/Bifidelity-Surrogate-Modelling

Implementation of the work presented in "Bi-fidelity Surrogate Modelling: Showcasing the need for new test instances" (2022) by Andres-Thio N, Munoz MA, Smith-Miles K

Primary LanguageC++

Bi-fidelity Surrogate Modelling

This repository contains the code used to run and analyse all experiments in "Bi-fidelity Surrogate Modelling: Showcasing the need for new test instances" (2022) by Andrés-Thió N, Muñoz MA, and Smith-Miles K.

The code implements Kriging12 and Co-Kriging34 as surrogate models. That is, the implementation generates a sample of a bi-fidelity function (a high fidelity sample and a low fidelity sample of specified size), and trains the chosen surrogate model, without the added functionality of choosing further samples. Multiple literature test instances are implemented here56789101112131415, as well as a novel instance creation procedure which adds a disturbance to a high-fidelity function to create a low-fidelity function. In this implementation functions from the COCO test suite16 are used as the high fidelity functions. The performance of both Kriging and Co-Kriging is assessed by calculating the Relative Root Mean Squared Error (RRMSE) between the trained model and the high fidelity source.

All instructions on how to rerun all experiments are given in the runAllExperiments.bash file. As given, all experiments and analysis can be run sequentially by simply running the script, although this is not recommended. Rather, it is recommmended to use a computer cluster to run the main experiments as indicated in the bash script.

After completing all experiments and analysis, the folder data and its subfolders should contain all of the experimental results and analysis plots. The same folder containing all of the data is given in figshare17 and can be accessed here. Note however that the features of the instances created using the COCO suite and disturbances will vary based on the system these experiments are run on, as function instantiation includes randomness. Whilst all random functions are seeded by constants to allow for reproducibility on the same system, the random sequences (and therefore the final functions) generated by different systems might vary.

The following are required for this code to be compiled and executed:

  • gcc: Although any C++ compiler should work, make sure if using a different compiler to modify the Makefile files inside cpp_code.
  • cmake
  • Eigen: For details consult Eigen's getting started. Make sure you modify the path to eigen inside Makefile.local to match that of your download location.
  • R: Also certain libraries are needed: stringr, ggplot2, gridExtra, egg, rpart, tibble, bitops and rattle.

Footnotes

  1. Krige DG (1951) "A statistical approach to some basic mine valuation problems on the witwatersrand". Journal of the Southern African Institute of Mining and Metallurgy 52(6):119–139. ↩

  2. Jones DR (2001) "A taxonomy of global optimization methods based on response surfaces". Journal of global optimization 21(4):345–383. ↩

  3. Kennedy MC, O’Hagan A (2000) "Predicting the output from a complex computer code when fast approximations are available". Biometrika 87(1):1–13. ↩

  4. Forrester AI, S ́obester A, Keane AJ (2007) "Multi-fidelity optimization via surrogate modelling". Proceedings of the royal society a: mathematical, physical and engineering sciences 463(2088):3251–3269. ↩

  5. Song X, Lv L, Sun W, Zhang J (2019) "A radial basis function-based multi-fidelity surrogate model: exploring correlation between high-fidelity and low-fidelity models". Structural and Multidisciplinary Optimization 60(3):965–981. ↩

  6. March A, Willcox K (2012) "Provably convergent multifidelity optimization algorithm not requiring high-fidelity derivatives". AIAA journal 50(5):1079–1089. ↩

  7. Rajnarayan D, Haas A, Kroo I (2008) "A multifidelity gradient-free optimization method and application to aerodynamic design". 12th AIAA/ISSMO multidisciplinary analysis and optimization conference, 6020. ↩

  8. Liu B, Koziel S, Zhang Q (2016) "A multi-fidelity surrogate-model-assisted evolutionary algorithm for computationally expensive optimization problems". Journal of computational science 12:28–37. ↩

  9. Wang H, Jin Y, Doherty J (2017) "A generic test suite for evolutionary multifidelity optimization". IEEE Transactions on Evolutionary Computation 22(6):836–850. ↩

  10. Liu H, Ong YS, Cai J, Wang Y (2018b) "Cope with diverse data structures in multi-fidelity modeling: a gaussian process method". Engineering Applications of Artificial Intelligence 67:211–225. ↩

  11. Wu Y, Hu J, Zhou Q, Wang S, Jin P (2020) "An active learning multi-fidelity metamodeling method based on the bootstrap estimator". Aerospace Science and Technology 106:106116. ↩

  12. Shi M, Lv L, Sun W, Song X (2020) "A multi-fidelity surrogate model based on support vector regression". Structural and Multidisciplinary Optimization 1–13. ↩

  13. Dong H, Song B, Wang P, Huang S (2015) "Multi-fidelity information fusion based on prediction of kriging". Structural and Multidisciplinary Optimization 51(6):1267–1280. ↩

  14. Xiong S, Qian PZ, Wu CJ (2013) "Sequential design and analysis of high-accuracy and low-accuracy computer codes". Technometrics 55(1):37–46. ↩

  15. Park C, Haftka RT, Kim NH (2018) "Low-fidelity scale factor improves bayesian multi-fidelity prediction by reducing bumpiness of discrepancy function". Structural and Multidisciplinary Optimization 58(2):399–414. ↩

  16. Hansen N, Auger A, Ros R, Mersmann O, Tuˇsar T, Brockhoff D (2020) "COCO: A platform for comparing continuous optimizers in a black-box setting". Optimization Methods and Software URL http://dx.doi.org/10.1080/10556788.2020.1808977 ↩

  17. Andres-Thio, Nicolau; Munoz Acosta, Mario Andres; Smith-Miles, Kate (2022): Data folder. figshare. Dataset. https://dx.doi.org/10.6084/m9.figshare.19196594.v1 ↩