Problems from Vladislavleva
These problems are introduced and studied in the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
- dcgpy.generate_kotanchek()
Generates the problem Kotanchek from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = \frac{e^{-(x_1-1)^2}}{1.2+(x_2-2.5)^2}\]\(x_1\) and \(x_2\) are sampled in one hundred randomly selected points in [0.3,4]x[0.3,4].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> from mpl_toolkits.mplot3d import Axes3D >>> import matplotlib.pyplot as plt >>> X, Y = generate_kotanchek() >>> fig = plt.figure() >>> ax = fig.gca(projection='3d') >>> ax.scatter(X[:,0], X[:,1], Y)
- dcgpy.generate_salutowicz()
Generates the problem Salutowicz from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = e^{-x} x^3 \cos x\sin x (\cos x \sin^2 x - 1)\]x is sampled in one hundred points uniformly sampled in [0.5,10].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_salutowicz() >>> plt.plot(X,Y, '.')
- dcgpy.generate_salutowicz2d()
Generates the problem Salutowicz2D from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = e^{-x} x^3 \cos x_1\sin x_1 (\cos x_1 \sin^2 x_1 - 1) * (x_2 - 5)\]\(x_1\) and \(x_2\) are sampled in 601 randomly selected points in [0.05,10]x[0.05,10].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> from mpl_toolkits.mplot3d import Axes3D >>> import matplotlib.pyplot as plt >>> X, Y = generate_kotanchek() >>> fig = plt.figure() >>> ax = fig.gca(projection='3d') >>> ax.scatter(X[:,0], X[:,1], Y)
- dcgpy.generate_uball5d()
Generates the problem UBall5D from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = \frac{10}{5 + \sum_{i=1}^5 (x_i-3)^2}\]\(x_i\) are sampled in 1024 randomly selected points in \([0.05,6.05]^5\).
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_uball5d() >>> plt.plot(X,Y, '.')
- dcgpy.generate_ratpol3d()
Generates the problem RatPol3D from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = 30 \frac{(x_1 - 3)(x_3 - 1)}{x_2^2(x_1-10)}\]\(x_1\), \(x_2\), \(x_3\) are sampled in 300 randomly selected points in [0.05,2] x [1,2].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> import matplotlib.pyplot as plt >>> X, Y = generate_ratpol3d() >>> plt.plot(X,Y, '.')
- dcgpy.generate_sinecosine()
Generates the problem SineCosine from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = 6 \sin(x_1)\cos(x_2)\]\(x_1\), \(x_2\) are sampled in 30 randomly selected points in [0.1,5.9] x [0.1,5.9].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> from mpl_toolkits.mplot3d import Axes3D >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.gca(projection='3d') >>> ax.scatter(X[:,0], X[:,1], Y)
- dcgpy.generate_ripple()
Generates the problem Ripple from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = (x_1-3)(x_2-3) + 2\sin((x_1-4)(x_2-4))\]\(x_1\), \(x_2\) are sampled in 300 randomly selected points in [0.05,6.05] x [0.05,6.05].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> from mpl_toolkits.mplot3d import Axes3D >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.gca(projection='3d') >>> ax.scatter(X[:,0], X[:,1], Y)
- dcgpy.generate_ratpol2d()
Generates the problem RatPol2D from the paper:
Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2008): 333-349.
The functional form of such a problem is:
\[y = \frac{(x_1-3)^4+(x_2-3)^3-(x_2-3)}{(x_2-2)^4+10}\]\(x_1\), \(x_2\) are sampled in 50 randomly selected points in [0.05,6.05] x [0.05,6.05].
- Returns
A tuple containing the points (
2D NumPy float array) and labels (2D NumPy float array).
Examples:
>>> from dcgpy import * >>> from mpl_toolkits.mplot3d import Axes3D >>> import matplotlib.pyplot as plt >>> fig = plt.figure() >>> ax = fig.gca(projection='3d') >>> ax.scatter(X[:,0], X[:,1], Y)