507 research outputs found
Randomized rounding algorithms for large scale unsplittable flow problems
Unsplittable flow problems cover a wide range of telecommunication and
transportation problems and their efficient resolution is key to a number of
applications. In this work, we study algorithms that can scale up to large
graphs and important numbers of commodities. We present and analyze in detail a
heuristic based on the linear relaxation of the problem and randomized
rounding. We provide empirical evidence that this approach is competitive with
state-of-the-art resolution methods either by its scaling performance or by the
quality of its solutions. We provide a variation of the heuristic which has the
same approximation factor as the state-of-the-art approximation algorithm. We
also derive a tighter analysis for the approximation factor of both the
variation and the state-of-the-art algorithm. We introduce a new objective
function for the unsplittable flow problem and discuss its differences with the
classical congestion objective function. Finally, we discuss the gap in
practical performance and theoretical guarantees between all the aforementioned
algorithms
Lagrangian-based methods for single and multi-layer multicommodity capacitated network design
Le problÚme de conception de réseau avec coûts fixes et capacités (MCFND) et le problÚme
de conception de réseau multicouches (MLND) sont parmi les problÚmes de
conception de réseau les plus importants. Dans le problÚme MCFND monocouche, plusieurs
produits doivent ĂȘtre acheminĂ©s entre des paires origine-destination diffĂ©rentes
dâun rĂ©seau potentiel donnĂ©. Des liaisons doivent ĂȘtre ouvertes pour acheminer les produits,
chaque liaison ayant une capacité donnée. Le problÚme 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 problÚme MLND, il existe plusieurs réseaux potentiels,
chacun correspondant à une couche donnée. Dans chaque couche, les demandes pour un
ensemble de produits doivent ĂȘtre satisfaites. Pour ouvrir un lien dans une couche particuliĂšre,
une chaĂźne de liens de support dans une autre couche doit ĂȘtre ouverte. Nous
abordons le problÚme de conception de réseau multiproduits multicouches à flot unique
avec coĂ»ts fixes et capacitĂ©s (MSMCFND), oĂč les produits doivent ĂȘtre acheminĂ©s uniquement
dans lâune des couches.
Les algorithmes basĂ©s sur la relaxation lagrangienne sont lâune des mĂ©thodes de rĂ©solution
les plus efficaces pour résoudre les problÚmes de conception de réseau. Nous
prĂ©sentons de nouvelles relaxations Ă base de noeuds, oĂč le sous-problĂšme rĂ©sultant se
décompose par noeud. Nous montrons que la décomposition lagrangienne améliore significativement
les limites des relaxations traditionnelles.
Les problÚmes de conception du réseau ont été étudiés dans la littérature. Cependant,
ces derniÚres années, des applications intéressantes des problÚmes MLND sont apparues,
qui ne sont pas couvertes dans ces études. Nous présentons un examen des problÚmes 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 problÚme 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
A Column Generation Based Heuristic for the Multicommodity-ring Vehicle Routing Problem
AbstractWe study a new routing problem arising in City Logistics. Given a ring connecting a set of urban distribution centers (UDCs) in the outskirts of a city, the problem consists in delivering goods from virtual gates located outside the city to the customers inside of it. Goods are transported from a gate to a UDC, then either go to another UDC before being delivered to customers or are directly shipped from the first UDC. The reverse process occurs for pick-up. Routes are performed by electric vans and may be open. The objective is to find a set of routes that visit each customer and to determine ring and gates-UDC flows so that the total transportation and routing cost is minimized. We solve this problem using a column generation-based heuristic, which is tested over a set of benchmark instances issued from a more strategic location-routing problem
A heuristic approach for big bucket multi-level production planning problems
Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems
An oil pipeline design problem
Copyright @ 2003 INFORMSWe consider a given set of offshore platforms and onshore wells producing known (or estimated) amounts of oil to be connected to a port. Connections may take place directly between platforms, well sites, and the port, or may go through connection points at given locations. The configuration of the network and sizes of pipes used must be chosen to minimize construction costs. This problem is expressed as a mixed-integer program, and solved both heuristically by Tabu Search and Variable Neighborhood Search methods and exactly by a branch-and-bound method. Two new types of valid inequalities are introduced. Tests are made with data from the South Gabon oil field and randomly generated problems.The work of the first author was supported by NSERC grant #OGP205041. The work of the second author was supported by FCAR (Fonds pour la Formation des Chercheurs et lâAide Ă la Recherche) grant #95-ER-1048, and NSERC grant #GP0105574
Solving a Continent-Scale Inventory Routing Problem at Renault
This paper is the fruit of a partnership with Renault. Their backward
logistic requires to solve a continent-scale multi-attribute inventory routing
problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers
spread across a continent, our instances are orders of magnitude larger than
those in the literature. Existing algorithms do not scale. We propose a large
neighborhood search (LNS). To make it work, (1) we generalize existing split
delivery vehicle routing problem and IRP neighborhoods to this context, (2) we
turn a state-of-the art matheuristic for medium-scale IRP into a large
neighborhood, and (3) we introduce two novel perturbations: the reinsertion of
a customer and that of a commodity into the IRP solution. We also derive a new
lower bound based on a flow relaxation. In order to stimulate the research on
large-scale IRP, we introduce a library of industrial instances. We benchmark
our algorithms on these instances and make our code open-source. Extensive
numerical experiments highlight the relevance of each component of our LNS
Decomposition methods for large-scale network expansion problems
Network expansion problems are a special class of multi-period network design problems in which arcs can be opened gradually in different time periods but can never be closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over a discrete time horizon. Arc opening decisions are taken in every period, and once an arc is opened it can be used throughout the remaining horizon to route several commodities. Our model captures a key timing trade-off: the earlier an arc is opened, the more periods it can be used for, but its fixed cost is higher, since it accounts not only for construction but also for maintenance over the remaining horizon. An overview of practical applications indicates that this trade-off is relevant in various settings. For the capacitated variant, we develop an arc-based Lagrange relaxation, combined with local improvement heuristics. For uncapacitated problems, we develop four Benders decompositi
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