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#!/usr/bin/env python
"""
Simulated annealing optimiser. Derives from basic optimiser class.
The simulated annealing optimiser is a translation into Python of the fortran
program simman.f authored by Bill Goffe (bgoffe@whale.st.usm.edu). The original
citation is "Global Optimization of Statistical Functions with Simulated
Annealing," Goffe, Ferrier and Rogers, Journal of Econometrics, vol. 60, no. 1/2,
Jan./Feb. 1994, pp. 65-100.
"""
from optimiser import OptimiserBase
import numpy
Float = numpy.core.numerictypes.sctype2char(float)
import time
__author__ = "Andrew Butterfield"
__copyright__ = "Copyright 2007-2009, The Cogent Project"
__credits__ = ["Gavin Huttley", "Andrew Butterfield", "Peter Maxwell"]
__license__ = "GPL"
__version__ = "1.4.1"
__maintainer__ = "Gavin Huttley"
__email__ = "gavin.huttley@anu.edu.au"
__status__ = "Production"
class AnnealingSchedule(object):
"""Responsible for the shape of the simulated annealing temperature profile"""
def __init__(self, temp_reduction, initial_temp, temp_iterations, step_cycles):
if initial_temp < 0.0 :
raise RuntimeError, "Initial temperature not +ve"
self.T = self.initial_temp = initial_temp
self.temp_reduction = temp_reduction
self.temp_iterations = temp_iterations
self.step_cycles = step_cycles
self.dwell = temp_iterations * step_cycles
def checkSameConditions(self, other):
for attr in ['temp_reduction', 'initial_temp', 'temp_iterations', 'step_cycles']:
if getattr(self, attr) != getattr(other, attr):
raise ValueError('Checkpoint file ignored - %s different' % attr)
def cool(self):
self.T = self.temp_reduction * self.T
def willAccept(self, newF, oldF, random_series):
deltaF = newF - oldF
return deltaF >= 0 or random_series.uniform(0.0, 1.0) < numpy.exp(deltaF / self.T)
class AnnealingHistory(object):
"""Keeps the last few results, for convergence testing"""
def __init__(self, sample=4):
self.values = [None] * sample
self.i = 0
def note(self, F):
self.values[self.i] = F
self.i = (self.i + 1) % len(self.values)
def hasConverged(self, tolerance):
return None not in self.values and max(self.values) - min(self.values) < tolerance
class AnnealingState(object):
def __init__(self, X, function, random_series):
self.random_series = random_series
self.NFCNEV = 1
self.VM = numpy.ones(len(X), Float)
self.setX(X, function(X))
(self.XOPT, self.FOPT) = (X, self.F)
self.NACP = [0] * len(X)
self.NTRY = 0
self.elapsed_time = 0
def setX(self, X, F):
self.X = numpy.array(X, Float)
self.F = F
def step(self, function, accept_test):
# One attempted move in each dimension
t0 = time.time()
X = self.X
self.NTRY += 1
for H in range(len(X)):
self.NFCNEV += 1
current_value = X[H]
X[H] += self.VM[H] * self.random_series.uniform(-1.0, 1.0)
F = function(X)
if accept_test(F, self.F, self.random_series):
self.NACP[H] += 1
self.F = F
if F > self.FOPT:
(self.FOPT, self.XOPT) = (F, X.copy())
else:
X[H] = current_value
self.elapsed_time += time.time() - t0
def adjustStepSizes(self):
# Adjust velocity in each dimension to keep acceptance ratios near 50%
if self.NTRY == 0:
return
for I in range(len(self.X)):
RATIO = (self.NACP[I]*1.0) / self.NTRY
if RATIO > 0.6:
self.VM[I] *= (1.0 + (2.0 * ((RATIO-0.6)/0.4)))
elif RATIO < 0.4:
self.VM[I] /= (1.0 + (2.0 * ((0.4 - RATIO)/0.4)))
self.NACP[I] = 0
self.NTRY = 0
class AnnealingRun(object):
def __init__(self, function, X, schedule, random_series):
self.history = AnnealingHistory()
self.schedule = schedule
self.state = AnnealingState(X, function, random_series)
self.test_count = 0
def checkFunction(self, function, xopt, checkpointing_filename):
if len(xopt) != len(self.state.XOPT):
raise ValueError(
"Number of parameters in checkpoint file '%s' (%s) " \
"don't match current function (%s)" % (
checkpointing_filename, len(self.state.XOPT), len(xopt)))
# if f(x) != g(x) then f isn't g.
then = self.state.FOPT
now = function(self.state.XOPT)
if not numpy.allclose(now, then, 1e-8):
raise ValueError(
"Function to optimise doesn't match checkpoint file " \
"'%s': F=%s now, %s in file." % (
checkpointing_filename, now, then))
def run(self, function, tolerance, max_iterations, checkpointer,
show_progress):
state = self.state
history = self.history
schedule = self.schedule
while not history.hasConverged(tolerance):
if show_progress:
print "Outer loop = %d" % self.test_count
self.save(checkpointer)
for i in range(self.schedule.dwell):
state.step(function, self.schedule.willAccept)
self.test_count += 1
if max_iterations and self.test_count >= max_iterations:
raise MaximumEvaluationsReached(state)
if self.test_count % schedule.step_cycles == 0:
state.adjustStepSizes()
history.note(state.F)
if show_progress:
print "\tF = %f EVALS = %s" % (state.FOPT, state.NFCNEV)
state.setX(state.XOPT, state.FOPT)
schedule.cool()
self.save(checkpointer, final=True)
return state
def save(self, checkpointer, final=False):
msg = "Number of function evaluations = %d; current F = %s" % \
(self.state.NFCNEV, self.state.FOPT)
checkpointer.record(self, msg, final)
class MaximumEvaluationsReached(Exception):
# Used to pass out the results when iteration has to stop early
"""FORCED EXIT from SimulatedAnnealing:
Too many function evaluations, results are likely to be poor.
You can increase max_evaluations or decrease tolerance."""
class SimulatedAnnealing(OptimiserBase):
"""Simulated annealing optimiser for bounded functions
"""
# this is a maximiser
algorithm_direction = +1
def _setdefaults(self):
"""set all the conditions for the sim annealing algorithm to default values"""
self.setConditions(tolerance = 1E-6, temp_reduction = 0.5, init_temp=5.0,
temp_iterations = 5, step_cycles = 20, max_evaluations=1e100)
def setConditions(self, tolerance = None, temp_reduction = None, init_temp=None,
temp_iterations = None, step_cycles = None, max_evaluations=None):
"""Set the conditions that control the optimisation.
Arguments:
- tolerance: the error condition for termination, default is
1E-6
- temp_reduction: the factor by which the annealing
"temperature" is reduced, default is 0.5
- temp_iterations: the number of iterations before a
temperature reduction, default is 5
- step_cycles: the number of cycles after which the step size
is modified, default is 20
- max_evaluations: the maximum number of function
evaluations, default is 1E100. Note that a full run across
the vector will be always be performed, with the outcome that
the program will excape number of evaluations is greater than
or equal to max_evaluations.
"""
for (attr, value) in locals().items():
if value is not None:
setattr(self, attr, value)
def runInner(self, function, xopt, show_progress, random_series):
"""Optimise the vector within the bounds specified by the base class.
Arguments:
- show_progress: whether the function values are printed as
the optimisation proceeds. Default is True.
Returns function value, parameter vector, evaluation count
"""
if len(xopt) == 0:
return function(xopt), xopt, 0, 0.0
schedule = AnnealingSchedule(
self.temp_reduction, self.init_temp, self.temp_iterations, self.step_cycles)
max_iterations = (self.max_evaluations-1) / len(xopt) + 1
if self.restore and self.checkpointer.available():
run = self.checkpointer.load()
run.checkFunction(function, xopt, self.checkpointer.filename)
run.schedule.checkSameConditions(schedule)
else:
run = AnnealingRun(function, xopt, schedule, random_series)
self.restore = False
try:
result = run.run(
function,
self.tolerance,
max_iterations,
checkpointer = self.checkpointer,
show_progress = show_progress)
except MaximumEvaluationsReached, detail:
print detail.__doc__
result = detail.args[0]
return result.FOPT, result.XOPT, result.NFCNEV, result.elapsed_time
|
