32,080 research outputs found
On the Routing and Location of Mobile Facilities
Mobile facilities play important roles in many applications, including health care, public services, telecommunications, and humanitarian relief logistics. While mobile facilities operate in different manners, it is generally considered important for a decision maker to be capable of efficiently deploying mobile facilities. This dissertation discusses two problems on the use of mathematical models and algorithms for determining efficient deployments of mobile facilities.
First we discuss the mobile facility routing problem (MFRP), which effectively models the operations of a wide class of mobile facilities that have significant relocation times and cannot service demand during transit. Chapter 2 discusses the single MFRP (SMFRP), which is to determine a route for a single mobile facility to maximize the demand serviced during a continuous-time planning horizon. We present two exact algorithms, and supporting theoretical results, when the rate demand is generated is modeled using piecewise constant functions. The first is a dynamic program that easily extends to solve cases where the demand functions take on more general forms. The second exact algorithm has a polynomial worst-case runtime.
Chapter 3 discusses the MFRP, which addresses the situation when multiple mobile facilities are operating in an area. In such a case, mobile facilities at different locations may provide service to a single event, necessitating the separation of the events generating demand from the locations mobile facilities may visit in our model. We show that the MFRP is NP-hard, present several heuristics for generating effective routes, and extensively test these heuristics on a variety of simulated data sets.
Chapter 4 discusses formulations and local search heuristics for the (minisum) mobile facility location problem (MFLP). This problem is to relocate a set of existing facilities and assign clients to these facilities while minimizing the movement costs of facilities and clients. We show that in a certain sense the MFLP generalizes the uncapacitated facility location and p-median problems. We observe that given a set of facility destinations, the MFLP decomposes into two polynomially solvable subproblems. Using this decomposition observation, we propose a new, compact IP formulation and novel local search heuristics. We report results from extensive computational experiments
Coordination of Mobile Mules via Facility Location Strategies
In this paper, we study the problem of wireless sensor network (WSN)
maintenance using mobile entities called mules. The mules are deployed in the
area of the WSN in such a way that would minimize the time it takes them to
reach a failed sensor and fix it. The mules must constantly optimize their
collective deployment to account for occupied mules. The objective is to define
the optimal deployment and task allocation strategy for the mules, so that the
sensors' downtime and the mules' traveling distance are minimized. Our
solutions are inspired by research in the field of computational geometry and
the design of our algorithms is based on state of the art approximation
algorithms for the classical problem of facility location. Our empirical
results demonstrate how cooperation enhances the team's performance, and
indicate that a combination of k-Median based deployment with closest-available
task allocation provides the best results in terms of minimizing the sensors'
downtime but is inefficient in terms of the mules' travel distance. A
k-Centroid based deployment produces good results in both criteria.Comment: 12 pages, 6 figures, conferenc
Serving Online Requests with Mobile Servers
We study an online problem in which a set of mobile servers have to be moved
in order to efficiently serve a set of requests that arrive in an online
fashion. More formally, there is a set of nodes and a set of mobile
servers that are placed at some of the nodes. Each node can potentially host
several servers and the servers can be moved between the nodes. There are
requests that are adversarially issued at nodes one at a time. An
issued request at time needs to be served at all times . The
cost for serving the requests is a function of the number of servers and
requests at the different nodes. The requirements on how to serve the requests
are governed by two parameters and . An algorithm
needs to guarantee at all times that the total service cost remains within a
multiplicative factor of and an additive term of the current
optimal service cost. We consider online algorithms for two different
minimization objectives. We first consider the natural problem of minimizing
the total number of server movements. We show that in this case for every ,
the competitive ratio of every deterministic online algorithm needs to be at
least . Given this negative result, we then extend the minimization
objective to also include the current service cost. We give almost tight bounds
on the competitive ratio of the online problem where one needs to minimize the
sum of the total number of movements and the current service cost. In
particular, we show that at the cost of an additional additive term which is
roughly linear in , it is possible to achieve a multiplicative competitive
ratio of for every constant .Comment: 25 page
Approximation Algorithms for Clustering and Facility Location Problems
Facility location problems arise in a wide range of applications such as plant or warehouse location problems, cache placement problems, and network design problems, and have been widely studied in Computer Science and Operations Research literature. These problems typically involve an underlying set F of facilities that provide service, and an underlying set D of clients that require service, which need to be assigned to facilities in a cost-effective fashion. This abstraction is quite versatile and also captures clustering problems, where one typically seeks to partition a set of data points into k clusters, for some given k, in a suitable way, which themselves find applications in data mining, machine learning, and bioinformatics.
Basic variants of facility location problems are now relatively well-u
nderstood, but we have much-less understanding of more-sophisticated models that better model the real-world concerns. In this thesis, we focus on three models inspired by some real-world optimization scenarios.
In Chapter 2, we consider mobile facility location (MFL) problem, wherein we seek to relocate a given set of facilities to destinations closer to the clients as to minimize the sum of facility-movement and client-assignment costs. This abstracts facility-location settings where one has the flexibility of moving
facilities from their current locations to other destinations so as to serve clients more efficiently by reducing their assignment costs. We give the first local-search based approximation algorithm for this problem and
achieve the best-known approximation guarantee. Our main result is
(3+epsilon)-approximation for this problem for any constant epsilon > 0 using local
search which improves the previous best guarantee of 8-approximation algorithm due to [34] based on LP-rounding. Our results extend to the weighted generalization wherein each facility i has a
non-negative weight w_i and the movement cost for i is w_i times the distance
traveled by i.
In Chapter 3, we consider a facility-location problem that we call the minimum-load k-facility location (MLkFL), which abstracts settings where the cost of
serving the clients assigned to a facility is incurred by the facility. This problem was studied under the name of min-max star cover in [32,10], who
(among other results) gave bicriteria approximation algorithms for MLkFL when F=D. MLkFL is rather poorly understood, and only an O(k)-approximation is currently
known for MLkFL, even for line metrics. Our main result is the first polytime approximation scheme (PTAS) for MLkFL on line
metrics (note that no non-trivial true approximation of any kind was known for this metric).
Complementing this, we prove that MLkFL is strongly NP-hard on line metrics.
In Chapter 4, we consider clustering problems with non-uniform lower bounds and outliers, and
obtain the first approximation guarantees for these problems.
We consider objective functions involving the radii of open facilities, where the radius of a facility i is the maximum distance between i and a client assigned to it. We consider two problems: minimizing the sum of the radii of the open facilities, which yields the lower-bounded min-sum-of-radii with outliers (LBkSRO) problem, and minimizing the maximum radius, which yields the lower-bounded k-supplier with outliers (LBkSupO) problem. We obtain an approximation factor of 12.365 for LBkSRO, which improves to 3.83 for the non-outlier version. These also constitute the first approximation bounds for the min-sum-of-radii objective when we consider lower bounds and outliers separately. We obtain approximation factors of 5 and 3 respectively for LBkSupO and its non-outlier version. These are the first approximation results for k-supplier with non-uniform lower bounds
Enabling Communication Technologies for Automated Unmanned Vehicles in Industry 4.0
Within the context of Industry 4.0, mobile robot systems such as automated
guided vehicles (AGVs) and unmanned aerial vehicles (UAVs) are one of the major
areas challenging current communication and localization technologies. Due to
stringent requirements on latency and reliability, several of the existing
solutions are not capable of meeting the performance required by industrial
automation applications. Additionally, the disparity in types and applications
of unmanned vehicle (UV) calls for more flexible communication technologies in
order to address their specific requirements. In this paper, we propose several
use cases for UVs within the context of Industry 4.0 and consider their
respective requirements. We also identify wireless technologies that support
the deployment of UVs as envisioned in Industry 4.0 scenarios.Comment: 7 pages, 1 figure, 1 tabl
On the Benefit of Virtualization: Strategies for Flexible Server Allocation
Virtualization technology facilitates a dynamic, demand-driven allocation and
migration of servers. This paper studies how the flexibility offered by network
virtualization can be used to improve Quality-of-Service parameters such as
latency, while taking into account allocation costs. A generic use case is
considered where both the overall demand issued for a certain service (for
example, an SAP application in the cloud, or a gaming application) as well as
the origins of the requests change over time (e.g., due to time zone effects or
due to user mobility), and we present online and optimal offline strategies to
compute the number and location of the servers implementing this service. These
algorithms also allow us to study the fundamental benefits of dynamic resource
allocation compared to static systems. Our simulation results confirm our
expectations that the gain of flexible server allocation is particularly high
in scenarios with moderate dynamics
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