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@PHDTHESIS{Claen:465292,
author = {Claßen, Grit},
othercontributors = {Koster, Arie M. C. A. and Schmeink, Anke},
title = {{O}ptimisation under {D}ata {U}ncertainty in {W}ireless
{C}ommunication {N}etworks},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {Publikationsserver der RWTH Aachen University},
reportid = {RWTH-2015-01650},
pages = {VIII, 258 S. : Ill., graph. Darst.},
year = {2015},
note = {Aachen, Techn. Hochsch., Diss., 2015},
abstract = {In this thesis, we study robustness concepts of
mathematical optimisation and apply these to wireless
network problems which are subject to data uncertainty.
Uncertainties occur quite frequently in radio networks as,
for instance, the quality of the transmission signal varies
or user demands fluctuate. Robust and stochastic
optimisation are two methodologies to tackle such deviations
already in the planning phase of the network. While
stochastic optimisation is a suitable technique in case that
the uncertain data obeys a previously known probability
distribution, robust optimisation is able to handle
uncertain data which can be modelled by a so-called
uncertainty set, which may, e.g., be constructed from
historical information. One reason for the popularity of
robust optimisation is that the theoretical complexity of
the original problem is not increased by the incorporation
of uncertainty. We investigate one specific area of
stochastic optimisation, chance constraints, which are
related to robust optimisation, and three robustness
concepts. These concepts comprise Γ-robustness, the more
general multi-band robustness, and the two-stage approach
recoverable robustness.For reliable fixed broadband wireless
networks, we develop miscellaneous (linear) formulations
based on chance constraints and propose performance
improvements such as valid inequalities and a primal
heuristic. Furthermore, we apply all three robustness
concepts to the planning problem of mobile wireless networks
and propose integer linear programming formulations for each
robust problem. For the Γ-robust wireless network planning
problem (WNPP), we additionally develop valid inequalities
and an alternative formulation via a complete
branch-and-price framework. Since the knapsack problem (KP),
which is one of the most fundamental combinatorial problems,
is a subproblem of the WNPP, we study the multi-band robust
KP theoretically and derive new complexity results via a
dynamic programming algorithm. To apply this algorithm to a
variant of the multi-band robust WNPP, we adopt Lagrangian
relaxation. Additionally, we incorporate recoverable
robustness to the WNPP to model the option of switching base
stations off during low traffic times. Furthermore, to
obtain a full description of mobile wireless networks, we
develop novel approaches and discuss modifications of
existing formulations to model interference in the WNPP. All
theoretical investigations are supported by several
extensive computational studies performed on realistic test
instances. Moreover, we compare the two different
formulations of the Γ-robust WNPP and Γ-robust to
multi-band robust solutions via a numerical evaluation.
Finally, we discuss the interpretation of computational
studies critically based on the so-called performance
variability which is intrinsic to mixed integer linear
programs. We conclude by final remarks on the investigated
robustness concepts and present future research topics.},
cin = {113320 / 617120 / 110000},
ddc = {510},
cid = {$I:(DE-82)113320_20140620$ / $I:(DE-82)617120_20140620$ /
$I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
urn = {urn:nbn:de:hbz:82-rwth-2015-016505},
url = {https://publications.rwth-aachen.de/record/465292},
}
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