Journal ArticleDOI
A Comparison of Optimal Methods for Local Access Uncapacitated Network Design
TLDR
A well tailored Benders partitioning approach emerges as a robust method to cope with that fabricated cases where the linear programming relaxation exhibits a gap between the continuous and the integral optimal values.Abstract:
We compare some optimal methods addressed to a problem of local access network design. We see this problem arising in telecommunication as a flow extension of the Steiner problem in directed graphs, thus including as particular cases some alternative approaches based on the spanning tree problem. We work with two equivalent flow formulations for the problem, the first referring to a single commodity and the second being a multicommodity flow model. The objective in both cases is the cost minimization of the sum of the fixed (structural) and variable (operational) costs of all the arcs composing an arborescence that links the origin node (switching center) to every demand node. The weak single commodity flow formulation is solved by a branch-and-bound strategy that applies Lagrangian relaxation for computing the bounds. The strong multicommodity flow model is solved by a branch-and-cut algorithm and by Benders decomposition. The use of a linear programming solver to address both the single commodity and the multicommodity models has also been investigated. Our experience suggests that a certain number of these modeling and solution strategies can be applied to the frequently occurring problems where basic optimal solutions to the linear program are automatically integral, so it also solves the combinatorial optimization problem right away. On the other hand, our main conclusion is that a well tailored Benders partitioning approach emerges as a robust method to cope with that fabricated cases where the linear programming relaxation exhibits a gap between the continuous and the integral optimal values.read more
Citations
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Journal ArticleDOI
A survey on benders decomposition applied to fixed-charge network design problems
TL;DR: Network design problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of origin-destination pair demands.
Journal ArticleDOI
Benders decomposition for the uncapacitated multiple allocation hub location problem
TL;DR: Efficient Benders decomposition algorithms based on a well known formulation to tackle the UMAHLP are presented, able to solve some large instances, considered 'out of reach' of other exact methods in reasonable time.
Journal ArticleDOI
Multiple allocation hub-and-spoke network design under hub congestion
R. S. de Camargo,Gilberto de Miranda,Ricardo Poley Martins Ferreira,Henrique Pacca Loureiro Luna +3 more
TL;DR: The main contribution of this work is to establish a compromise between the transportation cost savings induced by the economies of scale exploitation and the costs associated with the congestion effects.
Journal ArticleDOI
Decomposition based hybrid metaheuristics
TL;DR: A general review of design patterns for hybrid metaheuristics that combine principles of classical metaheuristic techniques with advanced methods from fields like mathematical programming, dynamic programming, and constraint programming.
Journal ArticleDOI
Towards optimizing the deployment of optical access networks
TL;DR: A unified integer programming model is constructed that combines all sub-models and provides a global view of all these FTTx problems and summarizes computational studies of various special cases.
References
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Book
Linear Programming and Extensions
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Journal ArticleDOI
Partitioning procedures for solving mixed-variables programming problems
TL;DR: In this article, the 8th International Meeting of the Institute of Management Sciences, Brussels, August 23-26, 1961, the authors presented a paper entitled "The International Journal of Management Science and Management Sciences".
Book
Modern heuristic techniques for combinatorial problems
TL;DR: In this paper, the Lagrangian relaxation and dual ascent tree search were used to solve the graph bisection problem and the graph partition problem, and the traveling salesman problem scheduling problems.
Journal ArticleDOI
The Lagrangian Relaxation Method for Solving Integer Programming Problems
TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.
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