# CR-FM-NES [[slide]](slide_cec2022.pdf)
[CR-FM-NES](https://arxiv.org/abs/2201.11422) [1] implementation.
The main feature of CR-FM-NES is that both time and space complexity are linear, with partially considering variable dependencies.
Therefore, it is especially suitable for high-dimensional problems (about hundreds to thousands of dimensions).
On the other hand, it often achieves high performance even on low-dimensional problems.
This is an extension of [FM-NES (Fast Moving Natural Evolution Strategy)](https://arxiv.org/abs/2108.09455) [2] to be
applicable in high-dimensional problems.
Please e-mail at masahironomura5325@gmail.com if you have any issue.
<img width="1215" alt="188303830-aa7b11d0-c6ff-4d1a-9bd8-2ccbf4d7e2dd" src="https://user-images.githubusercontent.com/10880858/211967554-65d632bd-3e77-4725-998c-20f69bb8f5ce.png">
If you find this code useful in your research then please cite:
```bibtex
@INPROCEEDINGS{nomura2022fast,
title={Fast Moving Natural Evolution Strategy for High-Dimensional Problems},
author={Nomura, Masahiro and Ono, Isao},
booktitle={2022 IEEE Congress on Evolutionary Computation (CEC)},
pages={1-8},
year={2022},
}
```
## News
* **(2022/07)** The paper [Fast Moving Natural Evolution Strategy for High-Dimensional Problems](https://arxiv.org/abs/2201.11422) has been accepted at IEEE CEC'22.
* **(2022/12)** CR-FM-NES has been integrated into [evosax](https://github.com/RobertTLange/evosax), which provides JAX-based evolution strategies implementation. Thanks [@RobertTLange](https://github.com/RobertTLange) and [@Obliman](https://github.com/Obliman)!
## Getting Started
### Prerequisites
You need only [NumPy](http://www.numpy.org/) that is the package for scientific computing.
### Installing
Please run the following command.
```bash
$ pip install crfmnes
```
## Example
This is a simple example that objective function is sphere function.
Note that the optimization problem is formulated as **minimization** problem.
```python
import numpy as np
from crfmnes import CRFMNES
dim = 3
f = lambda x: np.sum(x**2)
mean = np.ones([dim, 1]) * 0.5
sigma = 0.2
lamb = 6
crfmnes = CRFMNES(dim, f, mean, sigma, lamb)
x_best, f_best = crfmnes.optimize(100)
print("x_best:{}, f_best:{}".format(x_best, f_best))
# x_best:[1.64023896e-05 2.41682149e-05 3.40657594e-05], f_best:2.0136169613476005e-09
```
## For Constrained Problems
CR-FM-NES can be applied to (implicitly) constrained black-box optimization problems.
Please set the objective function value of the infeasible solution to `np.inf`.
CR-FM-NES reflects the information and performs an efficient search.
Please refer to [3] for the details of the constraint handling methods implemented in this repository.
## Other Versions of CR-FM-NES
I really appreciate that CR-FM-NES is implemented in other settings.
* C# Implementation: [bakanaouji/CRFMNES_CS](https://github.com/bakanaouji/CRFMNES_CS)
* C++ Implementation: [dietmarwo/fast-cma-es](https://github.com/dietmarwo/fast-cma-es/blob/master/_fcmaescpp/crfmnes.cpp)
* Jax(Python) Implementation: [RobertTLange/evosax](https://github.com/RobertTLange/evosax/blob/main/evosax/strategies/cr_fm_nes.py)
## References
* [1] [M. Nomura, I. Ono, Fast Moving Natural Evolution Strategy for High-Dimensional Problems, IEEE CEC, 2022.](https://arxiv.org/abs/2201.11422)
* [2] [M. Nomura, I. Ono, Natural Evolution Strategy for Unconstrained and Implicitly Constrained Problems with Ridge Structure, IEEE SSCI, 2021.](https://arxiv.org/abs/2108.09455)
* [3] [M. Nomura, N. Sakai, N. Fukushima, and I. Ono, Distance-weighted Exponential Natural Evolution Strategy for Implicitly Constrained Black-Box Function Optimization, IEEE CEC, 2021.](https://ieeexplore.ieee.org/document/9504865)
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"description": "# CR-FM-NES [[slide]](slide_cec2022.pdf)\n\n[CR-FM-NES](https://arxiv.org/abs/2201.11422) [1] implementation.\nThe main feature of CR-FM-NES is that both time and space complexity are linear, with partially considering variable dependencies.\nTherefore, it is especially suitable for high-dimensional problems (about hundreds to thousands of dimensions).\nOn the other hand, it often achieves high performance even on low-dimensional problems.\nThis is an extension of [FM-NES (Fast Moving Natural Evolution Strategy)](https://arxiv.org/abs/2108.09455) [2] to be\napplicable in high-dimensional problems.\nPlease e-mail at masahironomura5325@gmail.com if you have any issue.\n\n<img width=\"1215\" alt=\"188303830-aa7b11d0-c6ff-4d1a-9bd8-2ccbf4d7e2dd\" src=\"https://user-images.githubusercontent.com/10880858/211967554-65d632bd-3e77-4725-998c-20f69bb8f5ce.png\">\n\nIf you find this code useful in your research then please cite:\n```bibtex\n@INPROCEEDINGS{nomura2022fast,\n title={Fast Moving Natural Evolution Strategy for High-Dimensional Problems},\n author={Nomura, Masahiro and Ono, Isao},\n booktitle={2022 IEEE Congress on Evolutionary Computation (CEC)}, \n pages={1-8},\n year={2022},\n}\n```\n\n## News\n* **(2022/07)** The paper [Fast Moving Natural Evolution Strategy for High-Dimensional Problems](https://arxiv.org/abs/2201.11422) has been accepted at IEEE CEC'22.\n* **(2022/12)** CR-FM-NES has been integrated into [evosax](https://github.com/RobertTLange/evosax), which provides JAX-based evolution strategies implementation. Thanks [@RobertTLange](https://github.com/RobertTLange) and [@Obliman](https://github.com/Obliman)!\n\n\n## Getting Started\n\n\n### Prerequisites\n\nYou need only [NumPy](http://www.numpy.org/) that is the package for scientific computing.\n\n### Installing\n\nPlease run the following command.\n\n```bash\n$ pip install crfmnes\n```\n\n## Example\n\nThis is a simple example that objective function is sphere function.\nNote that the optimization problem is formulated as **minimization** problem.\n\n```python\nimport numpy as np\nfrom crfmnes import CRFMNES\n\ndim = 3\nf = lambda x: np.sum(x**2)\nmean = np.ones([dim, 1]) * 0.5\nsigma = 0.2\nlamb = 6\ncrfmnes = CRFMNES(dim, f, mean, sigma, lamb)\n\nx_best, f_best = crfmnes.optimize(100)\nprint(\"x_best:{}, f_best:{}\".format(x_best, f_best))\n# x_best:[1.64023896e-05 2.41682149e-05 3.40657594e-05], f_best:2.0136169613476005e-09\n```\n\n## For Constrained Problems\n\nCR-FM-NES can be applied to (implicitly) constrained black-box optimization problems.\nPlease set the objective function value of the infeasible solution to `np.inf`.\nCR-FM-NES reflects the information and performs an efficient search. \nPlease refer to [3] for the details of the constraint handling methods implemented in this repository.\n\n## Other Versions of CR-FM-NES\n\nI really appreciate that CR-FM-NES is implemented in other settings.\n\n* C# Implementation: [bakanaouji/CRFMNES_CS](https://github.com/bakanaouji/CRFMNES_CS)\n* C++ Implementation: [dietmarwo/fast-cma-es](https://github.com/dietmarwo/fast-cma-es/blob/master/_fcmaescpp/crfmnes.cpp)\n* Jax(Python) Implementation: [RobertTLange/evosax](https://github.com/RobertTLange/evosax/blob/main/evosax/strategies/cr_fm_nes.py)\n\n\n## References\n* [1] [M. Nomura, I. Ono, Fast Moving Natural Evolution Strategy for High-Dimensional Problems, IEEE CEC, 2022.](https://arxiv.org/abs/2201.11422)\n* [2] [M. Nomura, I. Ono, Natural Evolution Strategy for Unconstrained and Implicitly Constrained Problems with Ridge Structure, IEEE SSCI, 2021.](https://arxiv.org/abs/2108.09455)\n* [3] [M. Nomura, N. Sakai, N. Fukushima, and I. Ono, Distance-weighted Exponential Natural Evolution Strategy for Implicitly Constrained Black-Box Function Optimization, IEEE CEC, 2021.](https://ieeexplore.ieee.org/document/9504865)\n",
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