doc/en/ref_algorithm_DifferentialEvolution.rst

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   2    Copyright (C) 2008-2024 EDF R&D
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  20    See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
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  22    Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
  23
  24 .. index:: single: DifferentialEvolution
  25 .. _section_ref_algorithm_DifferentialEvolution:
  26
  27 Calculation algorithm "*DifferentialEvolution*"
  28 ----------------------------------------------------
  29
  30 .. ------------------------------------ ..
  31 .. include:: snippets/Header2Algo01.rst
  32
  33 This algorithm realizes an estimation of the state of a system by minimization
  34 without gradient of a cost function :math:`J`, using an evolutionary strategy
  35 of differential evolution. It is a method that does not use the derivatives of
  36 the cost function. It falls in the same category than the
  37 :ref:`section_ref_algorithm_DerivativeFreeOptimization`,
  38 :ref:`section_ref_algorithm_ParticleSwarmOptimization` or
  39 :ref:`section_ref_algorithm_TabuSearch`.
  40
  41 This is an optimization method allowing for global minimum search of a general
  42 error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
  43 with or without weights. The default error function is the augmented weighted
  44 least squares function, classically used in data assimilation.
  45
  46 .. ------------------------------------ ..
  47 .. include:: snippets/Header2Algo12.rst
  48
  49 .. include:: snippets/FeaturePropNonLocalOptimization.rst
  50
  51 .. include:: snippets/FeaturePropDerivativeFree.rst
  52
  53 .. ------------------------------------ ..
  54 .. include:: snippets/Header2Algo02.rst
  55
  56 .. include:: snippets/Background.rst
  57
  58 .. include:: snippets/BackgroundError.rst
  59
  60 .. include:: snippets/Observation.rst
  61
  62 .. include:: snippets/ObservationError.rst
  63
  64 .. include:: snippets/ObservationOperator.rst
  65
  66 .. ------------------------------------ ..
  67 .. include:: snippets/Header2Algo03AdOp.rst
  68
  69 .. include:: snippets/Minimizer_DE.rst
  70
  71 .. include:: snippets/BoundsWithExtremes.rst
  72
  73 .. include:: snippets/CrossOverProbability_CR.rst
  74
  75 .. include:: snippets/MaximumNumberOfIterations.rst
  76
  77 .. include:: snippets/MaximumNumberOfFunctionEvaluations.rst
  78
  79 .. include:: snippets/MutationDifferentialWeight_F.rst
  80
  81 .. include:: snippets/PopulationSize.rst
  82
  83 .. include:: snippets/QualityCriterion.rst
  84
  85 .. include:: snippets/SetSeed.rst
  86
  87 StoreSupplementaryCalculations
  88   .. index:: single: StoreSupplementaryCalculations
  89
  90   *List of names*. This list indicates the names of the supplementary
  91   variables, that can be available during or at the end of the algorithm, if
  92   they are initially required by the user. Their availability involves,
  93   potentially, costly calculations or memory consumptions. The default is then
  94   a void list, none of these variables being calculated and stored by default
  95   (excepted the unconditional variables). The possible names are in the
  96   following list (the detailed description of each named variable is given in
  97   the following part of this specific algorithmic documentation, in the
  98   sub-section "*Information and variables available at the end of the
  99   algorithm*"): [
 100   "Analysis",
 101   "BMA",
 102   "CostFunctionJ",
 103   "CostFunctionJb",
 104   "CostFunctionJo",
 105   "CostFunctionJAtCurrentOptimum",
 106   "CostFunctionJbAtCurrentOptimum",
 107   "CostFunctionJoAtCurrentOptimum",
 108   "CurrentIterationNumber",
 109   "CurrentOptimum",
 110   "CurrentState",
 111   "IndexOfOptimum",
 112   "Innovation",
 113   "InnovationAtCurrentState",
 114   "OMA",
 115   "OMB",
 116   "SimulatedObservationAtBackground",
 117   "SimulatedObservationAtCurrentOptimum",
 118   "SimulatedObservationAtCurrentState",
 119   "SimulatedObservationAtOptimum",
 120   ].
 121
 122   Example :
 123   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 124
 125 .. ------------------------------------ ..
 126 .. include:: snippets/Header2Algo04.rst
 127
 128 .. include:: snippets/Analysis.rst
 129
 130 .. include:: snippets/CostFunctionJ.rst
 131
 132 .. include:: snippets/CostFunctionJb.rst
 133
 134 .. include:: snippets/CostFunctionJo.rst
 135
 136 .. include:: snippets/CurrentState.rst
 137
 138 .. ------------------------------------ ..
 139 .. include:: snippets/Header2Algo05.rst
 140
 141 .. include:: snippets/Analysis.rst
 142
 143 .. include:: snippets/BMA.rst
 144
 145 .. include:: snippets/CostFunctionJ.rst
 146
 147 .. include:: snippets/CostFunctionJb.rst
 148
 149 .. include:: snippets/CostFunctionJo.rst
 150
 151 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
 152
 153 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
 154
 155 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
 156
 157 .. include:: snippets/CurrentIterationNumber.rst
 158
 159 .. include:: snippets/CurrentOptimum.rst
 160
 161 .. include:: snippets/CurrentState.rst
 162
 163 .. include:: snippets/IndexOfOptimum.rst
 164
 165 .. include:: snippets/Innovation.rst
 166
 167 .. include:: snippets/InnovationAtCurrentState.rst
 168
 169 .. include:: snippets/OMA.rst
 170
 171 .. include:: snippets/OMB.rst
 172
 173 .. include:: snippets/SimulatedObservationAtBackground.rst
 174
 175 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
 176
 177 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 178
 179 .. include:: snippets/SimulatedObservationAtOptimum.rst
 180
 181 .. ------------------------------------ ..
 182 .. _section_ref_algorithm_DifferentialEvolution_examples:
 183
 184 .. include:: snippets/Header2Algo06.rst
 185
 186 - :ref:`section_ref_algorithm_DerivativeFreeOptimization`
 187 - :ref:`section_ref_algorithm_ParticleSwarmOptimization`
 188 - :ref:`section_ref_algorithm_TabuSearch`
 189
 190 .. ------------------------------------ ..
 191 .. include:: snippets/Header2Algo07.rst
 192
 193 - [Chakraborty08]_
 194 - [Das11]_
 195 - [Das16]_
 196 - [Price05]_
 197 - [Storn97]_