2016.01.013
fatcat:lycve3yaorfmvefjvjj57tt73y
Lagrangian relaxation based decomposition for well scheduling in shale-gas systems
2014
Computers and Chemical Engineering
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In this paper, we present a Lagrangian relaxation based scheme for shut-in scheduling of distributed shale multiwell systems. ...
The scheme optimizes shut-in times and a reference rate for each multi-well pad, such that the total produced rate tracks a given short-term gas demand for the field. ...
Still, any effi- cient implementation of a Lagrangian relaxation requires a stable and reliable method for finding optimal Lagrangian multipliers, as well as a heuristic for finding primal feasible solutions ...
doi:10.1016/j.compchemeng.2014.02.005
fatcat:oswn4nyywrafbgybqhzsoupi2a
Fast Trust Region for Segmentation
2013
2013 IEEE Conference on Computer Vision and Pattern Recognition
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In this paper we propose a Fast Trust Region (FTR) approach for optimization of segmentation energies with nonlinear regional terms, which are known to be challenging for existing algorithms. ...
In general, this approach can be used only when some efficient constrained optimization algorithm is available for the selected non-linear (more accurate) approximation model. ...
We use the floating point precision in the standard code for graph-cuts [5] . ...
doi:10.1109/cvpr.2013.224
dblp:conf/cvpr/GorelickSB13
fatcat:c5dbzfrsnng5hmmuotuqfmjyim
Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry
2016
TEMA
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Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. ...
of items for each period. ...
The authors proposed two heuristic methods for the solution based on the Lagrangian relaxation of the integration constraints, which proved to be appropriated to address the integrated problem. ...
doi:10.5540/tema.2016.017.03.0305
fatcat:idqrlz7glfak5fg276tqlkm3wy
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