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https://github.com/tsudalab/conbqa
https://github.com/tsudalab/conbqa
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- Host: GitHub
- URL: https://github.com/tsudalab/conbqa
- Owner: tsudalab
- License: mit
- Created: 2021-05-10T00:16:13.000Z (over 3 years ago)
- Default Branch: master
- Last Pushed: 2022-07-25T06:35:20.000Z (over 2 years ago)
- Last Synced: 2023-02-27T19:43:36.138Z (almost 2 years ago)
- Language: Python
- Size: 9.77 KB
- Stars: 1
- Watchers: 8
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# conbqa
conbqa is a library for converting continuous black-box optimization into quadratic unconstrained binary optimization (QUBO) so that Ising machines and other QUBO solvers may be applied.
Based on a dataset of several input and output values, the `CONBQA` class instance trains a regression model of the objective function on a coarse-grained random subspace.
The resulting model with appropriate constraints is converted into a QUBO matrix, by solving which we can tell which subspace is the promising area for the next evaluation. Once a new evaluation is made, the regression model is trained again and the loop goes on.
## Install
conbqa package depends on numpy, and scikit-learn.
IBM's cplex package is an optional dependency (Please refer [the product page](https://www.ibm.com/products/ilog-cplex-optimization-studio) for details).
Once you satisfied the dependency, download the repository and run `pip install .` inside the directory.
```console
$ git clone https://github.com/tsudalab/conbqa.git
$ cd conbqa
$ pip install .
```
## Example
Here shows an example case of minimizing a benchmarking function, Hartmann-6.
We firstly load all the modules and define the objective function as a callable object `h6`.
```python
import conbqa
import dimod
import matplotlib.pyplot as plt
from neal import SimulatedAnnealingSampler
import numpy as np
class _H6():
'''
Hartmann 6-Dimensional function
Based on the MATLAB code available on
https://www.sfu.ca/~ssurjano/hart6.html
'''
def __init__(self):
self.lower_bounds = np.array([0, 0, 0, 0, 0, 0])
self.upper_bounds = np.array([1, 1, 1, 1, 1, 1])
self.min = np.array([
0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573
])
self.fmin = -3.32237
self.ndim = 6
self.alpha = np.array([1.0, 1.2, 3.0, 3.2])
self.A = np.array([
[10, 3, 17, 3.5, 1.7, 8],
[0.05, 10, 17, 0.1, 8, 14],
[3, 3.5, 1.7, 10, 17, 8],
[17, 8, 0.05, 10, 0.1, 14]
])
self.P = 1e-4 * np.array([
[1312, 1696, 5569, 124, 8283, 5886],
[2329, 4135, 8307, 3736, 1004, 9991],
[2348, 1451, 3522, 2883, 3047, 6650],
[4047, 8828, 8732, 5743, 1091, 381]
])
def __call__(self, xx : np.ndarray):
if len(xx.shape) == 2:
return np.apply_along_axis(self, 1, xx)
assert len(xx) == 6, "Input vector should be 6 dimensional."
outer = 0
for ii in range(4):
inner = 0
for jj in range(6):
xj = xx[jj]
Aij = self.A[ii, jj]
Pij = self.P[ii, jj]
inner = inner + Aij*(xj-Pij)**2
new = self.alpha[ii] * np.exp(-inner)
outer = outer + new
return -outer
h6 = _H6()
```
The `h6` takes its minimum value $-3.32237$ at point $(0.20169, 0.150011, 0.476874, 0.275332, 0.311652, 0.6573)\in\mathbb{R}^6$.
We evaluate the objective function on 10 scattered points to get initial dataset:
```python
num_init = 10
X = np.stack([
np.linspace(0, 1, num_init)[np.random.permutation(num_init)]
for _ in range(h6.ndim)
], axis=1)
Y = h6(X)
```
The `CONBQA` object is generated by providing initial dataset and the lower and upper bounds of the input.
We have to tell it that we are aiming at minimization.
```python
model = conbqa.CONBQA(X, Y, h6.lower_bounds, h6.upper_bounds, maximization=False)
```
In this example, we encode the search space into 60-bits binary space, and make the regression model be linear model.
```python
model.set_encoding_method_to_RandomSubspaceCoding(60, v=20.0)
model.set_learning_model_to_linear()
```
The parameter `v=20.0` modifies the random subspace coding by dirichlet process method. See references for details.
Then, run 190 times of guessing and evaluation.
We use [dwave-neal](https://docs.ocean.dwavesys.com/projects/neal/en/latest/)'s simulated annealing sampler for solving the QUBO.
Note that the `CONBQA` instance has a method `decode` to convert the obtained binary vector back to continuous vector.
The `add_data` method appends the new data point into the training dataset.
```python
solver = SimulatedAnnealingSampler()
nepoch = 190
for i in range(nepoch):
model.generate_hyperrectangles_and_encode()
model.learn_weights()
q = model.convert_maximization_of_learned_function_into_qubo()
bqm = dimod.BQM.from_qubo(q)
res = solver.sample(bqm)
new_z = res.record['sample'][0]
new_x = model.decode(new_z)
new_y = h6(new_x)
model.add_data(new_x, new_y)
# progress bar
print("\r", "="*int((i+1) / nepoch * 50), ">", "."*(50 - int((i+1) / nepoch * 50)), end="", sep="")
```
We would compare the result with random uniform sampling.
```python
randX = np.random.uniform(size=(200, 6))
randY = h6(randX)
```
Plot the results.
```python
plt.figure(figsize=(8,3), dpi=90)
plt.subplot(1,2,1)
plt.plot(pd.DataFrame(model.y).cummin())
plt.plot(model.y, '.')
plt.ylim(h6.fmin, 0.2)
plt.title("conbqa")
plt.text(100, -3.0, "mean={:.3f}".format(np.mean(model.y)))
plt.ylabel("Objective value")
plt.xlabel("Sampling No.")
plt.subplot(1,2,2)
plt.plot(pd.DataFrame(randY).cummin())
plt.plot(randY, '.')
plt.ylim(h6.fmin, 0.2)
plt.title("random")
plt.text(100, -3.0, "mean={:.3f}".format(np.mean(randY)))
plt.xlabel("Sampling No.")
plt.show()
```
We can see conbqa is generally picking the lower values than random sampling.
## License
The conbqa package is licensed under the MIT "Expat" License.
## Citation
If you find conbqa useful, please cite the article [*Phys. Rev. Research* 4, 023062 (2022).](https://link.aps.org/doi/10.1103/PhysRevResearch.4.023062)
```
@article{izawa_continuous_2022,
title = {Continuous black-box optimization with an {Ising} machine and random subspace coding},
volume = {4},
issn = {2643-1564},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.4.023062},
doi = {10.1103/PhysRevResearch.4.023062},
language = {en},
number = {2},
journal = {Physical Review Research},
author = {Izawa, Syun and Kitai, Koki and Tanaka, Shu and Tamura, Ryo and Tsuda, Koji},
month = apr,
year = {2022},
pages = {023062},
}
```