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problems.dynamic.gts

Classes

GTS1 

GTS1(**kwargs)

Bases: GTS

\[\begin{equation} \text{min} \begin{cases} f_1(\mathbf{x},t) = x_1 \\ f_2(\mathbf{x},t) = g(\mathbf{x},t)(1 - (\frac{x_1}{g(\mathbf{x},t)})^{H(t)}) \end{cases} \end{equation}\]

GTS1 PS

GTS1 PF

Source code in pydmoo/problems/dynamic/gts.py 
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def __init__(self, **kwargs):
    super().__init__(part_idx=1, bounds=((0, 1), (-1, 1), (-1, 2)), **kwargs)

GTS2 

GTS2(**kwargs)

Bases: GTS

\[\begin{equation} \text{min} \begin{cases} f_1(\mathbf{x},t) = 0.5x_1+x_2 \\ f_2(\mathbf{x},t) = g(\mathbf{x},t)(2.8 - (\frac{0.5x_1+x_2}{g(\mathbf{x},t)})^{H(t)}) \end{cases} \end{equation}\]

GTS2 PS

GTS2 PF

Source code in pydmoo/problems/dynamic/gts.py 
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def __init__(self, **kwargs):
    super().__init__(part_idx=2, bounds=((0, 1), (0, 1), (-1, 2)), **kwargs)

Functions

G_t 

G_t(t)

\( G(t) = \sin(0.5\pi t) \)

Source code in pydmoo/problems/dynamic/gts.py 
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def G_t(t):
    """\\( G(t) = \\sin(0.5\\pi t) \\)"""
    return np.sin(0.5 * np.pi * t)

H_t 

H_t(t)

\( H(t) = 1.5 + G(t) \)

Source code in pydmoo/problems/dynamic/gts.py 
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def H_t(t):
    """\\( H(t) = 1.5 + G(t) \\)"""
    return 1.5 + G_t(t)

a_t 

a_t(t)

\( a(t) = \sin(0.5\pi t) \)

Source code in pydmoo/problems/dynamic/gts.py 
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def a_t(t):
    """\\( a(t) = \\sin(0.5\\pi t) \\)"""
    return np.sin(0.5 * np.pi * t)

alpha_t 

alpha_t(t)

\( \alpha_t = 5\cos(0.5\pi t) \)

Source code in pydmoo/problems/dynamic/gts.py 
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def alpha_t(t):
    """\\( \\alpha_t = 5\\cos(0.5\\pi t) \\)"""
    return 5 * np.cos(0.5 * np.pi * t)

b_t 

b_t(t)

\( b(t) = 1 + |\cos(0.5\pi t)| \)

Source code in pydmoo/problems/dynamic/gts.py 
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def b_t(t):
    """\\( b(t) = 1 + |\\cos(0.5\\pi t)| \\)"""
    return 1 + np.abs(np.cos(0.5 * np.pi * t))

beta_t 

beta_t(t)

\( \beta_t = 0.2 + 2.8|G(t)| \)

Source code in pydmoo/problems/dynamic/gts.py 
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def beta_t(t):
    """\\( \\beta_t = 0.2 + 2.8|G(t)| \\)"""
    return 0.2 + 2.8 * np.abs(G_t(t))

omega_t 

omega_t(t)

\( \omega_t = \lfloor 10G(t) \rfloor \)

Source code in pydmoo/problems/dynamic/gts.py 
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def omega_t(t):
    """\\( \\omega_t = \\lfloor 10G(t) \\rfloor \\)"""
    return np.floor(10 * G_t(t))

p_t 

p_t(t)

\( p_t = \lfloor 6G(t) \rfloor \)

Source code in pydmoo/problems/dynamic/gts.py 
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def p_t(t):
    """\\( p_t = \\lfloor 6G(t) \\rfloor \\)"""
    return np.floor(6 * G_t(t))

y_t 

y_t(x1, t)

\( y_t(x_1) = 0.5 + G(t)(x_1 - 0.5) \)

Source code in pydmoo/problems/dynamic/gts.py 
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def y_t(x1, t):
    """\\( y_t(x_1) = 0.5 + G(t)(x_1 - 0.5) \\)"""
    return 0.5 + G_t(t) * (x1 - 0.5)