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A Nested Differential Evolution Based Algorithm for Solving Multi-objective Bilevel Optimization Problems

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Artificial Life and Computational Intelligence (ACALCI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9592))

Abstract

Bilevel optimization is a challenging class of problems, with applicability in several domains such as transportation, economics and engineering. In a bilevel problem, the aim is to identify the optimum solution(s) of an upper level (“leader”) problem, subject to optimality of a corresponding lower level (“follower”) problem. Most of the studies reported in the literature have focussed on single-objective bilevel problems, wherein both the levels contain only one objective. Several nested algorithms have been proposed in the literature to solve single objective problems, which have been subsequently enhanced through hybridization with local search in order to improve computational efficiency. The handful of algorithms used for multi-objective algorithms so far have used additional enhancements such as use of scalarization, sub-populations or hybridization. However, interestingly, unlike single-objective problems, the performance of a simple nested evolutionary algorithm has not been reported for multi-objective bilevel problems. In this paper, we attempt to address this gap by designing an algorithm which uses differential evolution at both levels. Numerical experiments show that on popular benchmarks, the proposed algorithm exhibits competitive performance with respect to existing state-of-the-art methods.

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Acknowledgment

The third author acknowledges support from Australian Research Council Future Fellowship.

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Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT, 2600, Australia

    Md Monjurul Islam, Hemant Kumar Singh & Tapabrata Ray

Authors
  1. Md Monjurul Islam
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  2. Hemant Kumar Singh
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  3. Tapabrata Ray
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Corresponding author

Correspondence to Hemant Kumar Singh .

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Editors and Affiliations

  1. Canberra, Aust Capital Terr, Australia

    Tapabrata Ray

  2. University of New South Wales, Canberra, Aust Capital Terr, Australia

    Ruhul Sarker

  3. RMIT University, Melbourne, Victoria, Australia

    Xiaodong Li

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Islam, M.M., Singh, H.K., Ray, T. (2016). A Nested Differential Evolution Based Algorithm for Solving Multi-objective Bilevel Optimization Problems. In: Ray, T., Sarker, R., Li, X. (eds) Artificial Life and Computational Intelligence. ACALCI 2016. Lecture Notes in Computer Science(), vol 9592. Springer, Cham. https://doi.org/10.1007/978-3-319-28270-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-28270-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28269-5

  • Online ISBN: 978-3-319-28270-1

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