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Implementation of Cartesian grids to accelerate Delaunay-based derivative-free optimization

Author

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  • Pooriya Beyhaghi

    (University of California, San Diego)

  • Thomas Bewley

    (University of California, San Diego)

Abstract

This paper introduces a modification of our original Delaunay-based optimization algorithm (developed in JOGO DOI: 10.1007/s10898-015-0384-2 ) that reduces the number of function evaluations on the boundary of feasibility as compared with the original algorithm. A weaknesses we have identified with the original algorithm is the sometimes faulty behavior of the generated uncertainty function near the boundary of feasibility, which leads to more function evaluations along the boundary of feasibility than might otherwise be necessary. To address this issue, a second search function is introduced which has improved behavior near the boundary of the search domain. Additionally, the datapoints are quantized onto a Cartesian grid, which is successively refined, over the search domain. These two modifications lead to a significant reduction of datapoints accumulating on the boundary of feasibility, and faster overall convergence.

Suggested Citation

  • Pooriya Beyhaghi & Thomas Bewley, 2017. "Implementation of Cartesian grids to accelerate Delaunay-based derivative-free optimization," Journal of Global Optimization, Springer, vol. 69(4), pages 927-949, December.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:4:d:10.1007_s10898-017-0548-3
    DOI: 10.1007/s10898-017-0548-3
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    References listed on IDEAS

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    1. Pooriya Beyhaghi & Thomas R. Bewley, 2016. "Delaunay-based derivative-free optimization via global surrogates, part II: convex constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 383-415, November.
    2. Pooriya Beyhaghi & Daniele Cavaglieri & Thomas Bewley, 2016. "Delaunay-based derivative-free optimization via global surrogates, part I: linear constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 331-382, November.
    3. Paul Belitz & Thomas Bewley, 2013. "New horizons in sphere-packing theory, part II: lattice-based derivative-free optimization via global surrogates," Journal of Global Optimization, Springer, vol. 56(1), pages 61-91, May.
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    Cited by:

    1. Ryan Alimo & Daniele Cavaglieri & Pooriya Beyhaghi & Thomas R. Bewley, 2021. "Design of IMEXRK time integration schemes via Delaunay-based derivative-free optimization with nonconvex constraints and grid-based acceleration," Journal of Global Optimization, Springer, vol. 79(3), pages 567-591, March.
    2. Pooriya Beyhaghi & Ryan Alimo & Thomas Bewley, 2020. "A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging," Computational Optimization and Applications, Springer, vol. 76(1), pages 1-31, May.

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