Changeset 766

Timestamp:

10/23/14 15:06:42 (19 months ago)

Author:

mmckerns

Message:

moved corana, griewangk, and zimmermann to storn to fix pickling of models;
fixed import of corana in examples

Location:

mystic

Files:

• examples/mpl_corana.py (modified) (1 diff)
• examples/test_corana.py (modified) (3 diffs)
• models/__init__.py (modified) (1 diff)
• models/griewangk.py (deleted)
• models/storn.py (moved) (moved from mystic/models/corana.py) (4 diffs)
• models/zimmermann.py (deleted)

mystic/examples/mpl_corana.py

@@ -15 +15 @@
 from mystic.tools import getch
 
-from mystic.models.corana import corana1d as Corana1
+from mystic.models.storn import Corana
+Corana1 = Corana(1)
 
 x = numpy.arange(-2., 2., 0.01)

mystic/examples/test_corana.py

@@ -25 +25 @@
 random.seed(123)
 
-from mystic.models import corana as Corana
-from mystic.models.corana import corana1d as Corana1
+from mystic.models import corana
+from mystic.models.storn import Corana as Corana1
+corana1 = Corana1(1)
 
 ND = 4
@@ -38 +39 @@
     solver.SetEvaluationLimits(generations=MAX_GENERATIONS)
 
-    solver.Solve(Corana, termination=VTR(0.00000001), strategy=Rand1Exp,\
+    solver.Solve(corana, termination=VTR(0.00000001), strategy=Rand1Exp,\
                  CrossProbability=0.5, ScalingFactor=0.9)
 
@@ -58 +59 @@
         import random
         print  "\nScipy: "
-        sol = fmin(Corana, [random.random() for j in range(4)], full_output=0, retall=1)
+        sol = fmin(corana, [random.random() for j in range(4)], full_output=0, retall=1)
         print "solution: ", sol[-1][0]
         print "\nCorana 1 with Scipy"
-        sol = fmin(Corana1, [random.random()], full_output=1, retall=1)
+        sol = fmin(corana1, [random.random()], full_output=1, retall=1)
         print "solution: ", sol[-1][0]
     except:

mystic/models/__init__.py

@@ -76 +76 @@
 # functions
 from dejong import sphere, rosen, step, quartic, shekel
-from corana import corana
+from storn import corana, griewangk, zimmermann
 from wolfram import fosc3d, nmin51
-from griewangk import griewangk
-from zimmermann import zimmermann
 from nag import peaks
 from venkataraman import venkat91

mystic/models/storn.py

@@ -8 +8 @@
 __doc__ = _doc = """
 This is part of Storn's "Differential Evolution" test suite, as defined
-in [2], with 'Corana' function definitions drawn from [3,4].
+in [2], with 'Corana' function definitions drawn from [3,4], 'Griewangk'
+function definitions drawn from [5], and 'Zimmermann' function definitions
+drawn from [6].
 
 References::
@@ -26 +28 @@
     'Simulated Annealing Algorithm'" ACM Transactions on Mathematical
     Software, March, 272-280, 1987.
+
+    [5] Griewangk, A.O. "Generalized Descent for Global Optimization"
+    Journal of Optimization Theory and Applications 34: 11-39, 1981.
+
+    [6] Zimmermann, W. "Operations Research" Oldenbourg Munchen, Wien, 1990.
 """
 from abstract_model import AbstractFunction
 
 from numpy import asarray
-from math import pow
+from math import pow, cos, sqrt
 from numpy import sign, floor
 
@@ -94 +101 @@
     pass
 
+class Griewangk(AbstractFunction):
+    __doc__ = \
+    """a Griewangk's function generator
+
+Griewangk's function [1,2,5] is a multi-dimensional cosine
+function that provides several periodic local minima, with
+the global minimum at the origin. The local minima are 
+fractionally more shallow than the global minimum, such that
+when viewed at a very coarse scale the function appears as
+a multi-dimensional parabola similar to De Jong's sphere.
+
+The generated function f(x) is a modified version of equation (23)
+of [2], where len(x) >= 0.
+    """ + _doc
+    def __init__(self, ndim=10): # is n-dimensional (n=10 in ref)
+        AbstractFunction.__init__(self, ndim=ndim)
+        return
+
+    def function(self,coeffs):
+        """evaluates an N-dimensional Griewangk's function for a list of coeffs
+
+f(x) = f_0(x) - f_1(x) + 1
+
+Where:
+f_0(x) = \sum_(i=0)^(N-1) x_(i)^(2) / 4000.
+and:
+f_1(x) = \prod_(i=0)^(N-1) \cos( x_i / (i+1)^(1/2) )
+
+Inspect with mystic_model_plotter using::
+    mystic.models.griewangk -b "-10:10:.1, -10:10:.1" -d -x 5
+
+The minimum is f(x)=0.0 for x_i=0.0"""
+       #x = asarray(x) #XXX: converting to numpy.array slows by 10x
+        term1 = sum([c*c for c in coeffs])/4000.
+        term2 = 1
+        for i in range(len(coeffs)):
+            term2 = term2 * cos( coeffs[i] / sqrt(i+1.0) )
+        return term1 - term2 + 1
+
+
+    minimizers = [0.] #XXX: there are many periodic local minima
+    pass
+
+class Zimmermann(AbstractFunction):
+    __doc__ = \
+    """a Zimmermann function generator
+
+A Zimmermann function [1,2,6] poses difficulty for minimizers
+as the minimum is located at the corner of the constrained region.
+A penalty is applied to all values outside the constrained region,
+creating a local minimum.
+
+The generated function f(x) is a modified version of equation (24-26)
+of [2], and requires len(x) == 2.
+    """ + _doc
+    def __init__(self, ndim=2):
+        AbstractFunction.__init__(self, ndim=ndim)
+        return
+
+    def function(self,coeffs):
+        """evaluates a Zimmermann function for a list of coeffs
+
+f(x) = max(f_0(x), p_i(x)), with i = 0,1,2,3
+
+Where:
+f_0(x) = 9 - x_0 - x_1
+with for x_0 < 0:
+p_0(x) = -100 * x_0
+and for x_1 < 0:
+p_1(x) = -100 * x_1
+and for c_2(x) > 16 and c_3(x) > 14:
+p_i(x) = 100 * c_i(x), with i = 2,3
+c_2(x) = (x_0 - 3)^2 + (x_1 - 2)^2
+c_3(x) = x_0 * x_1
+Otherwise, p_i(x)=0 for i=0,1,2,3 and c_i(x)=0 for i=2,3.
+
+Inspect with mystic_model_plotter using::
+    mystic.models.zimmermann -b "-5:10:.1, -5:10:.1" -d -x 1
+
+The minimum is f(x)=0.0 at x=(7.0,2.0)"""
+        x0, x1 = coeffs #must provide 2 values (x0,y0)
+        f8 = 9 - x0 - x1
+        #XXX: apply penalty p(k) = 100 + 100*k; k = |f(x) - c(x)|
+        c0,c1,c2,c3 = 0,0,0,0
+        if x0 < 0: c0 = -100 * x0
+        if x1 < 0: c1 = -100 * x1
+        xx =  (x0-3.)*(x0-3) + (x1-2.)*(x1-2)
+        if xx > 16: c2 = 100 * (xx-16)
+        if x0 * x1 > 14: c3 = 100 * (x0*x1-14.)
+        return max(f8,c0,c1,c2,c3)
+
+    minimizers = [(7., 2.), (2.35477650,  5.94832200)]
+   #minima = [0.0, 0.69690150]
+    pass
+
 # cleanup
 del _doc
@@ -99 +201 @@
 # prepared instances
 corana = Corana().function
+griewangk = Griewangk().function
+zimmermann = Zimmermann().function
 
 # End of file