655 research outputs found
Modeling and Analysis of Multicommodity Network Flows via Goal Programming
In this research we focused on the mobility system modeled by the AMC mobility planner\u27s calculator (AMPCALC). We developed AMPCALC as a user-friendly tool and allow the user to easily carry out strategic airlift, air refueling and aeromedical evacuation calculations that are covered in Air Force Pamphlet 10-1403. In this study, Excel software and its macro language, Visual Basic for Application, are our two main tools. In the methodology of the thesis we examined fundamental aspects of the mobility system in AMPCALC. We discussed formulation logic of the mobility cycle. We presented ramp use optimization and tanker optimization processes. We also conducted verification and validation of AMPCALC. Sensitivity analysis of the model includes a response surface study. To be able to investigate the main effects and interaction effects of the input factors on closure time, we performed a 26 factorial design. No linear relations are observed, but some relations between inputs and closure time are observed
Separable Concave Optimization Approximately Equals Piecewise-Linear Optimization
We study the problem of minimizing a nonnegative separable concave function
over a compact feasible set. We approximate this problem to within a factor of
1+epsilon by a piecewise-linear minimization problem over the same feasible
set. Our main result is that when the feasible set is a polyhedron, the number
of resulting pieces is polynomial in the input size of the polyhedron and
linear in 1/epsilon. For many practical concave cost problems, the resulting
piecewise-linear cost problem can be formulated as a well-studied discrete
optimization problem. As a result, a variety of polynomial-time exact
algorithms, approximation algorithms, and polynomial-time heuristics for
discrete optimization problems immediately yield fully polynomial-time
approximation schemes, approximation algorithms, and polynomial-time heuristics
for the corresponding concave cost problems.
We illustrate our approach on two problems. For the concave cost
multicommodity flow problem, we devise a new heuristic and study its
performance using computational experiments. We are able to approximately solve
significantly larger test instances than previously possible, and obtain
solutions on average within 4.27% of optimality. For the concave cost facility
location problem, we obtain a new 1.4991+epsilon approximation algorithm.Comment: Full pape
Interior-point solver for convex separable block-angular problems
Constraints matrices with block-angular structures are pervasive in Optimization. Interior-point methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solved the normal equations using sparse Cholesky factorizations for the block constraints, and a preconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based on a power series expansion which approximates the inverse of the matrix of the linking constraints system. In this work we present an efficient solver based on this algorithm. Some of its features are: it solves linearly constrained convex separable problems (linear, quadratic or nonlinear); both Newton and second-order predictor-corrector directions can be used, either with the Cholesky+PCG scheme or with a Cholesky factorization of normal equations; the preconditioner
may include any number of terms of the power series; for any number of these terms, it estimates the spectral radius of the matrix in the power series (which is instrumental for the quality of the precondi-
tioner). The solver has been hooked to SML, a structure-conveying modelling language based on the popular AMPL modeling language. Computational results are reported for some large and/or difficult instances in the literature: (1) multicommodity flow problems; (2) minimum congestion problems; (3) statistical data protection problems using l1 and l2 distances (which are linear and quadratic problems, respectively), and the pseudo-Huber function, a nonlinear approximation to l1 which improves the preconditioner. In the largest instances, of up to 25 millions of variables and 300000 constraints, this approach is from two to three orders of magnitude faster than state-of-the-art linear and quadratic optimization solvers.Preprin
Optimization in Telecommunication Networks
Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Mengerâs disjoint paths theorem, and Ford-Fulkersonâs max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;
An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design
We investigate the 3-architecture Connected Facility Location Problem arising
in the design of urban telecommunication access networks. We propose an
original optimization model for the problem that includes additional variables
and constraints to take into account wireless signal coverage. Since the
problem can prove challenging even for modern state-of-the art optimization
solvers, we propose to solve it by an original primal heuristic which combines
a probabilistic fixing procedure, guided by peculiar Linear Programming
relaxations, with an exact MIP heuristic, based on a very large neighborhood
search. Computational experiments on a set of realistic instances show that our
heuristic can find solutions associated with much lower optimality gaps than a
state-of-the-art solver.Comment: This is the authors' final version of the paper published in:
Squillero G., Burelli P. (eds), EvoApplications 2016: Applications of
Evolutionary Computation, LNCS 9597, pp. 283-298, 2016. DOI:
10.1007/978-3-319-31204-0_19. The final publication is available at Springer
via http://dx.doi.org/10.1007/978-3-319-31204-0_1
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
Energy management in communication networks: a journey through modelling and optimization glasses
The widespread proliferation of Internet and wireless applications has
produced a significant increase of ICT energy footprint. As a response, in the
last five years, significant efforts have been undertaken to include
energy-awareness into network management. Several green networking frameworks
have been proposed by carefully managing the network routing and the power
state of network devices.
Even though approaches proposed differ based on network technologies and
sleep modes of nodes and interfaces, they all aim at tailoring the active
network resources to the varying traffic needs in order to minimize energy
consumption. From a modeling point of view, this has several commonalities with
classical network design and routing problems, even if with different
objectives and in a dynamic context.
With most researchers focused on addressing the complex and crucial
technological aspects of green networking schemes, there has been so far little
attention on understanding the modeling similarities and differences of
proposed solutions. This paper fills the gap surveying the literature with
optimization modeling glasses, following a tutorial approach that guides
through the different components of the models with a unified symbolism. A
detailed classification of the previous work based on the modeling issues
included is also proposed
Robust network optimization under polyhedral demand uncertainty is NP-hard
AbstractMinimum cost network design/dimensioning problems where feasibility has to be ensured w.r.t. a given (possibly infinite) set of scenarios of requirements form an important subclass of robust LP problems with right-hand side uncertainty. Such problems arise in many practical contexts such as Telecommunications, logistic networks, power distribution networks, etc. Though some evidence of the computational difficulty of such problems can be found in the literature, no formal NP-hardness proof was available up to now. In the present paper, this pending complexity issue is settled for all robust network optimization problems featuring polyhedral demand uncertainty, both for the single-commodity and multicommodity case, even if the corresponding deterministic versions are polynomially solvable as regular (continuous) linear programs. A new family of polynomially solvable instances is also discussed
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