src/daComposant/daAlgorithms/DerivativeFreeOptimization.py

   1 # -*- coding: utf-8 -*-
   2 #
   3 # Copyright (C) 2008-2020 EDF R&D
   4 #
   5 # This library is free software; you can redistribute it and/or
   6 # modify it under the terms of the GNU Lesser General Public
   7 # License as published by the Free Software Foundation; either
   8 # version 2.1 of the License.
   9 #
  10 # This library is distributed in the hope that it will be useful,
  11 # but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13 # Lesser General Public License for more details.
  14 #
  15 # You should have received a copy of the GNU Lesser General Public
  16 # License along with this library; if not, write to the Free Software
  17 # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
  18 #
  19 # See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
  20 #
  21 # Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  22
  23 import logging
  24 from daCore import BasicObjects, PlatformInfo
  25 import numpy, scipy.optimize
  26
  27 # ==============================================================================
  28 class ElementaryAlgorithm(BasicObjects.Algorithm):
  29     def __init__(self):
  30         BasicObjects.Algorithm.__init__(self, "DERIVATIVEFREEOPTIMIZATION")
  31         self.defineRequiredParameter(
  32             name     = "Minimizer",
  33             default  = "BOBYQA",
  34             typecast = str,
  35             message  = "Minimiseur utilisé",
  36             listval  = ["BOBYQA", "COBYLA", "NEWUOA", "POWELL", "SIMPLEX", "SUBPLEX"],
  37             )
  38         self.defineRequiredParameter(
  39             name     = "MaximumNumberOfSteps",
  40             default  = 15000,
  41             typecast = int,
  42             message  = "Nombre maximal de pas d'optimisation",
  43             minval   = -1,
  44             )
  45         self.defineRequiredParameter(
  46             name     = "MaximumNumberOfFunctionEvaluations",
  47             default  = 15000,
  48             typecast = int,
  49             message  = "Nombre maximal d'évaluations de la fonction",
  50             minval   = -1,
  51             )
  52         self.defineRequiredParameter(
  53             name     = "StateVariationTolerance",
  54             default  = 1.e-4,
  55             typecast = float,
  56             message  = "Variation relative maximale de l'état lors de l'arrêt",
  57             )
  58         self.defineRequiredParameter(
  59             name     = "CostDecrementTolerance",
  60             default  = 1.e-7,
  61             typecast = float,
  62             message  = "Diminution relative minimale du cout lors de l'arrêt",
  63             )
  64         self.defineRequiredParameter(
  65             name     = "QualityCriterion",
  66             default  = "AugmentedWeightedLeastSquares",
  67             typecast = str,
  68             message  = "Critère de qualité utilisé",
  69             listval  = ["AugmentedWeightedLeastSquares","AWLS","DA",
  70                         "WeightedLeastSquares","WLS",
  71                         "LeastSquares","LS","L2",
  72                         "AbsoluteValue","L1",
  73                         "MaximumError","ME"],
  74             )
  75         self.defineRequiredParameter(
  76             name     = "StoreInternalVariables",
  77             default  = False,
  78             typecast = bool,
  79             message  = "Stockage des variables internes ou intermédiaires du calcul",
  80             )
  81         self.defineRequiredParameter(
  82             name     = "StoreSupplementaryCalculations",
  83             default  = [],
  84             typecast = tuple,
  85             message  = "Liste de calculs supplémentaires à stocker et/ou effectuer",
  86             listval  = [
  87                 "Analysis",
  88                 "BMA",
  89                 "CostFunctionJ",
  90                 "CostFunctionJb",
  91                 "CostFunctionJo",
  92                 "CostFunctionJAtCurrentOptimum",
  93                 "CostFunctionJbAtCurrentOptimum",
  94                 "CostFunctionJoAtCurrentOptimum",
  95                 "CurrentOptimum",
  96                 "CurrentState",
  97                 "IndexOfOptimum",
  98                 "Innovation",
  99                 "InnovationAtCurrentState",
 100                 "OMA",
 101                 "OMB",
 102                 "SimulatedObservationAtBackground",
 103                 "SimulatedObservationAtCurrentOptimum",
 104                 "SimulatedObservationAtCurrentState",
 105                 "SimulatedObservationAtOptimum",
 106                 ]
 107             )
 108         self.defineRequiredParameter( # Pas de type
 109             name     = "Bounds",
 110             message  = "Liste des valeurs de bornes",
 111             )
 112         self.requireInputArguments(
 113             mandatory= ("Xb", "Y", "HO", "R", "B" ),
 114             )
 115         self.setAttributes(tags=(
 116             "Optimization",
 117             "NonLinear",
 118             "MetaHeuristic",
 119             ))
 120
 121     def run(self, Xb=None, Y=None, U=None, HO=None, EM=None, CM=None, R=None, B=None, Q=None, Parameters=None):
 122         self._pre_run(Parameters, Xb, Y, R, B, Q)
 123         #
 124         if not PlatformInfo.has_nlopt and not self._parameters["Minimizer"] in ["COBYLA", "POWELL", "SIMPLEX"]:
 125             logging.warning("%s Minimization by SIMPLEX is forced because %s is unavailable (COBYLA, POWELL are also available)"%(self._name,self._parameters["Minimizer"]))
 126             self._parameters["Minimizer"] = "SIMPLEX"
 127         #
 128         # Opérateurs
 129         # ----------
 130         Hm = HO["Direct"].appliedTo
 131         #
 132         # Précalcul des inversions de B et R
 133         # ----------------------------------
 134         BI = B.getI()
 135         RI = R.getI()
 136         #
 137         # Définition de la fonction-coût
 138         # ------------------------------
 139         def CostFunction(x, QualityMeasure="AugmentedWeightedLeastSquares"):
 140             _X  = numpy.asmatrix(numpy.ravel( x )).T
 141             self.StoredVariables["CurrentState"].store( _X )
 142             _HX = Hm( _X )
 143             _HX = numpy.asmatrix(numpy.ravel( _HX )).T
 144             _Innovation = Y - _HX
 145             if self._toStore("SimulatedObservationAtCurrentState") or \
 146                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 147                 self.StoredVariables["SimulatedObservationAtCurrentState"].store( _HX )
 148             if self._toStore("InnovationAtCurrentState"):
 149                 self.StoredVariables["InnovationAtCurrentState"].store( _Innovation )
 150             #
 151             if QualityMeasure in ["AugmentedWeightedLeastSquares","AWLS","DA"]:
 152                 if BI is None or RI is None:
 153                     raise ValueError("Background and Observation error covariance matrix has to be properly defined!")
 154                 Jb  = 0.5 * (_X - Xb).T * BI * (_X - Xb)
 155                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 156             elif QualityMeasure in ["WeightedLeastSquares","WLS"]:
 157                 if RI is None:
 158                     raise ValueError("Observation error covariance matrix has to be properly defined!")
 159                 Jb  = 0.
 160                 Jo  = 0.5 * (_Innovation).T * RI * (_Innovation)
 161             elif QualityMeasure in ["LeastSquares","LS","L2"]:
 162                 Jb  = 0.
 163                 Jo  = 0.5 * (_Innovation).T * (_Innovation)
 164             elif QualityMeasure in ["AbsoluteValue","L1"]:
 165                 Jb  = 0.
 166                 Jo  = numpy.sum( numpy.abs(_Innovation) )
 167             elif QualityMeasure in ["MaximumError","ME"]:
 168                 Jb  = 0.
 169                 Jo  = numpy.max( numpy.abs(_Innovation) )
 170             #
 171             J   = float( Jb ) + float( Jo )
 172             #
 173             self.StoredVariables["CostFunctionJb"].store( Jb )
 174             self.StoredVariables["CostFunctionJo"].store( Jo )
 175             self.StoredVariables["CostFunctionJ" ].store( J )
 176             if self._toStore("IndexOfOptimum") or \
 177                 self._toStore("CurrentOptimum") or \
 178                 self._toStore("CostFunctionJAtCurrentOptimum") or \
 179                 self._toStore("CostFunctionJbAtCurrentOptimum") or \
 180                 self._toStore("CostFunctionJoAtCurrentOptimum") or \
 181                 self._toStore("SimulatedObservationAtCurrentOptimum"):
 182                 IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 183             if self._toStore("IndexOfOptimum"):
 184                 self.StoredVariables["IndexOfOptimum"].store( IndexMin )
 185             if self._toStore("CurrentOptimum"):
 186                 self.StoredVariables["CurrentOptimum"].store( self.StoredVariables["CurrentState"][IndexMin] )
 187             if self._toStore("SimulatedObservationAtCurrentOptimum"):
 188                 self.StoredVariables["SimulatedObservationAtCurrentOptimum"].store( self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin] )
 189             if self._toStore("CostFunctionJAtCurrentOptimum"):
 190                 self.StoredVariables["CostFunctionJAtCurrentOptimum" ].store( self.StoredVariables["CostFunctionJ" ][IndexMin] )
 191             if self._toStore("CostFunctionJbAtCurrentOptimum"):
 192                 self.StoredVariables["CostFunctionJbAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJb"][IndexMin] )
 193             if self._toStore("CostFunctionJoAtCurrentOptimum"):
 194                 self.StoredVariables["CostFunctionJoAtCurrentOptimum"].store( self.StoredVariables["CostFunctionJo"][IndexMin] )
 195             return J
 196         #
 197         # Point de démarrage de l'optimisation : Xini = Xb
 198         # ------------------------------------
 199         Xini = numpy.ravel(Xb)
 200         if len(Xini) < 2 and self._parameters["Minimizer"] == "NEWUOA":
 201             raise ValueError("The minimizer %s can not be used when the optimisation state dimension is 1. Please choose another minimizer."%self._parameters["Minimizer"])
 202         #
 203         # Minimisation de la fonctionnelle
 204         # --------------------------------
 205         nbPreviousSteps = self.StoredVariables["CostFunctionJ"].stepnumber()
 206         #
 207         if self._parameters["Minimizer"] == "POWELL":
 208             Minimum, J_optimal, direc, niter, nfeval, rc = scipy.optimize.fmin_powell(
 209                 func        = CostFunction,
 210                 x0          = Xini,
 211                 args        = (self._parameters["QualityCriterion"],),
 212                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 213                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 214                 xtol        = self._parameters["StateVariationTolerance"],
 215                 ftol        = self._parameters["CostDecrementTolerance"],
 216                 full_output = True,
 217                 disp        = self._parameters["optdisp"],
 218                 )
 219         elif self._parameters["Minimizer"] == "COBYLA" and not PlatformInfo.has_nlopt:
 220             def make_constraints(bounds):
 221                 constraints = []
 222                 for (i,(a,b)) in enumerate(bounds):
 223                     lower = lambda x: x[i] - a
 224                     upper = lambda x: b - x[i]
 225                     constraints = constraints + [lower] + [upper]
 226                 return constraints
 227             if self._parameters["Bounds"] is None:
 228                 raise ValueError("Bounds have to be given for all axes as a list of lower/upper pairs!")
 229             Minimum = scipy.optimize.fmin_cobyla(
 230                 func        = CostFunction,
 231                 x0          = Xini,
 232                 cons        = make_constraints( self._parameters["Bounds"] ),
 233                 args        = (self._parameters["QualityCriterion"],),
 234                 consargs    = (), # To avoid extra-args
 235                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 236                 rhobeg      = 1.0,
 237                 rhoend      = self._parameters["StateVariationTolerance"],
 238                 catol       = 2.*self._parameters["StateVariationTolerance"],
 239                 disp        = self._parameters["optdisp"],
 240                 )
 241         elif self._parameters["Minimizer"] == "COBYLA" and PlatformInfo.has_nlopt:
 242             import nlopt
 243             opt = nlopt.opt(nlopt.LN_COBYLA, Xini.size)
 244             def _f(_Xx, Grad):
 245                 # DFO, so no gradient
 246                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 247             opt.set_min_objective(_f)
 248             if self._parameters["Bounds"] is not None:
 249                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 250                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 251                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 252                 if self._parameters["optdisp"]:
 253                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 254                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 255                 opt.set_upper_bounds(ub)
 256                 opt.set_lower_bounds(lb)
 257             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 258             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 259             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 260             Minimum = opt.optimize( Xini )
 261             if self._parameters["optdisp"]:
 262                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 263                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 264                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 265         elif self._parameters["Minimizer"] == "SIMPLEX" and not PlatformInfo.has_nlopt:
 266             Minimum, J_optimal, niter, nfeval, rc = scipy.optimize.fmin(
 267                 func        = CostFunction,
 268                 x0          = Xini,
 269                 args        = (self._parameters["QualityCriterion"],),
 270                 maxiter     = self._parameters["MaximumNumberOfSteps"]-1,
 271                 maxfun      = self._parameters["MaximumNumberOfFunctionEvaluations"],
 272                 xtol        = self._parameters["StateVariationTolerance"],
 273                 ftol        = self._parameters["CostDecrementTolerance"],
 274                 full_output = True,
 275                 disp        = self._parameters["optdisp"],
 276                 )
 277         elif self._parameters["Minimizer"] == "SIMPLEX" and PlatformInfo.has_nlopt:
 278             import nlopt
 279             opt = nlopt.opt(nlopt.LN_NELDERMEAD, Xini.size)
 280             def _f(_Xx, Grad):
 281                 # DFO, so no gradient
 282                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 283             opt.set_min_objective(_f)
 284             if self._parameters["Bounds"] is not None:
 285                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 286                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 287                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 288                 if self._parameters["optdisp"]:
 289                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 290                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 291                 opt.set_upper_bounds(ub)
 292                 opt.set_lower_bounds(lb)
 293             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 294             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 295             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 296             Minimum = opt.optimize( Xini )
 297             if self._parameters["optdisp"]:
 298                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 299                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 300                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 301         elif self._parameters["Minimizer"] == "BOBYQA" and PlatformInfo.has_nlopt:
 302             import nlopt
 303             opt = nlopt.opt(nlopt.LN_BOBYQA, Xini.size)
 304             def _f(_Xx, Grad):
 305                 # DFO, so no gradient
 306                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 307             opt.set_min_objective(_f)
 308             if self._parameters["Bounds"] is not None:
 309                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 310                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 311                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 312                 if self._parameters["optdisp"]:
 313                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 314                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 315                 opt.set_upper_bounds(ub)
 316                 opt.set_lower_bounds(lb)
 317             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 318             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 319             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 320             Minimum = opt.optimize( Xini )
 321             if self._parameters["optdisp"]:
 322                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 323                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 324                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 325         elif self._parameters["Minimizer"] == "NEWUOA" and PlatformInfo.has_nlopt:
 326             import nlopt
 327             opt = nlopt.opt(nlopt.LN_NEWUOA, Xini.size)
 328             def _f(_Xx, Grad):
 329                 # DFO, so no gradient
 330                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 331             opt.set_min_objective(_f)
 332             if self._parameters["Bounds"] is not None:
 333                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 334                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 335                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 336                 if self._parameters["optdisp"]:
 337                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 338                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 339                 opt.set_upper_bounds(ub)
 340                 opt.set_lower_bounds(lb)
 341             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 342             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 343             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 344             Minimum = opt.optimize( Xini )
 345             if self._parameters["optdisp"]:
 346                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 347                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 348                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 349         elif self._parameters["Minimizer"] == "SUBPLEX" and PlatformInfo.has_nlopt:
 350             import nlopt
 351             opt = nlopt.opt(nlopt.LN_SBPLX, Xini.size)
 352             def _f(_Xx, Grad):
 353                 # DFO, so no gradient
 354                 return CostFunction(_Xx, self._parameters["QualityCriterion"])
 355             opt.set_min_objective(_f)
 356             if self._parameters["Bounds"] is not None:
 357                 lub = numpy.array(self._parameters["Bounds"],dtype=float).reshape((Xini.size,2))
 358                 lb = lub[:,0] ; lb[numpy.isnan(lb)] = -float('inf')
 359                 ub = lub[:,1] ; ub[numpy.isnan(ub)] = +float('inf')
 360                 if self._parameters["optdisp"]:
 361                     print("%s: upper bounds %s"%(opt.get_algorithm_name(),ub))
 362                     print("%s: lower bounds %s"%(opt.get_algorithm_name(),lb))
 363                 opt.set_upper_bounds(ub)
 364                 opt.set_lower_bounds(lb)
 365             opt.set_ftol_rel(self._parameters["CostDecrementTolerance"])
 366             opt.set_xtol_rel(2.*self._parameters["StateVariationTolerance"])
 367             opt.set_maxeval(self._parameters["MaximumNumberOfFunctionEvaluations"])
 368             Minimum = opt.optimize( Xini )
 369             if self._parameters["optdisp"]:
 370                 print("%s: optimal state: %s"%(opt.get_algorithm_name(),Minimum))
 371                 print("%s: minimum of J: %s"%(opt.get_algorithm_name(),opt.last_optimum_value()))
 372                 print("%s: return code: %i"%(opt.get_algorithm_name(),opt.last_optimize_result()))
 373         else:
 374             raise ValueError("Error in Minimizer name: %s"%self._parameters["Minimizer"])
 375         #
 376         IndexMin = numpy.argmin( self.StoredVariables["CostFunctionJ"][nbPreviousSteps:] ) + nbPreviousSteps
 377         MinJ     = self.StoredVariables["CostFunctionJ"][IndexMin]
 378         Minimum  = self.StoredVariables["CurrentState"][IndexMin]
 379         #
 380         # Obtention de l'analyse
 381         # ----------------------
 382         Xa = numpy.asmatrix(numpy.ravel( Minimum )).T
 383         #
 384         self.StoredVariables["Analysis"].store( Xa.A1 )
 385         #
 386         # Calculs et/ou stockages supplémentaires
 387         # ---------------------------------------
 388         if self._toStore("OMA" ) or \
 389             self._toStore("SimulatedObservationAtOptimum"):
 390             if self._toStore("SimulatedObservationAtCurrentState"):
 391                 HXa = self.StoredVariables["SimulatedObservationAtCurrentState"][IndexMin]
 392             elif self._toStore("SimulatedObservationAtCurrentOptimum"):
 393                 HXa = self.StoredVariables["SimulatedObservationAtCurrentOptimum"][-1]
 394             else:
 395                 HXa = Hm(Xa)
 396         if self._toStore("Innovation") or \
 397             self._toStore("OMB"):
 398             d  = Y - HXb
 399         if self._toStore("Innovation"):
 400             self.StoredVariables["Innovation"].store( numpy.ravel(d) )
 401         if self._toStore("OMB"):
 402             self.StoredVariables["OMB"].store( numpy.ravel(d) )
 403         if self._toStore("BMA"):
 404             self.StoredVariables["BMA"].store( numpy.ravel(Xb) - numpy.ravel(Xa) )
 405         if self._toStore("OMA"):
 406             self.StoredVariables["OMA"].store( numpy.ravel(Y) - numpy.ravel(HXa) )
 407         if self._toStore("SimulatedObservationAtBackground"):
 408             self.StoredVariables["SimulatedObservationAtBackground"].store( numpy.ravel(Hm(Xb)) )
 409         if self._toStore("SimulatedObservationAtOptimum"):
 410             self.StoredVariables["SimulatedObservationAtOptimum"].store( numpy.ravel(HXa) )
 411         #
 412         self._post_run()
 413         return 0
 414
 415 # ==============================================================================
 416 if __name__ == "__main__":
 417     print('\n AUTODIAGNOSTIC\n')