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

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Publication Details

Author list: Woldemariam AT, Kassa SM

Publisher: Springer (part of Springer Nature): Springer Open Choice Hybrid Journals

Place: DORDRECHT

Publication year: 2015

Journal: Annals of Operations Research (0254-5330)

Journal acronym: ANN OPER RES

Volume number: 229

Issue number: 1

Start page: 771

End page: 790

Number of pages: 20

ISSN: 0254-5330

eISSN: 1572-9338

Languages: English-Great Britain (EN-GB)

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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 non-differentiable functions. Moreover, a new concept of -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.

Keywords

Evolutionary algorithm, Hierarchical decision, Multilevel Stackelberg problems, Systematic sampling

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