# DX-NES-ICI
[DX-NES-ICI](https://doi.org/10.1145/3583131.3590518) [1] is a Natural Evolution Strategy (NES) for Mixed-Integer Black-Box Optimization (MI-BBO).
DX-NES-ICI reportedly improves the performance of DX-NES-IC [2], one of the most promising continuous BBO methods, on MI-BBO problems.
Simultaneously, DX-NES-ICI outperforms CMA-ES w. Margin [3], one of the most leading MI-BBO methods.
## Getting Started
### Prerequisites
You need [NumPy](https://numpy.org/) and [SciPy](https://scipy.org/) that are the packages for scientific computing.
### Installing
Please install via pip.
```bash
$ pip install dxnesici
```
## Usage
### Problem setting
Set the number of dimensions (dim), dimensions of continuous variables (dim_co), and dimensions of integer variables (dim_int).
Then, set objective function and the domains of integer variables, where
the decision variables must be arranged in such a way as to concatenate a (dim_co)-dimensional continuous vector and a (dim_int)-dimensional integer vector.
Note that the number of elements of the domain in an integer variable must be greater than or equal to 2.
```python
dim = 20
dim_co = dim // 2
dim_int = dim // 2
domain_int = [list(range(-10, 11)) for _ in range(dim_int)]
def n_int_tablet(x):
xbar = np.array(x)
xbar[dim_co:] = np.round(xbar[dim_co:])
xbar[:dim_co] *= 100
return np.sum(xbar**2)
```
### The hyperparameters of DX-NES-ICI
Set initial mean vector (m), initial step size (sigma), and population size (lamb).
Note that population size should be an even number.
Set the minimum marginal probability (margin).
1.0 / (dim * lamb) [3] is the recommended value of minimum marginal probability.
```python
m = np.ones([dim, 1]) * 2.
sigma = 1.0
lamb = 6
margin = 1.0 / (dim * lamb)
```
### Running DX-NES-ICI
Pass variables to construct DXNESICI.
You must pass the maximal number of evaluations and a target evaluation value to run the optimizer.
Return values are a success flag, the best solution in the last generation, and the best evaluation value in the last generation.
```python
dxnesici = DXNESICI(dim_co, domain_int, n_int_tablet, m, sigma, lamb, margin)
success, x_best, f_best = dxnesici.optimize(dim * 1e4, 1e-10)
```
## Version History
* Version 1.0.3 (2023-12-09)
- Update README.
* Version 1.0.2 (2023-12-09)
- Fixed a bug in the return value of the best solution.
- Fixed misleading implementations of functions in sample programs. Note that in these sample programs, benchmark functions return exactly the same values before and after this fix.
- Add stdout of #Eval when DX-NES-ICI finish.
* Version 1.0.1 (2023-4-20)
- First implementation.
## Reference
1. Koki Ikeda and Isao Ono. 2023. Natural Evolution Strategy for Mixed-Integer Black-Box Optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’23). 8 pages. https://doi.org/10.1145/3583131.3590518
2. Masahiro Nomura, Nobuyuki Sakai, Nobusumi Fukushima, and Isao Ono. 2021. Distance-weighted Exponential Natural Evolution Strategy for Implicitly Constrained Black-Box Function Optimization. In IEEE Congress on Evolutionary Computation (CEC ’21). 1099–1106. https://doi.org/10.1109/CEC45853.2021.9504865
3. Ryoki Hamano, Shota Saito, Masahiro Nomura, and Shinichi Shirakawa. 2022. CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’22). 639–647. https://doi.org/10.1145/3512290.3528827
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"description": "# DX-NES-ICI\n[DX-NES-ICI](https://doi.org/10.1145/3583131.3590518) [1] is a Natural Evolution Strategy (NES) for Mixed-Integer Black-Box Optimization (MI-BBO).\nDX-NES-ICI reportedly improves the performance of DX-NES-IC [2], one of the most promising continuous BBO methods, on MI-BBO problems.\nSimultaneously, DX-NES-ICI outperforms CMA-ES w. Margin [3], one of the most leading MI-BBO methods.\n\n\n## Getting Started\n### Prerequisites\nYou need [NumPy](https://numpy.org/) and [SciPy](https://scipy.org/) that are the packages for scientific computing.\n\n### Installing\nPlease install via pip.\n```bash\n$ pip install dxnesici\n```\n\n\n## Usage\n### Problem setting\nSet the number of dimensions (dim), dimensions of continuous variables (dim_co), and dimensions of integer variables (dim_int).\nThen, set objective function and the domains of integer variables, where\nthe decision variables must be arranged in such a way as to concatenate a (dim_co)-dimensional continuous vector and a (dim_int)-dimensional integer vector.\nNote that the number of elements of the domain in an integer variable must be greater than or equal to 2.\n```python\ndim = 20\ndim_co = dim // 2\ndim_int = dim // 2\ndomain_int = [list(range(-10, 11)) for _ in range(dim_int)]\ndef n_int_tablet(x):\n xbar = np.array(x)\n xbar[dim_co:] = np.round(xbar[dim_co:])\n xbar[:dim_co] *= 100\n return np.sum(xbar**2)\n```\n\n### The hyperparameters of DX-NES-ICI\nSet initial mean vector (m), initial step size (sigma), and population size (lamb).\nNote that population size should be an even number.\nSet the minimum marginal probability (margin).\n 1.0 / (dim * lamb) [3] is the recommended value of minimum marginal probability.\n```python\nm = np.ones([dim, 1]) * 2.\nsigma = 1.0\nlamb = 6\nmargin = 1.0 / (dim * lamb)\n```\n\n### Running DX-NES-ICI\nPass variables to construct DXNESICI.\nYou must pass the maximal number of evaluations and a target evaluation value to run the optimizer.\nReturn values are a success flag, the best solution in the last generation, and the best evaluation value in the last generation.\n```python\ndxnesici = DXNESICI(dim_co, domain_int, n_int_tablet, m, sigma, lamb, margin)\nsuccess, x_best, f_best = dxnesici.optimize(dim * 1e4, 1e-10)\n```\n\n\n## Version History\n* Version 1.0.3 (2023-12-09)\n - Update README.\n* Version 1.0.2 (2023-12-09)\n - Fixed a bug in the return value of the best solution.\n - Fixed misleading implementations of functions in sample programs. Note that in these sample programs, benchmark functions return exactly the same values before and after this fix.\n - Add stdout of #Eval when DX-NES-ICI finish.\n* Version 1.0.1 (2023-4-20)\n - First implementation.\n\n\n## Reference\n1. Koki Ikeda and Isao Ono. 2023. Natural Evolution Strategy for Mixed-Integer Black-Box Optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201923). 8 pages. https://doi.org/10.1145/3583131.3590518\n\n2. Masahiro Nomura, Nobuyuki Sakai, Nobusumi Fukushima, and Isao Ono. 2021. Distance-weighted Exponential Natural Evolution Strategy for Implicitly Constrained Black-Box Function Optimization. In IEEE Congress on Evolutionary Computation (CEC \u201921). 1099\u20131106. https://doi.org/10.1109/CEC45853.2021.9504865\n\n3. Ryoki Hamano, Shota Saito, Masahiro Nomura, and Shinichi Shirakawa. 2022. CMA-ES with Margin: Lower-Bounding Marginal Probability for Mixed-Integer Black-Box Optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922). 639\u2013647. https://doi.org/10.1145/3512290.3528827\n\n\n",
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