h1

% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@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},
}