Merge pull request #5 from nathanrooy/dev

v0.0.11

Author: nathanrooy

landscapes/single_objective.py

@@ -15,8 +15,10 @@
 from math import sin
 from math import sqrt
 
-#--- FUNCTIONS ----------------------------------------------------------------+
+from landscapes.utils import prod
+from landscapes.utils import safe_division as safe_div
 
+#--- FUNCTIONS ----------------------------------------------------------------+
 
 def ackley(xy):
     '''
@@ -84,6 +86,38 @@ def adjiman(xy):
     return (cos(x) * sin(y)) - (x / (y**2.0 + 1.0))
 
 
+def amgm(x):
+    '''AMGM: Arithmetic Mean-Geometric Mean (Mishra's Function No.11)
+
+    Parameters
+    ----------
+    x : list, len(x)>=2
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum:  f(x*)=0 at x*=(x_i -> x_1,=x_2,...,=x_3)
+    bounds: x_i in [0,10] for i=2,...,n
+
+    *There are an infinite number of global minimums when all values of x are
+    non-negative and equal.
+
+    f(1,1) = 0
+    f(6,6,6) = 0
+    f(0.5, 0.5, 0.5, 0.5) = 0
+    etc...
+    '''
+    assert len(x) >= 2, 'len(x) must be >= 2'
+    
+    d = len(x)
+    a = sum([abs(v) for v in x]) / d
+    b = abs(prod(x))**(1/d)
+    return (a-b)**2
+
+
 def bartels_conn(xy):
     '''Bartels Conn Function
 
@@ -123,6 +157,30 @@ def beale(xy):
             (2.625 - x + x*y**3)**2)
 
 
+def bent_cigar(x):
+    '''Bent Cigar
+
+    Parameters
+    ----------
+    x : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(0,...,0)
+    bounds: x_i in [-100,100] for i=1,...,n
+
+    References
+    ----------
+    https://al-roomi.org/benchmarks/unconstrained/n-dimensions/164-bent-cigar-function
+    '''
+
+    return x[0]**2 + 1e6*sum([v**2 for v in x[1:]])
+
+
 def bird(xy):
     '''Bird Function
 
@@ -389,6 +447,78 @@ def camel_hump_6(xy):
     return a + b + c
 
 
+def carrom_table(xy):
+    '''Carrom Table
+
+    Parameters
+    ----------
+    xy : list
+
+    Returns
+    -------
+    float
+
+    References
+    ----------
+    [1]  S. K. Mishra, “Global Optimization By Differential Evolution and 
+    Particle Swarm Methods: Evaluation On Some Benchmark Functions,” Munich 
+    Research Papers in Economics, [Available Online]: 
+    http://mpra.ub.uni-muenchen.de/1005/
+    '''
+
+    x, y = xy[0], xy[1]
+    return (exp(2*abs(1 - (sqrt(x**2 + y**2)/pi))) * cos(x)**2 * cos(y)**2) / -30.0
+
+
+def chichinadze(xy):
+    '''Chichinadze
+
+    Parameters
+    ----------
+    xy : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*) = -42.9443870 at x*=(6.189866586965680, 0.5)
+    bounds: x_i in [-30, 30] for i=1,2
+    '''
+
+    x, y = xy[0], xy[1]
+    return (
+        x**2 - 12*x + 11 + 
+        10*cos(pi*x/2) + 8*sin(5*pi*x/2) - 
+        1.0/sqrt(5)*exp(-((y - 0.5)**2)/2))
+
+
+def chung_reynolds(x):
+    '''Chung Reynolds
+
+    Parameters
+    ----------
+    x : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(0,...,0)
+    bounds: x_i in [-100,100] for i=1,...,n
+
+    References
+    ----------
+    C. J. Chung, R. G. Reynolds, “CAEP: An Evolution-Based Tool for Real-Valued
+    Function Optimization Using Cultural Algorithms,” International Journal on
+    Artificial Intelligence Tool, vol. 7, no. 3, pp. 239-291, 1998.
+    '''
+    return sphere(x)**2
+
+
 def colville(xy):
     '''Colville Function
 
@@ -422,6 +552,32 @@ def colville(xy):
     return a + b + c + d + e + f
 
 
+def cosine_mixture(x):
+    '''COSINE MIXTURE
+
+    Parameters
+    ----------
+    x : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x_i)=-0.1N for x_i=0 for i=1,...,n
+    bounds: x_i in [-1, 1] for i=1,...,n
+
+    References
+    ----------
+    M. M. Ali, C. Khompatraporn, Z. B. Zabinsky, “A Numerical Evaluation of
+    Several Stochastic Algorithms on Selected Continuous Global Optimization
+    Test Problems,” Journal of Global Optimization, vol. 31, pp. 635-672, 2005.
+    '''
+
+    return -0.1 * sum([cos(5*pi*v) for v in x]) - sum([v**2 for v in x])
+
+
 def cross_in_tray(xy):
     '''
     Cross-in-tray Fucntion
@@ -437,6 +593,86 @@ def cross_in_tray(xy):
     return -0.0001*(abs(sin(x)*sin(y)*exp(abs(100-(sqrt(x**2 + y**2)/pi))))+1)**0.1
 
 
+def csendes(x):
+    '''Csendes
+
+    Parameters
+    ----------
+    x : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum f(x*)=0 for x*=(0,...,0)
+    bounds: x_i in [-1,1] for i=1,...,n
+    
+    References
+    ----------
+    T. Csendes, D. Ratz, “Subdivision Direction Selection in Interval Methods 
+    for Global Optimization,” SIAM Journal on Numerical Analysis, vol. 34, 
+    no. 3, pp. 922-938.
+    '''
+    
+    return sum([v**6 * (2+sin(safe_div(1,v))) for v in x])
+
+
+def cube(xy):
+    '''CUBE
+
+    Parameters
+    ----------
+    xy : list of length 2
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(0,0)
+    bounds: x_i in [-10, 10] for i=1,2
+    '''
+
+    x, y = xy[0], xy[1]
+    return 100 * (y - x**3)**2 + (1 - x)**2
+
+
+def damavandi(xy):
+    '''Damavandi
+
+    Parameters
+    ----------
+    xy : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(2,2)
+    bounds: x_i in [0,14] for i=1,2
+
+    References
+    ----------
+    N. Damavandi, S. Safavi-Naeini, “A Hybrid Evolutionary Programming Method
+    for Circuit Optimization,” IEEE Transaction on Circuit and Systems I, 
+    vol. 52, no. 5, pp.902-910, 2005.
+    '''
+
+    x, y = xy[0], xy[1]
+    # division by zero causes errors...
+    if x==2 and y==2: return 0
+    n = sin(pi*(x - 2)) * sin(pi*(y - 2))
+    d = pi**2 *(x - 2) * (y - 2)
+    a = 1.0 - (abs(n / d))**5
+    b = 2.0 + (x - 7)**2 + 2*(y - 7)**2
+    return a * b
+
+
 def deckkers_aarts(xy):
     '''Deckkers-Aarts Function
 
@@ -550,6 +786,34 @@ def exponential(x):
     return -exp(-0.5*sum([v**2 for v in x]))
 
 
+def freudenstein_roth(xy):
+    '''Freudenstein Roth
+
+    Parameters
+    ----------
+    xy : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(5,4)
+    bounds: x_i in [-10,10] for i=1,2
+    
+    References
+    ----------
+    S. S. Rao, “Engineering Optimization: Theory and Practice,” 
+    John Wiley & Sons, 2009.
+    '''
+
+    x, y = xy[0], xy[1]
+    a = (x - 13 + ((5-y)*y - 2)*y)**2
+    b = (x - 29 + ((y + 1)*y - 14)*y)**2
+    return a + b
+
+
 def goldstein_price(xy):
     '''
     Goldstein-Price Function
@@ -870,6 +1134,33 @@ def qing(x):
     return sum([(v**2 - (i+1))**2 for i, v in enumerate(x)])
 
 
+def quartic(x):
+    '''Quartic Function (does not include noise term)
+
+    Parameters
+    ----------
+    x : list
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    global minimum: f(x*)=0 at x*=(0,...,0)
+    bounds: x_i in [-1.28, 1.28] for i=1,...,n
+
+    References
+    ----------
+    R. Storn, K. Price, “Differntial Evolution - A Simple and Efficient Adaptive 
+    Scheme for Global Optimization over Continuous Spaces,” Technical Report 
+    no. TR-95-012, International Computer Science Institute, Berkeley, CA, 1996. 
+    [Available Online]: http://www1.icsi.berkeley.edu/~storn/TR-95-012.pdf
+    '''
+
+    return sum([(i+1)*v**4 for i, v in enumerate(x)])
+
+
 def rastrigin(x, safe_mode=False):
     '''Rastrigin Function
 

landscapes/utils.py

@@ -0,0 +1,41 @@
+def safe_division(n,d):
+    '''Safe Division
+
+    Parameters
+    ----------
+    n : float (numerator)
+    d : float (denominator)
+
+    Returns
+    -------
+    float
+
+    Notes
+    -----
+    Specifically for handling the case when the denominator is 0.
+    '''
+
+    try: return n/d
+    except ZeroDivisionError: return 0
+
+
+def prod(x):
+    '''Product (replaces math.prod)
+
+    Parameters
+    ----------
+    x : list
+
+    Returns 
+    -------
+    float
+
+    Notes
+    -----
+    keeping this here for backwards compatibility since math.prod was 
+    introduced in py3.8
+    '''
+
+    total = 1
+    for v in x: total *= v 
+    return total