Merge pull request DEAP#588 from bje-/whitespace-fixes

Remove trailing whitespace from *.py

deap/algorithms.py

@@ -470,7 +470,7 @@ def eaGenerateUpdate(toolbox, ngen, halloffame=None, stats=None,
 
     This function expects :meth:`toolbox.generate` and :meth:`toolbox.evaluate` aliases to be
     registered in the toolbox.
-    
+
     .. [Colette2010] Collette, Y., N. Hansen, G. Pujol, D. Salazar Aponte and
        R. Le Riche (2010). On Object-Oriented Programming of Optimizers -
        Examples in Scilab. In P. Breitkopf and R. F. Coelho, eds.:

deap/benchmarks/__init__.py

@@ -40,7 +40,7 @@ def rand(individual):
          - :math:`f(\mathbf{x}) = \\text{\\texttt{random}}(0,1)`
     """
     return random.random(),
-    
+
 def plane(individual):
     """Plane test objective function.
 
@@ -79,7 +79,7 @@ def sphere(individual):
 
 def cigar(individual):
     """Cigar test objective function.
-    
+
     .. list-table:: 
        :widths: 10 50
        :stub-columns: 1
@@ -110,7 +110,7 @@ def rosenbrock(individual):
          - :math:`x_i = 1, \\forall i \in \\lbrace 1 \\ldots N\\rbrace`, :math:`f(\mathbf{x}) = 0`
        * - Function
          - :math:`f(\\mathbf{x}) = \\sum_{i=1}^{N-1} (1-x_i)^2 + 100 (x_{i+1} - x_i^2 )^2`
-    
+
     .. plot:: code/benchmarks/rosenbrock.py
        :width: 67 %
     """
@@ -163,14 +163,14 @@ def ackley(individual):
        * - Function
          - :math:`f(\\mathbf{x}) = 20 - 20\exp\left(-0.2\sqrt{\\frac{1}{N} \
             \\sum_{i=1}^N x_i^2} \\right) + e - \\exp\\left(\\frac{1}{N}\sum_{i=1}^N \\cos(2\pi x_i) \\right)`
-    
+
     .. plot:: code/benchmarks/ackley.py
        :width: 67 %
     """
     N = len(individual)
     return 20 - 20 * exp(-0.2*sqrt(1.0/N * sum(x**2 for x in individual))) \
             + e - exp(1.0/N * sum(cos(2*pi*x) for x in individual)),
-            
+
 def bohachevsky(individual):
     """Bohachevsky test objective function.
 
@@ -187,7 +187,7 @@ def bohachevsky(individual):
        * - Function
          -  :math:`f(\mathbf{x}) = \sum_{i=1}^{N-1}(x_i^2 + 2x_{i+1}^2 - \
                    0.3\cos(3\pi x_i) - 0.4\cos(4\pi x_{i+1}) + 0.7)`
-    
+
     .. plot:: code/benchmarks/bohachevsky.py
        :width: 67 %
     """
@@ -196,7 +196,7 @@ def bohachevsky(individual):
 
 def griewank(individual):
     """Griewank test objective function.
-    
+
     .. list-table:: 
        :widths: 10 50
        :stub-columns: 1
@@ -216,7 +216,7 @@ def griewank(individual):
     """
     return 1.0/4000.0 * sum(x**2 for x in individual) - \
         reduce(mul, (cos(x/sqrt(i+1.0)) for i, x in enumerate(individual)), 1) + 1,
-            
+
 def rastrigin(individual):
     """Rastrigin test objective function.
 
@@ -241,7 +241,7 @@ def rastrigin(individual):
 
 def rastrigin_scaled(individual):
     """Scaled Rastrigin test objective function.
-    
+
     :math:`f_{\\text{RastScaled}}(\mathbf{x}) = 10N + \sum_{i=1}^N \
         \left(10^{\left(\\frac{i-1}{N-1}\\right)} x_i \\right)^2 x_i)^2 - \
         10\cos\\left(2\\pi 10^{\left(\\frac{i-1}{N-1}\\right)} x_i \\right)`
@@ -252,9 +252,9 @@ def rastrigin_scaled(individual):
 
 def rastrigin_skew(individual):
     """Skewed Rastrigin test objective function.
-    
+
      :math:`f_{\\text{RastSkew}}(\mathbf{x}) = 10N \sum_{i=1}^N \left(y_i^2 - 10 \\cos(2\\pi x_i)\\right)`
-        
+
      :math:`\\text{with } y_i = \
                             \\begin{cases} \
                                 10\\cdot x_i & \\text{ if } x_i > 0,\\\ \
@@ -266,7 +266,7 @@ def rastrigin_skew(individual):
                     - 10*cos(2*pi*(10*x if x > 0 else x)) for x in individual),
 def schaffer(individual):
     """Schaffer test objective function.
-    
+
     .. list-table:: 
        :widths: 10 50
        :stub-columns: 1
@@ -343,18 +343,18 @@ def shekel(individual, a, c):
     of maxima is given by the length of any of the arguments *a* or *c*, *a*
     is a matrix of size :math:`M\\times N`, where *M* is the number of maxima
     and *N* the number of dimensions and *c* is a :math:`M\\times 1` vector.
-    
+
     :math:`f_\\text{Shekel}(\mathbf{x}) = \\sum_{i = 1}^{M} \\frac{1}{c_{i} + 
     \\sum_{j = 1}^{N} (x_{j} - a_{ij})^2 }`
-    
+
     The following figure uses
-    
+
     :math:`\\mathcal{A} = \\begin{bmatrix} 0.5 & 0.5 \\\\ 0.25 & 0.25 \\\\ 
     0.25 & 0.75 \\\\ 0.75 & 0.25 \\\\ 0.75 & 0.75 \\end{bmatrix}` and
     :math:`\\mathbf{c} = \\begin{bmatrix} 0.002 \\\\ 0.005 \\\\ 0.005
     \\\\ 0.005 \\\\ 0.005 \\end{bmatrix}`, thus defining 5 maximums in
     :math:`\\mathbb{R}^2`.
-    
+
     .. plot:: code/benchmarks/shekel.py
         :width: 67 %
     """
@@ -363,9 +363,9 @@ def shekel(individual, a, c):
 # Multiobjectives
 def kursawe(individual):
     """Kursawe multiobjective function.
-    
+
     :math:`f_{\\text{Kursawe}1}(\\mathbf{x}) = \\sum_{i=1}^{N-1} -10 e^{-0.2 \\sqrt{x_i^2 + x_{i+1}^2} }`
-    
+
     :math:`f_{\\text{Kursawe}2}(\\mathbf{x}) = \\sum_{i=1}^{N} |x_i|^{0.8} + 5 \\sin(x_i^3)`
 
     .. plot:: code/benchmarks/kursawe.py
@@ -381,20 +381,20 @@ def schaffer_mo(individual):
     From: J. D. Schaffer, "Multiple objective optimization with vector
     evaluated genetic algorithms", in Proceedings of the First International
     Conference on Genetic Algorithms, 1987. 
-    
+
     :math:`f_{\\text{Schaffer}1}(\\mathbf{x}) = x_1^2`
-    
+
     :math:`f_{\\text{Schaffer}2}(\\mathbf{x}) = (x_1-2)^2`
     """
     return individual[0] ** 2, (individual[0] - 2) ** 2
-    
+
 def zdt1(individual):
     """ZDT1 multiobjective function.
-    
+
     :math:`g(\\mathbf{x}) = 1 + \\frac{9}{n-1}\\sum_{i=2}^n x_i`
-    
+
     :math:`f_{\\text{ZDT1}1}(\\mathbf{x}) = x_1`
-    
+
     :math:`f_{\\text{ZDT1}2}(\\mathbf{x}) = g(\\mathbf{x})\\left[1 - \\sqrt{\\frac{x_1}{g(\\mathbf{x})}}\\right]`
     """
     g  = 1.0 + 9.0*sum(individual[1:])/(len(individual)-1)
@@ -404,20 +404,20 @@ def zdt1(individual):
 
 def zdt2(individual):
     """ZDT2 multiobjective function.
-    
+
     :math:`g(\\mathbf{x}) = 1 + \\frac{9}{n-1}\\sum_{i=2}^n x_i`
-    
+
     :math:`f_{\\text{ZDT2}1}(\\mathbf{x}) = x_1`
-    
+
     :math:`f_{\\text{ZDT2}2}(\\mathbf{x}) = g(\\mathbf{x})\\left[1 - \\left(\\frac{x_1}{g(\\mathbf{x})}\\right)^2\\right]`
-    
+
     """
 
     g  = 1.0 + 9.0*sum(individual[1:])/(len(individual)-1)
     f1 = individual[0]
     f2 = g * (1 - (f1/g)**2)
     return f1, f2
-    
+
 def zdt3(individual):
     """ZDT3 multiobjective function.
 
@@ -436,28 +436,28 @@ def zdt3(individual):
 
 def zdt4(individual):
     """ZDT4 multiobjective function.
-    
+
     :math:`g(\\mathbf{x}) = 1 + 10(n-1) + \\sum_{i=2}^n \\left[ x_i^2 - 10\\cos(4\\pi x_i) \\right]`
 
     :math:`f_{\\text{ZDT4}1}(\\mathbf{x}) = x_1`
-    
+
     :math:`f_{\\text{ZDT4}2}(\\mathbf{x}) = g(\\mathbf{x})\\left[ 1 - \\sqrt{x_1/g(\\mathbf{x})} \\right]`
-    
+
     """
     g  = 1 + 10*(len(individual)-1) + sum(xi**2 - 10*cos(4*pi*xi) for xi in individual[1:])
     f1 = individual[0]
     f2 = g * (1 - sqrt(f1/g))
     return f1, f2
-    
+
 def zdt6(individual):
     """ZDT6 multiobjective function.
-    
+
     :math:`g(\\mathbf{x}) = 1 + 9 \\left[ \\left(\\sum_{i=2}^n x_i\\right)/(n-1) \\right]^{0.25}`
-    
+
     :math:`f_{\\text{ZDT6}1}(\\mathbf{x}) = 1 - \\exp(-4x_1)\\sin^6(6\\pi x_1)`
-    
+
     :math:`f_{\\text{ZDT6}2}(\\mathbf{x}) = g(\\mathbf{x}) \left[ 1 - (f_{\\text{ZDT6}1}(\\mathbf{x})/g(\\mathbf{x}))^2 \\right]`
-    
+
     """
     g  = 1 + 9 * (sum(individual[1:]) / (len(individual)-1))**0.25
     f1 = 1 - exp(-4*individual[0]) * sin(6*pi*individual[0])**6
@@ -473,19 +473,19 @@ def dtlz1(individual, obj):
     :math:`g(\\mathbf{x}_m) = 100\\left(|\\mathbf{x}_m| + \sum_{x_i \in \\mathbf{x}_m}\\left((x_i - 0.5)^2 - \\cos(20\pi(x_i - 0.5))\\right)\\right)`
 
     :math:`f_{\\text{DTLZ1}1}(\\mathbf{x}) = \\frac{1}{2} (1 + g(\\mathbf{x}_m)) \\prod_{i=1}^{m-1}x_i`
-    
+
     :math:`f_{\\text{DTLZ1}2}(\\mathbf{x}) = \\frac{1}{2} (1 + g(\\mathbf{x}_m)) (1-x_{m-1}) \\prod_{i=1}^{m-2}x_i`
-    
+
     :math:`\\ldots`
-    
+
     :math:`f_{\\text{DTLZ1}m-1}(\\mathbf{x}) = \\frac{1}{2} (1 + g(\\mathbf{x}_m)) (1 - x_2) x_1`
-    
+
     :math:`f_{\\text{DTLZ1}m}(\\mathbf{x}) = \\frac{1}{2} (1 - x_1)(1 + g(\\mathbf{x}_m))`
-    
+
     Where :math:`m` is the number of objectives and :math:`\\mathbf{x}_m` is a
     vector of the remaining attributes :math:`[x_m~\\ldots~x_n]` of the
     individual in :math:`n > m` dimensions.
-    
+
     """
     g = 100 * (len(individual[obj-1:]) + sum((xi-0.5)**2 - cos(20*pi*(xi-0.5)) for xi in individual[obj-1:]))
     f = [0.5 * reduce(mul, individual[:obj-1], 1) * (1 + g)]
@@ -497,17 +497,17 @@ def dtlz2(individual, obj):
     The individual must have at least *obj* elements.
     From: K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective 
     Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002.
-    
+
     :math:`g(\\mathbf{x}_m) = \\sum_{x_i \in \\mathbf{x}_m} (x_i - 0.5)^2`
-    
+
     :math:`f_{\\text{DTLZ2}1}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\prod_{i=1}^{m-1} \\cos(0.5x_i\pi)`
-    
+
     :math:`f_{\\text{DTLZ2}2}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{m-1}\pi ) \\prod_{i=1}^{m-2} \\cos(0.5x_i\pi)`
-    
+
     :math:`\\ldots`
-    
+
     :math:`f_{\\text{DTLZ2}m}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{1}\pi )`
-    
+
     Where :math:`m` is the number of objectives and :math:`\\mathbf{x}_m` is a
     vector of the remaining attributes :math:`[x_m~\\ldots~x_n]` of the
     individual in :math:`n > m` dimensions.
@@ -525,17 +525,17 @@ def dtlz3(individual, obj):
     The individual must have at least *obj* elements.
     From: K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective 
     Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002.
-    
+
     :math:`g(\\mathbf{x}_m) = 100\\left(|\\mathbf{x}_m| + \sum_{x_i \in \\mathbf{x}_m}\\left((x_i - 0.5)^2 - \\cos(20\pi(x_i - 0.5))\\right)\\right)`
-    
+
     :math:`f_{\\text{DTLZ3}1}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\prod_{i=1}^{m-1} \\cos(0.5x_i\pi)`
-    
+
     :math:`f_{\\text{DTLZ3}2}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{m-1}\pi ) \\prod_{i=1}^{m-2} \\cos(0.5x_i\pi)`
-    
+
     :math:`\\ldots`
-    
+
     :math:`f_{\\text{DTLZ3}m}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{1}\pi )`
-    
+
     Where :math:`m` is the number of objectives and :math:`\\mathbf{x}_m` is a
     vector of the remaining attributes :math:`[x_m~\\ldots~x_n]` of the
     individual in :math:`n > m` dimensions.
@@ -554,17 +554,17 @@ def dtlz4(individual, obj, alpha):
     x_i^\\alpha`, the authors suggest :math:`\\alpha = 100`.
     From: K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective 
     Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002.
-    
+
     :math:`g(\\mathbf{x}_m) = \\sum_{x_i \in \\mathbf{x}_m} (x_i - 0.5)^2`
-    
+
     :math:`f_{\\text{DTLZ4}1}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\prod_{i=1}^{m-1} \\cos(0.5x_i^\\alpha\pi)`
-    
+
     :math:`f_{\\text{DTLZ4}2}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{m-1}^\\alpha\pi ) \\prod_{i=1}^{m-2} \\cos(0.5x_i^\\alpha\pi)`
-    
+
     :math:`\\ldots`
-    
+
     :math:`f_{\\text{DTLZ4}m}(\\mathbf{x}) = (1 + g(\\mathbf{x}_m)) \\sin(0.5x_{1}^\\alpha\pi )`
-    
+
     Where :math:`m` is the number of objectives and :math:`\\mathbf{x}_m` is a
     vector of the remaining attributes :math:`[x_m~\\ldots~x_n]` of the
     individual in :math:`n > m` dimensions.
@@ -584,10 +584,10 @@ def dtlz5(ind, n_objs):
     """
     g = lambda x: sum([(a - 0.5)**2 for a in x])
     gval = g(ind[n_objs-1:])
-    
+
     theta = lambda x: pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)
     fit = [(1 + gval) * cos(pi / 2.0 * ind[0]) * reduce(lambda x,y: x*y, [cos(theta(a)) for a in ind[1:]])]
-           
+
     for m in reversed(range(1, n_objs)):
         if m == 1:
             fit.append((1 + gval) * sin(pi / 2.0 * ind[0]))
@@ -604,7 +604,7 @@ def dtlz6(ind, n_objs):
     """
     gval = sum([a**0.1 for a in ind[n_objs-1:]])
     theta = lambda x: pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)
-    
+
     fit = [(1 + gval) * cos(pi / 2.0 * ind[0]) *
            reduce(lambda x,y: x*y, [cos(theta(a)) for a in ind[1:]])]
 
@@ -633,9 +633,9 @@ def fonseca(individual):
     multiple constraint handling with evolutionary algorithms -- Part II:
     Application example", IEEE Transactions on Systems, Man and Cybernetics,
     1998.
-    
+
     :math:`f_{\\text{Fonseca}1}(\\mathbf{x}) = 1 - e^{-\\sum_{i=1}^{3}(x_i - \\frac{1}{\\sqrt{3}})^2}`
-    
+
     :math:`f_{\\text{Fonseca}2}(\\mathbf{x}) = 1 - e^{-\\sum_{i=1}^{3}(x_i + \\frac{1}{\\sqrt{3}})^2}`
     """
     f_1 = 1 - exp(-sum((xi - 1/sqrt(3))**2 for xi in individual[:3]))
@@ -646,17 +646,17 @@ def poloni(individual):
     """Poloni's multiobjective function on a two attribute *individual*. From:
     C. Poloni, "Hybrid GA for multi objective aerodynamic shape optimization",
     in Genetic Algorithms in Engineering and Computer Science, 1997.
-    
+
     :math:`A_1 = 0.5 \\sin (1) - 2 \\cos (1) + \\sin (2) - 1.5 \\cos (2)`
 
     :math:`A_2 = 1.5 \\sin (1) - \\cos (1) + 2 \\sin (2) - 0.5 \\cos (2)`
 
     :math:`B_1 = 0.5 \\sin (x_1) - 2 \\cos (x_1) + \\sin (x_2) - 1.5 \\cos (x_2)`
 
     :math:`B_2 = 1.5 \\sin (x_1) - cos(x_1) + 2 \\sin (x_2) - 0.5 \\cos (x_2)`
-    
+
     :math:`f_{\\text{Poloni}1}(\\mathbf{x}) = 1 + (A_1 - B_1)^2 + (A_2 - B_2)^2`
-    
+
     :math:`f_{\\text{Poloni}2}(\\mathbf{x}) = (x_1 + 3)^2 + (x_2 + 1)^2`
     """
     x_1 = individual[0]