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Author:
Burdakov, Oleg (Linköping University, Department of Mathematics, Optimization ) (Linköping University, The Institute of Technology)
Doherty, Patrick (Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab) (Linköping University, The Institute of Technology)
Holmberg, Kaj (Linköping University, Department of Mathematics, Optimization ) (Linköping University, The Institute of Technology)
Olsson, Per-Magnus (Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab) (Linköping University, The Institute of Technology)
Title:
Optimal placement of UV-based communications relay nodes
Department:
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, Department of Mathematics, Optimization
Linköping University, The Institute of Technology
Publication type:
Article in journal (Refereed)
Language:
English
Publisher: Springer
Status:
Published
In:
Journal of Global Optimization(ISSN 0925-5001)(EISSN 1573-2916)
Volume:
48
Issue:
4
Pages:
511-531
Year of publ.:
2010
URI:
urn:nbn:se:liu:diva-60067
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-60067
ISI:
000283223700001
Subject category:
Mathematics
SVEP category:
MATHEMATICS
Keywords(en) :
Unmanned vehicles, Global optimization, Hop-restricted shortest paths, Pareto solution, Label correcting algorithms
Abstract(en) :

We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.

Note:
The original publication is available at www.springerlink.com:Oleg Burdakov, Patrick Doherty, Kaj Holmberg and Per-Magnus Olsson, Optimal placement of UV-based communications relay nodes, 2010, Journal of Global Optimization, (48), 4, 511-531.http://dx.doi.org/10.1007/s10898-010-9526-8Copyright: Springer Science Business Mediahttp://www.springerlink.com/
Available from:
2010-10-05
Created:
2010-10-05
Last updated:
2013-08-29
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