Changeset 338 for branches/alta/mystic-0.2a1/test_problems_unconstrained.py

Timestamp:

07/21/10 09:10:59 (6 years ago)

Author:

altafang

Message:

Found some good sources of optimization test problems, and translated some of them into Python.

File:

• branches/alta/mystic-0.2a1/test_problems_unconstrained.py (modified) (2 diffs)

branches/alta/mystic-0.2a1/test_problems_unconstrained.py

@@ -4 +4 @@
 """
 from math import *
+import numpy
 
 def peaks(x_vector):
@@ -46 +47 @@
 
 #print venkataraman_corner([1., 1.])
+
+#---------------------------------------------------------------------
+# Below: functions from http://www.geatbx.com/docu/fcnindex-01.html
+# that are not already in mystic.models.
+# Another good source of test problems: 
+# http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm
+
+def rastrigin(x):
+    """Rastrigin's function. Global minimum at xi=0, f(x)=0. Contains
+many local minima regularly distributed. Can be n-dimensional.
+xi in [-5.12, 5.12]
+http://www.geatbx.com/docu/fcnindex-01.html"""
+    x = numpy.asarray(x)
+    return 10.*len(x) + numpy.sum(x**2 - 10*numpy.cos(2.*pi*x))
+
+#print 'Rastrigin:', rastrigin([0., 0.])
+
+def schwefel(x):
+    """'Schwefel's function [Sch81] is deceptive in that the global minimum is 
+geometrically distant, over the parameter space, from the next best local 
+minima. Therefore, the search algorithms are potentially prone to convergence 
+in the wrong direction.' - http://www.geatbx.com/docu/fcnindex-01.html
+xi in [-500, 500]
+global minimum: f(x) = -n*418.9829, xi=420.9687
+Can be n-dimensional.
+"""
+    x = numpy.asarray(x)
+    return numpy.sum(-x*numpy.sin(abs(x)**0.5))
+
+#print "Schwefel:", schwefel([420.9687, 420.9687, 420.9687])
+#print -3.*418.9829
+
+def ackley(x):
+    """Ackley's Path function.
+xi in [-32.768., 32.768]
+global minimum f(x)=0 at xi=0
+can be n-dimensional. http://www.geatbx.com/docu/fcnindex-01.html"""
+    x = numpy.asarray(x)
+    n = len(x)
+    return -20.*exp(-0.2*sqrt(1./n*numpy.sum(x**2))) - exp(1./n*numpy.sum(
+            numpy.cos(2.*pi*x))) + 20. + exp(1)
+
+#print "Ackley:", ackley([0., 0.])
+
+def easom(x):
+    """'The Easom function [Eas90] is a unimodal test function, where the global 
+minimum has a small area relative to the search space. The function was 
+inverted for minimization.' - http://www.geatbx.com/docu/fcnindex-01.html
+Global minimum f(x1, x2) = -1 at (x1, x2) = (pi, pi)
+xi in -100, 100. 2-dimensional."""
+    x1 = x[0]
+    x2 = x[1]
+    return -cos(x1)*cos(x2)*exp(-(x1-pi)**2 + (x2 - pi)**2)
+
+#print "Easom:", easom([pi, pi])
+