def test_rosenbrock():
"""Test the 2-dimensional Rosenbrock function.
Testing 2-D Rosenbrock:
Expected: x=[1., 1.] and f=0
Using DifferentialEvolutionSolver:
Solution: [ 1.00000037 1.0000007 ]
f value: 2.29478683682e-13
Iterations: 99
Function evaluations: 3996
Time elapsed: 0.582273006439 seconds
Using DifferentialEvolutionSolver2:
Solution: [ 0.99999999 0.99999999]
f value: 3.84824937598e-15
Iterations: 100
Function evaluations: 4040
Time elapsed: 0.577210903168 seconds
Using NelderMeadSimplexSolver:
Solution: [ 0.99999921 1.00000171]
f value: 1.08732211477e-09
Iterations: 70
Function evaluations: 130
Time elapsed: 0.0190329551697 seconds
Using PowellDirectionalSolver:
Solution: [ 1. 1.]
f value: 0.0
Iterations: 28
Function evaluations: 859
Time elapsed: 0.113857030869 seconds
"""
print "Testing 2-D Rosenbrock:"
print "Expected: x=[1., 1.] and f=0"
from mystic.models import rosen as costfunc
ndim = 2
lb = [-5.]*ndim
ub = [5.]*ndim
x0 = [2., 3.]
maxiter = 10000
# DifferentialEvolutionSolver
print "\nUsing DifferentialEvolutionSolver:"
npop = 40
from mystic.solvers import DifferentialEvolutionSolver
from mystic.termination import ChangeOverGeneration as COG
from mystic.strategy import Rand1Bin
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver(ndim, npop)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = COG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Bin)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 2.29478683682e-13, tol=3e-3)
# DifferentialEvolutionSolver2
print "\nUsing DifferentialEvolutionSolver2:"
npop = 40
from mystic.solvers import DifferentialEvolutionSolver2
from mystic.termination import ChangeOverGeneration as COG
from mystic.strategy import Rand1Bin
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver2(ndim, npop)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = COG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Bin)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 3.84824937598e-15, tol=3e-3)
# NelderMeadSimplexSolver
print "\nUsing NelderMeadSimplexSolver:"
from mystic.solvers import NelderMeadSimplexSolver
from mystic.termination import CandidateRelativeTolerance as CRT
esow = Monitor()
ssow = Monitor()
solver = NelderMeadSimplexSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = CRT()
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 1.08732211477e-09, tol=3e-3)
# PowellDirectionalSolver
print "\nUsing PowellDirectionalSolver:"
from mystic.solvers import PowellDirectionalSolver
from mystic.termination import NormalizedChangeOverGeneration as NCOG
esow = Monitor()
ssow = Monitor()
solver = PowellDirectionalSolver(ndim)
solver.SetInitialPoints(x0)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
term = NCOG(1e-10)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 0.0, tol=3e-3)
def test_griewangk():
"""Test Griewangk's function, which has many local minima.
Testing Griewangk:
Expected: x=[0.]*10 and f=0
Using DifferentialEvolutionSolver:
Solution: [ 8.87516194e-09 7.26058147e-09 1.02076001e-08 1.54219038e-08
-1.54328461e-08 2.34589663e-08 2.02809360e-08 -1.36385836e-08
1.38670373e-08 1.59668900e-08]
f value: 0.0
Iterations: 4120
Function evaluations: 205669
Time elapsed: 34.4936850071 seconds
Using DifferentialEvolutionSolver2:
Solution: [ -2.02709316e-09 3.22017968e-09 1.55275472e-08 5.26739541e-09
-2.18490470e-08 3.73725584e-09 -1.02315312e-09 1.24680355e-08
-9.47898116e-09 2.22243557e-08]
f value: 0.0
Iterations: 4011
Function evaluations: 200215
Time elapsed: 32.8412370682 seconds
"""
print "Testing Griewangk:"
print "Expected: x=[0.]*10 and f=0"
from mystic.models import griewangk as costfunc
ndim = 10
lb = [-400.]*ndim
ub = [400.]*ndim
maxiter = 10000
seed = 123 # Re-seed for each solver to have them all start at same x0
# DifferentialEvolutionSolver
print "\nUsing DifferentialEvolutionSolver:"
npop = 50
random_seed(seed)
from mystic.solvers import DifferentialEvolutionSolver
from mystic.termination import ChangeOverGeneration as COG
from mystic.termination import CandidateRelativeTolerance as CRT
from mystic.termination import VTR
from mystic.strategy import Rand1Bin, Best1Bin, Rand1Exp
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver(ndim, npop)
solver.SetRandomInitialPoints(lb, ub)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
solver.enable_signal_handler()
#term = COG(1e-10)
#term = CRT()
term = VTR(0.)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Exp, \
CrossProbability=0.3, ScalingFactor=1.0)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 0.0, tol=3e-3)
# DifferentialEvolutionSolver2
print "\nUsing DifferentialEvolutionSolver2:"
npop = 50
random_seed(seed)
from mystic.solvers import DifferentialEvolutionSolver2
from mystic.termination import ChangeOverGeneration as COG
from mystic.termination import CandidateRelativeTolerance as CRT
from mystic.termination import VTR
from mystic.strategy import Rand1Bin, Best1Bin, Rand1Exp
esow = Monitor()
ssow = Monitor()
solver = DifferentialEvolutionSolver2(ndim, npop)
solver.SetRandomInitialPoints(lb, ub)
solver.SetStrictRanges(lb, ub)
solver.SetEvaluationLimits(generations=maxiter)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
#term = COG(1e-10)
#term = CRT()
term = VTR(0.)
time1 = time.time() # Is this an ok way of timing?
solver.Solve(costfunc, term, strategy=Rand1Exp, \
CrossProbability=0.3, ScalingFactor=1.0)
sol = solver.Solution()
time_elapsed = time.time() - time1
fx = solver.bestEnergy
print "Solution: ", sol
print "f value: ", fx
print "Iterations: ", solver.generations
print "Function evaluations: ", len(esow.x)
print "Time elapsed: ", time_elapsed, " seconds"
assert almostEqual(fx, 0.0, tol=3e-3)
# xinit = [random.random() for j in range(ND)]
xinit = [0.8, 1.2, 0.7]
# xinit = [0.8,1.2,1.7] #... better when using "bad" range
min = [-0.999, -0.999, 0.999] #XXX: behaves badly when large range
max = [200.001, 100.001, inf] #... for >=1 x0 out of bounds; (up xtol)
# min = [-0.999, -0.999, -0.999]
# max = [200.001, 100.001, inf]
# min = [-0.999, -0.999, 0.999] #XXX: tight range and non-randomness
# max = [2.001, 1.001, 1.001] #...: is _bad_ for DE solvers
#print(diffev(rosen,xinit,NP,retall=0,full_output=0))
solver = DifferentialEvolutionSolver(len(xinit), NP)
solver.SetInitialPoints(xinit)
solver.SetStrictRanges(min, max)
solver.SetEvaluationLimits(generations=MAX_GENERATIONS)
solver.SetEvaluationMonitor(esow)
solver.SetGenerationMonitor(ssow)
solver.Solve(rosen, VTR(0.0001), \
CrossProbability=0.5, ScalingFactor=0.6, disp=1)
sol = solver.bestSolution
print(sol)
#print("Current function value: %s" % solver.bestEnergy)
#print("Iterations: %s" % solver.generations)
#print("Function evaluations: %s" % solver.evaluations)
times.append(time.time() - start)
algor.append('Differential Evolution\t')
for k, t in zip(algor, times):
print("%s\t -- took %s" % (k, t))