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Robust Optimization for Unconstrained Simulation-Based Problems

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Omid Nohadani

    (Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Kwong Meng Teo

    (Department of Industrial and Systems Engineering, National University of Singapore, 117576, Singapore)

Abstract

In engineering design, an optimized solution often turns out to be suboptimal when errors are encountered. Although the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method that is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations, such as large partial differential equations (PDE) solver, response surface, and Kriging metamodels. Moreover, this technique can be employed for most real-world problems because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiple scattering of aperiodically arranged dielectrics, relevant to nanophotonic design. The corresponding objective function is highly nonconvex and resides in a 100-dimensional design space. Starting from an “optimized” design, we report a robust solution with a significantly lower worst-case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.

Suggested Citation

  • Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Robust Optimization for Unconstrained Simulation-Based Problems," Operations Research, INFORMS, vol. 58(1), pages 161-178, February.
  • Handle: RePEc:inm:oropre:v:58:y:2010:i:1:p:161-178
    DOI: 10.1287/opre.1090.0715
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    References listed on IDEAS

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    Cited by:

    1. Chamari Pamoshika Jayarathna & Duzgun Agdas & Les Dawes & Tan Yigitcanlar, 2021. "Multi-Objective Optimization for Sustainable Supply Chain and Logistics: A Review," Sustainability, MDPI, vol. 13(24), pages 1-31, December.
    2. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    3. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    4. Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Nonconvex Robust Optimization for Problems with Constraints," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 44-58, February.
    5. Zheng, Liang & Bao, Ji & Xu, Chengcheng & Tan, Zhen, 2022. "Biobjective robust simulation-based optimization for unconstrained problems," European Journal of Operational Research, Elsevier, vol. 299(1), pages 249-262.
    6. J. Lasserre, 2011. "Min-max and robust polynomial optimization," Journal of Global Optimization, Springer, vol. 51(1), pages 1-10, September.
    7. Chung, Byung Do & Yao, Tao & Friesz, Terry L. & Liu, Hongcheng, 2012. "Dynamic congestion pricing with demand uncertainty: A robust optimization approach," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1504-1518.
    8. Emilio Carrizosa & Frédéric Messine, 2021. "An interval branch and bound method for global Robust optimization," Journal of Global Optimization, Springer, vol. 80(3), pages 507-522, July.
    9. Angelo Ciccazzo & Vittorio Latorre & Giampaolo Liuzzi & Stefano Lucidi & Francesco Rinaldi, 2015. "Derivative-Free Robust Optimization for Circuit Design," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 842-861, March.
    10. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Other publications TiSEM 9f3fba48-8501-4ec8-9241-5, Tilburg University, School of Economics and Management.
    11. Ying Cui & Ziyu He & Jong-Shi Pang, 2021. "Nonconvex robust programming via value-function optimization," Computational Optimization and Applications, Springer, vol. 78(2), pages 411-450, March.
    12. Gabriella Dellino & Jack P. C. Kleijnen & Carlo Meloni, 2012. "Robust Optimization in Simulation: Taguchi and Krige Combined," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 471-484, August.

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