9,102 research outputs found
A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption
The past decade has seen a substantial increase in the use of small unmanned
aerial vehicles (UAVs) in both civil and military applications. This article
addresses an important aspect of refueling in the context of routing multiple
small UAVs to complete a surveillance or data collection mission. Specifically,
this article formulates a multiple-UAV routing problem with the refueling
constraint of minimizing the overall fuel consumption for all of the vehicles
as a two-stage stochastic optimization problem with uncertainty associated with
the fuel consumption of each vehicle. The two-stage model allows for the
application of sample average approximation (SAA). Although the SAA solution
asymptotically converges to the optimal solution for the two-stage model, the
SAA run time can be prohibitive for medium- and large-scale test instances.
Hence, we develop a tabu-search-based heuristic that exploits the model
structure while considering the uncertainty in fuel consumption. Extensive
computational experiments corroborate the benefits of the two-stage model
compared to a deterministic model and the effectiveness of the heuristic for
obtaining high-quality solutions.Comment: 18 page
GIS and Network Analysis
Both geographic information systems (GIS) and network analysis are burgeoning fields, characterised by rapid methodological and scientific advances in recent years. A geographic information system (GIS) is a digital computer application designed for the capture, storage, manipulation, analysis and display of geographic information. Geographic location is the element that distinguishes geographic information from all other types of information. Without location, data are termed to be non-spatial and would have little value within a GIS. Location is, thus, the basis for many benefits of GIS: the ability to map, the ability to measure distances and the ability to tie different kinds of information together because they refer to the same place (Longley et al., 2001). GIS-T, the application of geographic information science and systems to transportation problems, represents one of the most important application areas of GIS-technology today. While traditional GIS formulation's strengths are in mapping display and geodata processing, GIS-T requires new data structures to represent the complexities of transportation networks and to perform different network algorithms in order to fulfil its potential in the field of logistics and distribution logistics. This paper addresses these issues as follows. The section that follows discusses data models and design issues which are specifically oriented to GIS-T, and identifies several improvements of the traditional network data model that are needed to support advanced network analysis in a ground transportation context. These improvements include turn-tables, dynamic segmentation, linear referencing, traffic lines and non-planar networks. Most commercial GIS software vendors have extended their basic GIS data model during the past two decades to incorporate these innovations (Goodchild, 1998). The third section shifts attention to network routing problems that have become prominent in GIS-T: the travelling salesman problem, the vehicle routing problem and the shortest path problem with time windows, a problem that occurs as a subproblem in many time constrained routing and scheduling issues of practical importance. Such problems are conceptually simple, but mathematically complex and challenging. The focus is on theory and algorithms for solving these problems. The paper concludes with some final remarks.
On green routing and scheduling problem
The vehicle routing and scheduling problem has been studied with much
interest within the last four decades. In this paper, some of the existing
literature dealing with routing and scheduling problems with environmental
issues is reviewed, and a description is provided of the problems that have
been investigated and how they are treated using combinatorial optimization
tools
Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes
We study the routing problem for vehicles with limited energy through a
network of inhomogeneous charging nodes. This is substantially more complicated
than the homogeneous node case studied in [1]. We seek to minimize the total
elapsed time for vehicles to reach their destinations considering both
traveling and recharging times at nodes when the vehicles do not have adequate
energy for the entire journey. We study two versions of the problem. In the
single vehicle routing problem, we formulate a mixed-integer nonlinear
programming (MINLP) problem and show that it can be reduced to a lower
dimensionality problem by exploiting properties of an optimal solution. We also
obtain a Linear Programming (LP) formulation allowing us to decompose it into
two simpler problems yielding near-optimal solutions. For a multi-vehicle
problem, where traffic congestion effects are included, we use a similar
approach by grouping vehicles into "subflows". We also provide an alternative
flow optimization formulation leading to a computationally simpler problem
solution with minimal loss in accuracy. Numerical results are included to
illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control
and Automation, MED'1
A Dynamic Boundary Guarding Problem with Translating Targets
We introduce a problem in which a service vehicle seeks to guard a deadline
(boundary) from dynamically arriving mobile targets. The environment is a
rectangle and the deadline is one of its edges. Targets arrive continuously
over time on the edge opposite the deadline, and move towards the deadline at a
fixed speed. The goal for the vehicle is to maximize the fraction of targets
that are captured before reaching the deadline. We consider two cases; when the
service vehicle is faster than the targets, and; when the service vehicle is
slower than the targets. In the first case we develop a novel vehicle policy
based on computing longest paths in a directed acyclic graph. We give a lower
bound on the capture fraction of the policy and show that the policy is optimal
when the distance between the target arrival edge and deadline becomes very
large. We present numerical results which suggest near optimal performance away
from this limiting regime. In the second case, when the targets are slower than
the vehicle, we propose a policy based on servicing fractions of the
translational minimum Hamiltonian path. In the limit of low target speed and
high arrival rate, the capture fraction of this policy is within a small
constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on
Decision and Control and 28th Chinese Control Conferenc
Locating Depots for Capacitated Vehicle Routing
We study a location-routing problem in the context of capacitated vehicle
routing. The input is a set of demand locations in a metric space and a fleet
of k vehicles each of capacity Q. The objective is to locate k depots, one for
each vehicle, and compute routes for the vehicles so that all demands are
satisfied and the total cost is minimized. Our main result is a constant-factor
approximation algorithm for this problem. To achieve this result, we reduce to
the k-median-forest problem, which generalizes both k-median and minimum
spanning tree, and which might be of independent interest. We give a
(3+c)-approximation algorithm for k-median-forest, which leads to a
(12+c)-approximation algorithm for the above location-routing problem, for any
constant c>0. The algorithm for k-median-forest is just t-swap local search,
and we prove that it has locality gap 3+2/t; this generalizes the corresponding
result known for k-median. Finally we consider the "non-uniform"
k-median-forest problem which has different cost functions for the MST and
k-median parts. We show that the locality gap for this problem is unbounded
even under multi-swaps, which contrasts with the uniform case. Nevertheless, we
obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur
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