58,410 research outputs found
Solving the median problem with continuous demand on a network
Where to locate one or several facilities on a network so as to minimize the expected users-closest facility transportation cost is a problem well studied in the OR literature under the name of median problem. In the median problem users are usually identified with nodes of the network. In many
situations, however, such assumption is unrealistic, since users should be better considered to be distributed also along the edges of the transportation network. In this paper we address the median problem with demand distributed along edges and nodes. This leads to a globaloptimization
problem, which can be solved to optimality by means of a branch-and-bound
with DC bounds. Our computational experience shows that the problem is solved in short time even for large instances.Ministerio de Educación, Cultura y DeporteJunta de AndalucíaEuropean Regional Development Fun
The variance location problem on a network with continuously distributed demand
Most location problems on networks consider discrete nodal demand. However, for many problems, demands are better represented by continuous functions along the edges, in addition to nodal demands. Several papers consider the optimal location problem of one or more facilities when demands are continuously distributed along the network, and the objective function dealt with is the median one. Nevertheless, in location of public services it is desirable to use an equity criterion.
One of the latter is variance of distance distribution which has been studied only for discrete nodal demands. In this paper the variance problem has been generalized to the case where one allows the demand to arise discretely on the nodes as well as continuously along the edges. Properties and behaviour of the objective function are studied. Likewise we present an exact algorithm for solving this problem in a network, which reduces the complexity of the exhaustive procedure.Spanish Research Council (DGICYT
Robust mean absolute deviation problems on networks with linear vertex weights
This article deals with incorporating the mean absolute
deviation objective function in several robust single facility
location models on networks with dynamic evolution
of node weights, which are modeled by means of linear
functions of a parameter. Specifically, we have considered
two robustness criteria applied to the mean absolute
deviation problem: the MinMax criterion, and the MinMax
regret criterion. For solving the corresponding optimization
problems, exact algorithms have been proposed and
their complexities have been also analyzed.Ministerio de Ciencia e Innovación MTM2007-67433-C02-(01,02)Ministerio de Ciencia e Innovación MTM2009-14243Ministerio de Ciencia e Innovación MTM2010-19576-C02-(01,02)Ministerio de Ciencia e Innovación DE2009-0057Junta de Andalucía P09-TEP-5022Junta de Andalucía FQM-584
Resilient Distributed Optimization Algorithms for Resource Allocation
Distributed algorithms provide flexibility over centralized algorithms for
resource allocation problems, e.g., cyber-physical systems. However, the
distributed nature of these algorithms often makes the systems susceptible to
man-in-the-middle attacks, especially when messages are transmitted between
price-taking agents and a central coordinator. We propose a resilient strategy
for distributed algorithms under the framework of primal-dual distributed
optimization. We formulate a robust optimization model that accounts for
Byzantine attacks on the communication channels between agents and coordinator.
We propose a resilient primal-dual algorithm using state-of-the-art robust
statistics methods. The proposed algorithm is shown to converge to a
neighborhood of the robust optimization model, where the neighborhood's radius
is proportional to the fraction of attacked channels.Comment: 15 pages, 1 figure, accepted to CDC 201
Median problems in networks
The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling
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