doc/en/ref_algorithm_ParticleSwarmOptimization.rst

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   2    Copyright (C) 2008-2023 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: ParticleSwarmOptimization
  25 .. index:: single: Global optimization
  26 .. _section_ref_algorithm_ParticleSwarmOptimization:
  27
  28 Calculation algorithm "*ParticleSwarmOptimization*"
  29 ---------------------------------------------------
  30
  31 .. ------------------------------------ ..
  32 .. include:: snippets/Header2Algo01.rst
  33
  34 This algorithm realizes an estimation of the state of a system by minimization
  35 of a cost function :math:`J` by using an evolutionary strategy of particle
  36 swarm. It is a method that does not use the derivatives of the cost function.
  37 It is based on the evolution of a population (called a "swarm") of states (each
  38 state is called a "particle" or an "insect"). It falls in the same category
  39 than the
  40 :ref:`section_ref_algorithm_DerivativeFreeOptimization`, the
  41 :ref:`section_ref_algorithm_DifferentialEvolution` or the
  42 :ref:`section_ref_algorithm_TabuSearch`.
  43
  44 This is an optimization method allowing for global minimum search of a general
  45 error function :math:`J` of type :math:`L^1`, :math:`L^2` or
  46 :math:`L^{\infty}`, with or without weights, as described in the section for
  47 :ref:`section_theory_optimization`. The default error function is the augmented
  48 weighted least squares function, classically used in data assimilation.
  49
  50 .There exists various variants of this algorithm. The following stable and
  51 robust formulations are proposed here:
  52
  53 .. index::
  54 .. index::
  55     pair: Variant ; PSO
  56     pair: Variant ; CanonicalPSO
  57     pair: Variant ; OGCR
  58
  59 - "PSO" (Canonical PSO, see [ZambranoBigiarini13]_), canonical algorithm of particle swarm, robust and defining the reference for particle swarm algorithms,
  60 - "OGCR" (Simple PSO with no bounds on insects or velocities), simplified algorithm of particle swarm, not recommanded because less robust, but sometimes a lot more efficient.
  61
  62 . ------------------------------------ ..
  63 .. include:: snippets/Header2Algo02.rst
  64
  65 .. include:: snippets/Background.rst
  66
  67 .. include:: snippets/BackgroundError.rst
  68
  69 .. include:: snippets/Observation.rst
  70
  71 .. include:: snippets/ObservationError.rst
  72
  73 .. include:: snippets/ObservationOperator.rst
  74
  75 .. ------------------------------------ ..
  76 .. include:: snippets/Header2Algo03AdOp.rst
  77
  78 .. include:: snippets/BoundsWithNone.rst
  79
  80 .. include:: snippets/BoxBounds.rst
  81
  82 .. include:: snippets/CognitiveAcceleration.rst
  83
  84 .. include:: snippets/InertiaWeight.rst
  85
  86 .. include:: snippets/InitializationPoint.rst
  87
  88 .. include:: snippets/MaximumNumberOfFunctionEvaluations.rst
  89
  90 .. include:: snippets/MaximumNumberOfIterations_50.rst
  91
  92 .. include:: snippets/NumberOfInsects.rst
  93
  94 .. include:: snippets/QualityCriterion.rst
  95
  96 .. include:: snippets/SetSeed.rst
  97
  98 .. include:: snippets/SocialAcceleration.rst
  99
 100 StoreSupplementaryCalculations
 101   .. index:: single: StoreSupplementaryCalculations
 102
 103   *List of names*. This list indicates the names of the supplementary
 104   variables, that can be available during or at the end of the algorithm, if
 105   they are initially required by the user. Their avalability involves,
 106   potentially, costly calculations or memory consumptions. The default is then
 107   a void list, none of these variables being calculated and stored by default
 108   (excepted the unconditionnal variables). The possible names are in the
 109   following list (the detailed description of each named variable is given in
 110   the following part of this specific algorithmic documentation, in the
 111   sub-section "*Information and variables available at the end of the
 112   algorithm*"): [
 113   "Analysis",
 114   "BMA",
 115   "CostFunctionJ",
 116   "CostFunctionJb",
 117   "CostFunctionJo",
 118   "CurrentIterationNumber",
 119   "CurrentState",
 120   "Innovation",
 121   "OMA",
 122   "OMB",
 123   "SimulatedObservationAtBackground",
 124   "SimulatedObservationAtCurrentState",
 125   "SimulatedObservationAtOptimum",
 126   ].
 127
 128   Example :
 129   ``{"StoreSupplementaryCalculations":["CurrentState", "Residu"]}``
 130
 131 .. include:: snippets/VelocityClampingFactor.rst
 132
 133 .. ------------------------------------ ..
 134 .. include:: snippets/Header2Algo04.rst
 135
 136 .. include:: snippets/Analysis.rst
 137
 138 .. include:: snippets/CostFunctionJ.rst
 139
 140 .. include:: snippets/CostFunctionJb.rst
 141
 142 .. include:: snippets/CostFunctionJo.rst
 143
 144 .. ------------------------------------ ..
 145 .. include:: snippets/Header2Algo05.rst
 146
 147 .. include:: snippets/Analysis.rst
 148
 149 .. include:: snippets/BMA.rst
 150
 151 .. include:: snippets/CostFunctionJ.rst
 152
 153 .. include:: snippets/CostFunctionJb.rst
 154
 155 .. include:: snippets/CostFunctionJo.rst
 156
 157 .. include:: snippets/CurrentIterationNumber.rst
 158
 159 .. include:: snippets/CurrentState.rst
 160
 161 .. include:: snippets/Innovation.rst
 162
 163 .. include:: snippets/OMA.rst
 164
 165 .. include:: snippets/OMB.rst
 166
 167 .. include:: snippets/SimulatedObservationAtBackground.rst
 168
 169 .. include:: snippets/SimulatedObservationAtCurrentState.rst
 170
 171 .. include:: snippets/SimulatedObservationAtOptimum.rst
 172
 173 .. ------------------------------------ ..
 174 .. _section_ref_algorithm_ParticleSwarmOptimization_examples:
 175
 176 .. include:: snippets/Header2Algo06.rst
 177
 178 - :ref:`section_ref_algorithm_DerivativeFreeOptimization`
 179 - :ref:`section_ref_algorithm_DifferentialEvolution`
 180 - :ref:`section_ref_algorithm_TabuSearch`
 181
 182 .. ------------------------------------ ..
 183 .. include:: snippets/Header2Algo07.rst
 184
 185 - [WikipediaPSO]_
 186 - [ZambranoBigiarini13]_