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Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem
Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department
of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council
of Canada, Grant OGPOO 39682
On the multisource hyperplanes location problem to fitting set of points
In this paper we study the problem of locating a given number of hyperplanes
minimizing an objective function of the closest distances from a set of points.
We propose a general framework for the problem in which norm-based distances
between points and hyperplanes are aggregated by means of ordered median
functions. A compact Mixed Integer Linear (or Non Linear) programming
formulation is presented for the problem and also an extended set partitioning
formulation with an exponential number of variables is derived. We develop a
column generation procedure embedded within a branch-and-price algorithm for
solving the problem by adequately performing its preprocessing, pricing and
branching. We also analyze geometrically the optimal solutions of the problem,
deriving properties which are exploited to generate initial solutions for the
proposed algorithms. Finally, the results of an extensive computational
experience are reported. The issue of scalability is also addressed showing
theoretical upper bounds on the errors assumed by replacing the original
datasets by aggregated versions.Comment: 30 pages, 5 Tables, 3 Figure
A two-stage method for the capacitated multi-facility location-allocation problem
This is the author accepted manuscript. The final version is available from Inderscience via the DOI in this recordThis paper examines the capacitated planar multi-facility
location-allocation problem, where the number of facilities to be located is
specified and each of which has a capacity constraint. A two-stage method is
put forward to deal with the problem where in the first stage a technique that
discretises continuous space into discrete cells is used to generate a relatively
good initial facility configurations. In stage 2, a variable neighbourhood search
(VNS) is implemented to improve the quality of solution obtained by the
previous stage. The performance of the proposed method is evaluated using
benchmark datasets from the literature. The numerical experiments show that
the proposed method yields competitive results when compared to the best
known results from the literature. In addition, some future research avenues are
also suggested
A branch-and-price approach for the continuous multifacility monotone ordered median problem
Acknowledgements
The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y TecnologĂa, Agencia Estatal de InvestigaciĂłn and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21. The authors also acknowledge partial support from project B-FQM-322-UGR20. The first, third and fourth authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas Fundacin BBVA a equipos de investigacin cientĂfica 2019. The first and second authors were par- tially supported by research group SEJ-584 (Junta de AndalucĂa). The first author was also partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033. The second author was supported by Spanish Ministry of Education and Science grant number PEJ2018-002962-A and the Doctoral Program in Mathematics at the Universidad of Granada. The third author also acknowledges the grant ContrataciĂłn de Personal Investigador Doctor (Convocatoria 2019) 43 Contratos Capital Humano LĂnea 2 Paidi 2020, supported by the European Social Fund and Junta de AndalucĂa.In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. The goal of this problem is to locate facilities in minimizing a monotone ordered weighted median function of the distances between given demand points and its closest facility. We propose a new branch-and-price procedure for this problem, and three families of matheuristics based on: solving heuristically the pricer problem, aggregating the demand points, and discretizing the decision space. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performances in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.Spanish Ministerio de Ciencia y TecnologĂa, Agencia Estatal de InvestigaciĂłn and Fondos Europeos de Desarrollo Regional (FEDER) via project PID2020-114594GB-C21Partial support from project B-FQM-322-UGR20Partial support from projects FEDER-US-1256951, Junta de Andaluca P18-FR-1422, CEI-3-FQM331, FQM-331, and NetmeetData: Ayudas FundaciĂłn BBVA a equipos de investigacin cientĂfica 2019Research group SEJ-584 (Junta de AndalucĂa)Partially supported by the IMAG-Maria de Maeztu grant CEX2020-001105-M/AEI/10.13039/50110 0 011033Spanish Ministry of Education and Science grant number PEJ2018-002962-AEuropean Social Fund and Junta de AndalucĂ
Sensor Deployment for Network-like Environments
This paper considers the problem of optimally deploying omnidirectional
sensors, with potentially limited sensing radius, in a network-like
environment. This model provides a compact and effective description of complex
environments as well as a proper representation of road or river networks. We
present a two-step procedure based on a discrete-time gradient ascent algorithm
to find a local optimum for this problem. The first step performs a coarse
optimization where sensors are allowed to move in the plane, to vary their
sensing radius and to make use of a reduced model of the environment called
collapsed network. It is made up of a finite discrete set of points,
barycenters, produced by collapsing network edges. Sensors can be also
clustered to reduce the complexity of this phase. The sensors' positions found
in the first step are then projected on the network and used in the second
finer optimization, where sensors are constrained to move only on the network.
The second step can be performed on-line, in a distributed fashion, by sensors
moving in the real environment, and can make use of the full network as well as
of the collapsed one. The adoption of a less constrained initial optimization
has the merit of reducing the negative impact of the presence of a large number
of local optima. The effectiveness of the presented procedure is illustrated by
a simulated deployment problem in an airport environment
A new local search for . . .
This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulatio
An elliptical cover problem in drone delivery network design and its solution algorithms
Given n demand points in a geographic area, the elliptical cover problem is to determine the location of p depots (anywhere in the area) so as to minimize the maximum distance of an economical delivery trip in which a delivery vehicle starts from the nearest depot to a demand point, visits the demand point and then returns to the second nearest depot to that demand point. We show that this problem is NP-hard, and adapt Cooper’s alternating locate-allocate heuristic to find locally optimal solutions for both the point-coverage and area-coverage scenarios. Experiments show that most locally optimal solutions perform similarly well, suggesting their sufficiency for practical use. The one-dimensional variant of the problem, in which the service area is reduced to a line segment, permits recursive algorithms that are more efficient than mathematical optimization approaches in practical cases. The solution also provides the best-known lower bound for the original problem at a negligible computational cost
The obnoxious facilities planar p-median problem
In this paper we propose the planar obnoxious p-median problem. In the
p-median problem the objective is to find p locations for facilities that
minimize the weighted sum of distances between demand points and their closest
facility. In the obnoxious version we add constraints that each facility must
be located at least a certain distance from a partial set of demand points
because they generate nuisance affecting these demand points. The resulting
problem is extremely non-convex and traditional non-linear solvers such as
SNOPT are not efficient. An efficient solution method based on Voronoi diagrams
is proposed and tested. We also constructed the efficient frontiers of the test
problems to assist the planers in making location decisions
Solving the planar p-median problem by variable neighborhood and concentric searches
Two new approaches for the solution of the p-median problem
in the plane are proposed. One is a Variable Neighborhood Search (VNS)
and the other one is a concentric search. Both approaches are enhanced by a
front-end procedure for finding good starting solutions and a decomposition
heuristic acting as a post optimization procedure. Computational results
confirm the effectiveness of the proposed algorithms
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