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Bilevel optimization based on iterative approximation of multiple mappings

Author

Listed:
  • Ankur Sinha

    (Indian Institute of Management)

  • Zhichao Lu

    (Michigan State University)

  • Kalyanmoy Deb

    (Michigan State University)

  • Pekka Malo

    (Aalto University School of Economics)

Abstract

A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical optimization community and evolutionary optimization community. Most of the solution procedures proposed until now are either computationally very expensive or applicable to only small classes of bilevel optimization problems adhering to mathematically simplifying assumptions. In this paper, we propose an evolutionary optimization method that tries to reduce the computational expense by iteratively approximating two important mappings in bilevel optimization; namely, the lower level rational reaction mapping and the lower level optimal value function mapping. The algorithm has been tested on a large number of test problems and comparisons have been performed with other algorithms. The results show the performance gain to be quite significant. To the best knowledge of the authors, a combined theory-based and population-based solution procedure utilizing mappings has not been suggested yet for bilevel problems.

Suggested Citation

  • Ankur Sinha & Zhichao Lu & Kalyanmoy Deb & Pekka Malo, 2020. "Bilevel optimization based on iterative approximation of multiple mappings," Journal of Heuristics, Springer, vol. 26(2), pages 151-185, April.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:2:d:10.1007_s10732-019-09426-9
    DOI: 10.1007/s10732-019-09426-9
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    Cited by:

    1. Jayaswal, Sachin & Sinha, Ankur, 2022. "Bilevel Optimization: Applications, Models and Solution Approaches," IIMA Working Papers WP 2022-05-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    2. Mejía-de-Dios, Jesús-Adolfo & Mezura-Montes, Efrén & Toledo-Hernández, Porfirio, 2022. "Pseudo-feasible solutions in evolutionary bilevel optimization: Test problems and performance assessment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    3. Rihab Said & Maha Elarbi & Slim Bechikh & Lamjed Ben Said, 2022. "Solving combinatorial bi-level optimization problems using multiple populations and migration schemes," Operational Research, Springer, vol. 22(3), pages 1697-1735, July.

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