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  <doc>
    <id>9734</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>doctoralthesis</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2024-04-29</thesisDateAccepted>
    <title language="eng">A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">This thesis introduces the novel hybrid algorithm DisCOptER for globally optimal flight planning. DisCOptER (Discrete-Continuous Optimization for Enhanced Resolution) com- bines discrete and continuous optimization in a two-stage approach to find optimal trajectories up to arbitrary precision in finite time. In the discrete phase, a directed auxiliary graph is created in order to define a set of candidate paths that densely covers the relevant part of the trajectory space. Then, Yen’s algorithm is employed to identify a set of promising candidate paths. These are used as starting points for the subsequent stage in which they are refined with a locally convergent optimal control method. The correctness, accuracy, and complexity of DisCOptER are intricately linked to the choice of the switch-over point, defined by the discretization coarseness. Only a sufficiently dense graph enables the algorithm to find a path within the convex domain surrounding the global minimizer. Initialized with such a path, the second stage rapidly converges to the optimum. Conversely, an excessively dense graph poses the risk of overly costly and redundant computations. The determination of the optimal switch-over point necessitates a profound understanding of the local behavior of the problem, the approximation properties of the graph, and the convergence characteristics of the employed optimal control method. These topics are explored extensively in this thesis. Crucially, the density of the auxiliary graph is solely dependent on the en- vironmental conditions, yet independent of the desired solution accuracy. As a consequence, the algorithm inherits the superior asymptotic convergence properties of the optimal control stage. The practical implications of this computational efficiency are demonstrated in realistic environments, where the DisCOptER algorithm consistently delivers highly accurate globally optimal trajectories with exceptional computational efficiency. This notable improvement upon existing approaches underscores the algorithm’s significance. Beyond its technical prowess, the DisCOptER algorithm stands as a valuable tool contributing to the reduction of costs and the overall enhancement of flight operations efficiency.</abstract>
    <identifier type="url">http://dx.doi.org/10.17169/refubium-43526</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY-NC - Namensnennung - Nicht kommerziell 4.0 International</licence>
    <advisor>Ralf Borndörfer</advisor>
    <author>Fabian Danecker</author>
    <submitter>Martin Weiser</submitter>
    <advisor>Martin Weiser</advisor>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
    <thesisGrantor>Freie Universität Berlin</thesisGrantor>
  </doc>
</export-example>
