Systematic evolutionary algorithm for general multilevel stackelberg problems with bounded decision variables (SEAMSP)

Ashenafi Teklay Woldemariam, Semu Mitiku Kassa

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    Multilevel Stackelberg problems are nested optimization problems which reply optimally to hierarchical decisions of subproblems. These kind of problems are common in hierarchical decision making systems and are known to be NP-hard. In this paper, a systematic evolutionary algorithm has been proposed for such types of problems. A unique feature of the algorithm is that it is not affected by the nature of the objective and constraint functions involved in the problem as long as the problem has a solution. The convergence proof of the proposed algorithm is given for special problems containing non-convex and nondifferentiable functions. Moreover, a new concept of (ε, δ)-approximation for Stackelberg solutions is defined. Using this definition comparison of approximate Stackelberg solutions has been studied in this work. The numerical results on various problems demonstrated that the proposed algorithm is very much promising to multilevel Stackelberg problems with bounded constraints, and it can be used as a benchmark for a comparison of approximate results by other algorithms.

    Original languageEnglish
    Pages (from-to)771-790
    Number of pages20
    JournalAnnals of Operations Research
    Volume229
    Issue number1
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Stackelberg
    Evolutionary algorithms
    Optimization problem
    Benchmark
    NP-hard
    Decision making
    Approximation

    All Science Journal Classification (ASJC) codes

    • Decision Sciences(all)
    • Management Science and Operations Research

    Cite this

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    abstract = "Multilevel Stackelberg problems are nested optimization problems which reply optimally to hierarchical decisions of subproblems. These kind of problems are common in hierarchical decision making systems and are known to be NP-hard. In this paper, a systematic evolutionary algorithm has been proposed for such types of problems. A unique feature of the algorithm is that it is not affected by the nature of the objective and constraint functions involved in the problem as long as the problem has a solution. The convergence proof of the proposed algorithm is given for special problems containing non-convex and nondifferentiable functions. Moreover, a new concept of (ε, δ)-approximation for Stackelberg solutions is defined. Using this definition comparison of approximate Stackelberg solutions has been studied in this work. The numerical results on various problems demonstrated that the proposed algorithm is very much promising to multilevel Stackelberg problems with bounded constraints, and it can be used as a benchmark for a comparison of approximate results by other algorithms.",
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    Systematic evolutionary algorithm for general multilevel stackelberg problems with bounded decision variables (SEAMSP). / Woldemariam, Ashenafi Teklay; Kassa, Semu Mitiku.

    In: Annals of Operations Research, Vol. 229, No. 1, 2014, p. 771-790.

    Research output: Contribution to journalArticle

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