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    Dynamic Programming Multi-Objective Combinatorial Optimization

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    Type
    Dissertation
    Authors
    Mankowski, Michal cc
    Advisors
    Moshkov, Mikhail cc
    Committee members
    Keyes, David E. cc
    Shihada, Basem cc
    Boros, Endre
    Program
    Computer Science
    KAUST Department
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Date
    2020-10-18
    Embargo End Date
    2021-10-31
    Permanent link to this record
    http://hdl.handle.net/10754/665627
    
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    Summary
    A modified version of this dissertation is available in book form at https://link.springer.com/book/10.1007%2F978-3-030-63920-4
    Access Restrictions
    At the time of archiving, the student author of this dissertation opted to temporarily restrict access to it. The full text of this dissertation became available to the public after the expiration of the embargo on 2021-10-31.
    Abstract
    In this dissertation, we consider extensions of dynamic programming for combinatorial optimization. We introduce two exact multi-objective optimization algorithms: the multi-stage optimization algorithm that optimizes the problem relative to the ordered sequence of objectives (lexicographic optimization) and the bi-criteria optimization algorithm that simultaneously optimizes the problem relative to two objectives (Pareto optimization). We also introduce a counting algorithm to count optimal solution before and after every optimization stage of multi-stage optimization. We propose a fairly universal approach based on so-called circuits without repetitions in which each element is generated exactly one time. Such circuits represent the sets of elements under consideration (the sets of feasible solutions) and are used by counting, multi-stage, and bi-criteria optimization algorithms. For a given optimization problem, we should describe an appropriate circuit and cost functions. Then, we can use the designed algorithms for which we already have proofs of their correctness and ways to evaluate the required number of operations and the time. We construct conventional (which work directly with elements) circuits without repetitions for matrix chain multiplication, global sequence alignment, optimal paths in directed graphs, binary search trees, convex polygon triangulation, line breaking (text justification), one-dimensional clustering, optimal bitonic tour, and segmented least squares. For these problems, we evaluate the number of operations and the time required by the optimization and counting algorithms, and consider the results of computational experiments. If we cannot find a conventional circuit without repetitions for a problem, we can either create custom algorithms for optimization and counting from scratch or can transform a circuit with repetitions into a so-called syntactical circuit, which is a circuit without repetitions that works not with elements but with formulas representing these elements. We apply both approaches to the optimization of matchings in trees and apply the second approach to the 0/1 knapsack problem. We also briefly introduce our work in operation research with applications to health care. This work extends our interest in the optimization field from developing new methods included in this dissertation towards the practical application.
    Citation
    Mankowski, M. (2020). Dynamic Programming Multi-Objective Combinatorial Optimization. KAUST Research Repository. https://doi.org/10.25781/KAUST-9FUC0
    DOI
    10.25781/KAUST-9FUC0
    Relations
    Is Previous Version Of:
    • [Book]
      Mankowski, M., & Moshkov, M. (2021). Dynamic Programming Multi-Objective Combinatorial Optimization. Studies in Systems, Decision and Control. DOI: 10.1007/978-3-030-63920-4 Handle: 10754/667880
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-9FUC0
    Scopus Count
    Collections
    PhD Dissertations; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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