ORBIT

ORBIT: optimization by radial basis function interpolation in trust-regions. We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points is sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points. We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also encouraging and support ORBIT’s effectiveness on blackbox functions for which no special mathematical structure is known or available.


References in zbMATH (referenced in 23 articles )

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  1. Sanguinetti, Guido (ed.); Huynh-Thu, Vân Anh (ed.): Gene regulatory networks. Methods and protocols (2019)
  2. Audet, Charles; Kokkolaras, Michael; Le Digabel, Sébastien; Talgorn, Bastien: Order-based error for managing ensembles of surrogates in mesh adaptive direct search (2018)
  3. Elisov, L. N.; Gorbachenko, V. I.; Zhukov, M. V.: Learning radial basis function networks with the trust region method for boundary problems (2018)
  4. He, Xinyu; Hu, Yangzhou; Powell, Warren B.: Optimal learning for nonlinear parametric belief models over multidimensional continuous spaces (2018)
  5. Nedělková, Zuzana; Lindroth, Peter; Patriksson, Michael; Strömberg, Ann-Brith: Efficient solution of many instances of a simulation-based optimization problem utilizing a partition of the decision space (2018)
  6. Nuñez, Luigi; Regis, Rommel G.; Varela, Kayla: Accelerated random search for constrained global optimization assisted by radial basis function surrogates (2018)
  7. Zhou, Zhe; Bai, Fusheng: An adaptive framework for costly black-box global optimization based on radial basis function interpolation (2018)
  8. Boukouvala, Fani; Faruque Hasan, M. M.; Floudas, Christodoulos A.: Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption (2017)
  9. Fang, Xiaowei; Ni, Qin: A frame-based conjugate gradients direct search method with radial basis function interpolation model (2017)
  10. Akhtar, Taimoor; Shoemaker, Christine A.: Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection (2016)
  11. Larson, Jeffrey; Wild, Stefan M.: A batch, derivative-free algorithm for finding multiple local minima (2016)
  12. Müller, Juliane: MISO: mixed-integer surrogate optimization framework (2016)
  13. Benner, Peter; Gugercin, Serkan; Willcox, Karen: A survey of projection-based model reduction methods for parametric dynamical systems (2015)
  14. Constantine, P. G.; Emory, M.; Larsson, J.; Iaccarino, G.: Exploiting active subspaces to quantify uncertainty in the numerical simulation of the hyshot II scramjet (2015)
  15. Yuan, Ya-xiang: Recent advances in trust region algorithms (2015)
  16. Müller, Juliane; Shoemaker, Christine A.; Piché, Robert: SO-I: a surrogate model algorithm for expensive nonlinear integer programming problems including global optimization applications (2014)
  17. Zhang, Zaikun: Sobolev seminorm of quadratic functions with applications to derivative-free optimization (2014)
  18. Rios, Luis Miguel; Sahinidis, Nikolaos V.: Derivative-free optimization: a review of algorithms and comparison of software implementations (2013)
  19. Le Thi, H. A.; Vaz, A. I. F.; Vicente, L. N.: Optimizing radial basis functions by d.c. programming and its use in direct search for global derivative-free optimization (2012)
  20. March, Andrew; Willcox, Karen: Constrained multifidelity optimization using model calibration (2012)

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