102 research outputs found
Lagrangian-based methods for single and multi-layer multicommodity capacitated network design
Le problème de conception de réseau avec coûts fixes et capacités (MCFND) et le problème
de conception de réseau multicouches (MLND) sont parmi les problèmes de
conception de réseau les plus importants. Dans le problème MCFND monocouche, plusieurs
produits doivent être acheminés entre des paires origine-destination différentes
d’un réseau potentiel donné. Des liaisons doivent être ouvertes pour acheminer les produits,
chaque liaison ayant une capacité donnée. Le problème est de trouver la conception
du réseau à coût minimum de sorte que les demandes soient satisfaites et que les capacités
soient respectées. Dans le problème MLND, il existe plusieurs réseaux potentiels,
chacun correspondant à une couche donnée. Dans chaque couche, les demandes pour un
ensemble de produits doivent être satisfaites. Pour ouvrir un lien dans une couche particulière,
une chaîne de liens de support dans une autre couche doit être ouverte. Nous
abordons le problème de conception de réseau multiproduits multicouches à flot unique
avec coûts fixes et capacités (MSMCFND), où les produits doivent être acheminés uniquement
dans l’une des couches.
Les algorithmes basés sur la relaxation lagrangienne sont l’une des méthodes de résolution
les plus efficaces pour résoudre les problèmes de conception de réseau. Nous
présentons de nouvelles relaxations à base de noeuds, où le sous-problème résultant se
décompose par noeud. Nous montrons que la décomposition lagrangienne améliore significativement
les limites des relaxations traditionnelles.
Les problèmes de conception du réseau ont été étudiés dans la littérature. Cependant,
ces dernières années, des applications intéressantes des problèmes MLND sont apparues,
qui ne sont pas couvertes dans ces études. Nous présentons un examen des problèmes de
MLND et proposons une formulation générale pour le MLND. Nous proposons également
une formulation générale et une méthodologie de relaxation lagrangienne efficace
pour le problème MMCFND. La méthode est compétitive avec un logiciel commercial
de programmation en nombres entiers, et donne généralement de meilleurs résultats.The multicommodity capacitated fixed-charge network design problem (MCFND) and
the multilayer network design problem (MLND) are among the most important network
design problems. In the single-layer MCFND problem, several commodities have to
be routed between different origin-destination pairs of a given potential network. Appropriate
capacitated links have to be opened to route the commodities. The problem
is to find the minimum cost design and routing such that the demands are satisfied and
the capacities are respected. In the MLND, there are several potential networks, each
at a given layer. In each network, the flow requirements for a set of commodities must
be satisfied. However, the selection of the links is interdependent. To open a link in a
particular layer, a chain of supporting links in another layer has to be opened. We address
the multilayer single flow-type multicommodity capacitated fixed-charge network
design problem (MSMCFND), where commodities are routed only in one of the layers.
Lagrangian-based algorithms are one of the most effective solution methods to solve
network design problems. The traditional Lagrangian relaxations for the MCFND problem
are the flow and knapsack relaxations, where the resulting Lagrangian subproblems
decompose by commodity and by arc, respectively. We present new node-based
relaxations, where the resulting subproblem decomposes by node. We show that the
Lagrangian dual bound improves significantly upon the bounds of the traditional relaxations.
We also propose a Lagrangian-based algorithm to obtain upper bounds.
Network design problems have been the object of extensive literature reviews. However,
in recent years, interesting applications of multilayer problems have appeared that
are not covered in these surveys. We present a review of multilayer problems and propose
a general formulation for the MLND. We also propose a general formulation and
an efficient Lagrangian-based solution methodology for the MMCFND problem. The
method is competitive with (and often significantly better than) a state-of-the-art mixedinteger
programming solver on a large set of randomly generated instances
Node-based Lagrangian relaxations for multicommodity capacitated fixed-charge network design
Classical Lagrangian relaxations for the multicommodity capacitated fixed-charge network design problem are the so-called flow and knapsack relaxations, where the resulting Lagrangian subproblems decompose by commodities and by arcs, respectively. We introduce node-based Lagrangian relaxations, where the resulting Lagrangian subproblem decomposes by nodes. We show that the Lagrangian dual bounds of these relaxations improve upon the linear programming relaxation bound, known to be equal to the Lagrangian dual bounds for the flow and knapsack relaxations. We also develop a Lagrangian matheuristic to compute upper bounds. The computational results on a set of benchmark instances show that the Lagrangian matheuristic is competitive with the state-of-the-art heuristics from the literature
Synthesis, Interdiction, and Protection of Layered Networks
This research developed the foundation, theory, and framework for a set of analysis techniques to assist decision makers in analyzing questions regarding the synthesis, interdiction, and protection of infrastructure networks. This includes extension of traditional network interdiction to directly model nodal interdiction; new techniques to identify potential targets in social networks based on extensions of shortest path network interdiction; extension of traditional network interdiction to include layered network formulations; and develops models/techniques to design robust layered networks while considering trade-offs with cost. These approaches identify the maximum protection/disruption possible across layered networks with limited resources, find the most robust layered network design possible given the budget limitations while ensuring that the demands are met, include traditional social network analysis, and incorporate new techniques to model the interdiction of nodes and edges throughout the formulations. In addition, the importance and effects of multiple optimal solutions for these (and similar) models is investigated. All the models developed are demonstrated on notional examples and were tested on a range of sample problem sets
Multi-level Facility Location Problems
We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field
A Multiple-objective ILP based Global Routing Approach for VLSI ASIC Design
A VLSI chip can today contain hundreds of millions transistors and is expected to
contain more than 1 billion transistors in the next decade.
In order to handle this rapid growth in integration technology,
the design procedure is therefore divided into a sequence of design
steps. Circuit layout is the design step in which a physical
realization of a circuit is obtained from its functional description.
Global routing is one of the key subproblems of the circuit layout
which involves finding an approximate path for the wires connecting the
elements of the circuit without violating resource constraints.
The global routing problem is NP-hard, therefore, heuristics capable of
producing high quality routes with little computational effort are required
as we move into the Deep Sub-Micron (DSM) regime.
In this thesis, different approaches for global routing problem are first
reviewed. The advantages and disadvantages of these approaches are also summarized.
According to this literature review, several mathematical programming based global
routing models are fully investigated. Quality of solution obtained by
these models are then compared with traditional Maze routing technique.
The experimental results show that the proposed model can optimize several global routing
objectives simultaneously and effectively. Also, it is easy to incorporate new
objectives into the proposed global routing model.
To speedup the computation time of the proposed ILP based global router, several
hierarchical methods are combined with the flat ILP based global routing
approach. The experimental results indicate that the bottom-up global routing
method can reduce the computation time effectively with a slight increase of maximum
routing density.
In addition to wire area, routability, and vias, performance and low power
are also important goals in global routing, especially in deep submicron designs.
Previous efforts that focused on power optimization for global routing
are hindered by excessively long run times or the routing of a subset of the
nets. Accordingly, a power efficient multi-pin global routing
technique (PIRT) is proposed in this thesis.
This integer linear programming based techniques strives to find a power
efficient global routing solution.
The results indicate that an average power savings as high as 32\% for the
130-nm technology can be achieved with no impact on the maximum chip frequency
Revisiting the Evolution and Application of Assignment Problem: A Brief Overview
The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on  a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc
A computer graphics approach to logistics strategy modelling
This thesis describes the development and application of a decision support
system for logistics strategy modelling. The decision support system that is
developed enables the modelling of logistics systems at a strategic level for
any country or area in the world. The model runs on IBM PC or compatible
computers under DOS (disk operating system).
The decision support system uses colour graphics to represent the different
physical functions of a logistics system. The graphics of the system is machine
independent. The model displays on the screen the map of the area or country
which is being considered for logistic planning.
The decision support system is hybrid in term of algorithm. It employs
optimisation for allocation. The customers are allocated by building a network
path from customer to the source points taking into consideration all the
production and throughput constraints on factories, distribution depots and
transshipment points.
The system uses computer graphic visually interactive heuristics to find the
best possible location for distribution depots and transshipment points. In a
one depot system it gives the optimum solution but where more than one
depot is involved, the optimum solution is not guaranteed.
The developed model is a cost-driven model. It represents all the logistics
system costs in their proper form. Its solution very much depends on the
relationship between all the costs. The locations of depots and transshipment
points depend on the relationship between inbound and outbound
transportation costs.
The model has been validated on real world problems, some of which are
described here. The advantages of such a decision support system for the
formulation of a problem are discussed. Also discussed is the contribution of
such an approach at the validation and solution presentation stages
Network Flexibility for Recourse Considerations in Bi-Criteria Facility Location
What is the best set of facility location decisions for the establishment of a logistics network when it is uncertain how a company’s distribution strategy will evolve? What is the best configuration of a distribution network that will most likely have to be altered in the future? Today’s business environment is turbulent, and operating conditions for firms can take a turn for the worse at any moment. This fact can and often does influence companies to occasionally expand or contract their distribution networks. For most companies operating in this chaotic business environment, there is a continuous struggle between staying cost efficient and supplying adequate service. Establishing a distribution network which is flexible or easily adaptable is the key to survival under these conditions. This research begins to address the problem of locating facilities in a logistics network in the face of an evolving strategic focus through the implicit consideration of the uncertainty of parameters. The trade-off of cost and customer service is thoroughly examined in a series of multi-criteria location problems. Modeling techniques for incorporating service restrictions for facility location in strategic network design are investigated. A flexibility metric is derived for the purposes of quantifying the similarity of a set of non-dominated solutions in strategic network design. Finally, a multi-objective greedy random adaptive search (MOG) metaheuristic is applied to solve a series of bi-criteria, multi-level facility location problems
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