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@PHDTHESIS{Kuhnke:860943,
author = {Kuhnke, Sascha David},
othercontributors = {Koster, Arie Marinus and Büsing, Christina Maria Katharina
and Liers, Frauke},
title = {{M}athematical optimization of engineering problems via
discretization : pooling, wastewater treatment, and central
receiver systems},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2022-11525},
pages = {1 Online-Ressource : Illustrationen, Diagramme},
year = {2022},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2023; Dissertation, RWTH Aachen University, 2022},
abstract = {Increasing demand and scarcity of resources require strong
and innovative solutions for engineering problems in the
energy industry. Such problems can often be formulated as
nonconvex optimization problems which require the
application of global optimization algorithms to solve them
to optimality. As these algorithms struggle to solve
real-world instances within reasonable running time,
heuristics are a common alternative since they are usually
much faster and obtain strong but not necessarily optimal
solutions. In this thesis, we develop efficient heuristics
based on discretization which approximate the nonconvex
problem by a mixed-integer linear program (MILP). This
discretized MILP is much easier to solve and may still yield
an optimal solution for the original problem if a suitable
discretization for the MILP is chosen. The main part of this
thesis addresses the selection of a suitable discretization
which is often very difficult to find in practice. To this
end, we develop adaptive discretization algorithms which
iteratively improve the discretization by solving different
discretized MILPs. In each iteration, the new discretization
is adapted based on the MILP solution of the previous
iteration. This yields discretizations that are tailored to
the problem structure and thus result in stronger solutions
for the original problem. We first apply this approach to
the general problem class of quadratically constrained
quadratic programs (QCQPs) and perform an extensive
computational study to show its effectiveness in comparison
to commercial solvers. Then, we develop problem specific
adaptive discretization algorithms for the pooling problem
and the design of water usage and treatment networks (WUTN
design). Again, extensive computational experiments
highlight the strength of the adaptive discretization
algorithms in comparison to commercial solvers and
alternative solution approaches. Since the discretized MILP
of WUTN design requires the main computational effort in the
above algorithm, we next investigate the polyhedral
structure of this MILP from a theoretical point of view. We
derive several classes of valid inequalities and prove that
some of them are facet-defining for a relaxation of this
MILP. In the last part of this thesis, we apply
discretization to introduce a robust MILP formulation for
the optimization of aiming strategies in central receiver
systems (CRS). A case study on real data shows that this
formulation obtains solutions with economical benefits over
a conventional approach while providing the same degree of
safety against material damage.},
cin = {113320 / 110000},
ddc = {510},
cid = {$I:(DE-82)113320_20140620$ / $I:(DE-82)110000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2022-11525},
url = {https://publications.rwth-aachen.de/record/860943},
}
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