EGObox - Efficient Global Optimization toolbox

Rust toolbox for Efficient Global Optimization method (arguably the most well-known bayesian optimization algorithm) which adresses the gradient-free optimization of expensive objective functions.

The egobox package is twofold:

1. for end-users: a Python module, the Python binding of the optimizer named Egor and the surrogate model Gpx, mixture of Gaussian processes, written in Rust.
2. for developers: a set of Rust libraries useful to implement bayesian optimization (EGO-like) algorithms,

The Python module

Installation

bash pip install egobox

Egor optimizer

```python import numpy as np import egobox as egx

Objective function

def f_obj(x: np.ndarray) -> np.ndarray: return (x - 3.5) * np.sin((x - 3.5) / (np.pi))

Minimize f_opt in [0, 25]

res = egx.Egor([[0.0, 25.0]], seed=42).minimize(fobj, maxiters=20) print(f"Optimization f={res.yopt} at {res.xopt}") # Optimization f=[-15.12510323] at [18.93525454] ```

See also this example written in Rust

Gpx surrogate model

```python import numpy as np import matplotlib.pyplot as plt import egobox as egx

Training

xtrain = np.array([0.0, 1.0, 2.0, 3.0, 4.0]) ytrain = np.array([0.0, 1.0, 1.5, 0.9, 1.0]) gpx = egx.Gpx.builder().fit(xtrain, ytrain)

Prediction

xtest = np.linspace(0, 4, 100).reshape((-1, 1)) ytest = gpx.predict(xtest)

Plot

plt.plot(xtest, ytest) plt.plot(xtrain, ytrain, "o") plt.show() ```

See also this example written in Rust

See the tutorial notebooks and examples folder for more information on the usage of the optimizer and mixture of Gaussian processes surrogate model.

The Rust libraries

egobox Rust libraries consists of the following sub-packages.

| Name | Version | Documentation | Description | | :---------------------------------------------------- | :---------------------------------------------------------------------------------------------- | :-------------------------------------------------------------------------- | :---------------------------------------------------------------------------------------- | | doe | | | sampling methods; contains LHS, FullFactorial, Random methods | | gp | | | gaussian process regression; contains Kriging, PLS dimension reduction and sparse methods | | moe | | | mixture of experts using GP models | | ego | | | efficient global optimization with constraints and mixed integer handling |

Usage

Depending on the sub-packages you want to use, you have to add following declarations to your Cargo.toml

text [dependencies] egobox-doe = { version = "0.32" } egobox-gp = { version = "0.32" } egobox-moe = { version = "0.32" } egobox-ego = { version = "0.32" }

Features

The table below presents the various features available depending on the subcrate

| Name | doe | gp | moe | ego | | :----------- | :--- | :--- | :--- | :--- | | serializable | ✔️ | ✔️ | ✔️ | | | persistent | | | ✔️ | ✔️(*) | | blas | | ✔️ | ✔️ | ✔️ | | nlopt | | ✔️ | | ✔️ |

(*) for persistent mixture of gaussian processes with discrete variable available in ego

serializable

When selected, the serialization with serde crate is enabled.

persistent

When selected, the save and load as a json file with serde_json crate is enabled.

blas

When selected, the usage of BLAS/LAPACK backend is possible, see below for more information.

nlopt

When selected, the nlopt crate is used to provide optimizer implementations (ie Cobyla, Slsqp)

Examples

Examples (in examples/ sub-packages folder) are run as follows:

bash cd doe && cargo run --example samplings --release

bash cd gp && cargo run --example kriging --release

bash cd moe && cargo run --example clustering --release

bash cd ego && cargo run --example ackley --release

BLAS/LAPACK backend (optional)

egobox relies on linfa project for methods like clustering and dimension reduction, but also try to adopt as far as possible the same coding structures.

As for linfa, the linear algebra routines used in gp, moe ad ego are provided by the pure-Rust linfa-linalg crate, the default linear algebra provider.

Otherwise, you can choose an external BLAS/LAPACK backend available through the ndarray-linalg crate. In this case, you have to specify the blas feature and a linfa BLAS/LAPACK backend feature (more information in linfa features).

Thus, for instance, to use gp with the Intel MKL BLAS/LAPACK backend, you could specify in your Cargo.toml the following features:

text [dependencies] egobox-gp = { version = "0.32", features = ["blas", "linfa/intel-mkl-static"] }

or you could run the gp example as follows:

bash cd gp && cargo run --example kriging --release --features blas,linfa/intel-mkl-static

Citation

If you find this project useful for your research, you may cite it as follows:

text @article{ Lafage2022, author = {Rémi Lafage}, title = {egobox, a Rust toolbox for efficient global optimization}, journal = {Journal of Open Source Software} year = {2022}, doi = {10.21105/joss.04737}, url = {https://doi.org/10.21105/joss.04737}, publisher = {The Open Journal}, volume = {7}, number = {78}, pages = {4737}, }

Additionally, you may consider adding a star to the repository. This positive feedback improves the visibility of the project.

References

Bartoli, N., Lefebvre, T., Dubreuil, S., Olivanti, R., Priem, R., Bons, N., Martins, J. R. R. A., & Morlier, J. (2019). Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design. Aerospace Science and Technology, 90, 85–102.

Bouhlel, M. A., Bartoli, N., Otsmane, A., & Morlier, J. (2016). Improving kriging surrogates of high-dimensional design models by partial least squares dimension reduction. Structural and Multidisciplinary Optimization, 53(5), 935–952.

Bouhlel, M. A., Hwang, J. T., Bartoli, N., Lafage, R., Morlier, J., & Martins, J. R. R. A. (2019). A python surrogate modeling framework with derivatives. Advances in Engineering Software, 102662.

Dubreuil, S., Bartoli, N., Gogu, C., & Lefebvre, T. (2020). Towards an efficient global multi-disciplinary design optimization algorithm Structural and Multidisciplinary Optimization, 62(4), 1739–1765.

Jones, D. R., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13(4), 455–492.

Diouane, Youssef, et al. TREGO: a trust-region framework for efficient global optimization. Journal of Global Optimization 86.1 (2023): 1-23.

Priem, Rémy, Nathalie Bartoli, and Youssef Diouane. On the use of upper trust bounds in constrained Bayesian optimization infill criteria. AIAA aviation 2019 forum. 2019.

Sasena M., Papalambros P., Goovaerts P., 2002. Global optimization of problems with disconnected feasible regions via surrogate modeling. AIAA Paper.

Ginsbourger, D., Le Riche, R., & Carraro, L. (2010). Kriging is well-suited to parallelize optimization

E.C. Garrido-Merchan and D. Hernandez-Lobato. Dealing with categorical and integer-valued variables in Bayesian Optimization with Gaussian processes.

Zhan, Dawei, et al. A cooperative approach to efficient global optimization. Journal of Global Optimization 88.2 (2024): 327-357

Lisa Pretsch et al. Bayesian optimization of cooperative components for multi-stage aero-structural compressor blade design. Struct Multidisc Optim 68, 84 (2025)

Appriou, T., Rullière, D. & Gaudrie, D, Combination of optimization-free kriging models for high-dimensional problems, Comput Stat 39, 3049–3071 (2024).

S Ament, S Daulton, D Eriksson, M Balandat, E Bakshy, Unexpected improvements to expected improvement for bayesian optimization, Advances in Neural Information Processing Systems, 2023

smtorg. (2018). Surrogate modeling toolbox. GitHub.

License

Licensed under the Apache License, Version 2.0 http://www.apache.org/licenses/LICENSE-2.0