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DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems

Author

Listed:
  • Burcu Beykal

    (Texas A&M University
    Texas A&M University)

  • Styliani Avraamidou

    (Texas A&M University
    Texas A&M University)

  • Ioannis P. E. Pistikopoulos

    (Texas A&M University
    Texas A&M University)

  • Melis Onel

    (Texas A&M University
    Texas A&M University)

  • Efstratios N. Pistikopoulos

    (Texas A&M University
    Texas A&M University)

Abstract

The Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework is presented for addressing the optimization of bi-level mixed-integer nonlinear programming problems. In this framework, bi-level optimization problems are approximated as single-level optimization problems by collecting samples of the upper-level objective and solving the lower-level problem to global optimality at those sampling points. This process is done through the integration of the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper-level objective, and to consecutively approximate and optimize bi-level mixed-integer nonlinear programming problems that are challenging to solve using exact methods. The performance of DOMINO is assessed through solving numerous bi-level benchmark problems, a land allocation problem in Food-Energy-Water Nexus, and through employing different data-driven optimization methodologies, including both local and global methods. Although this data-driven approach cannot provide a theoretical guarantee to global optimality, we present an algorithmic advancement that can guarantee feasibility to large-scale bi-level optimization problems when the lower-level problem is solved to global optimality at convergence.

Suggested Citation

  • Burcu Beykal & Styliani Avraamidou & Ioannis P. E. Pistikopoulos & Melis Onel & Efstratios N. Pistikopoulos, 2020. "DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems," Journal of Global Optimization, Springer, vol. 78(1), pages 1-36, September.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:1:d:10.1007_s10898-020-00890-3
    DOI: 10.1007/s10898-020-00890-3
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    References listed on IDEAS

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    3. Natnael Nigussie Goshu & Semu Mitiku Kassa, 2024. "A solution method for stochastic multilevel programming problems. A systematic sampling evolutionary approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 149-174.

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