2 Copyright (C) 2008-2016 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
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13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
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18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. index:: single: ParticleSwarmOptimization
25 .. _section_ref_algorithm_ParticleSwarmOptimization:
27 Calculation algorithm "*ParticleSwarmOptimization*"
28 ---------------------------------------------------
33 This algorithm realizes an estimation of the state of a dynamic system by
34 minimization of a cost function :math:`J` by using a particle swarm. It is a
35 method that doesn't use the derivatives of the cost function. It fall in the
36 same category then the :ref:`section_ref_algorithm_DerivativeFreeOptimization`.
38 This is an optimization method allowing for global minimum search of a general
39 error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
40 with or without weights. The default error function is the augmented weighted
41 least squares function, classicaly used in data assimilation.
43 Optional and required commands
44 ++++++++++++++++++++++++++++++
46 .. index:: single: AlgorithmParameters
47 .. index:: single: Background
48 .. index:: single: BackgroundError
49 .. index:: single: Observation
50 .. index:: single: ObservationError
51 .. index:: single: ObservationOperator
52 .. index:: single: MaximumNumberOfSteps
53 .. index:: single: NumberOfInsects
54 .. index:: single: SwarmVelocity
55 .. index:: single: GroupRecallRate
56 .. index:: single: QualityCriterion
57 .. index:: single: BoxBounds
58 .. index:: single: SetSeed
59 .. index:: single: StoreSupplementaryCalculations
61 The general required commands, available in the editing user interface, are the
65 *Required command*. This indicates the background or initial vector used,
66 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
67 "*Vector*" or a *VectorSerie*" type object.
70 *Required command*. This indicates the background error covariance matrix,
71 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
72 type object, a "*ScalarSparseMatrix*" type object, or a
73 "*DiagonalSparseMatrix*" type object.
76 *Required command*. This indicates the observation vector used for data
77 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
78 is defined as a "*Vector*" or a *VectorSerie* type object.
81 *Required command*. This indicates the observation error covariance matrix,
82 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
83 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
87 *Required command*. This indicates the observation operator, previously
88 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
89 results :math:`\mathbf{y}` to be compared to observations
90 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
91 a "*Matrix*" type one. In the case of "*Function*" type, different
92 functional forms can be used, as described in the section
93 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
94 included in the observation, the operator has to be applied to a pair
97 The general optional commands, available in the editing user interface, are
98 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
99 of the command "*AlgorithmParameters*" allows to choose the specific options,
100 described hereafter, of the algorithm. See
101 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
104 The options of the algorithm are the following:
107 This key indicates the maximum number of iterations allowed for iterative
108 optimization. The default is 50, which is an arbitrary limit. It is then
109 recommended to adapt this parameter to the needs on real problems.
111 Example : ``{"MaximumNumberOfSteps":100}``
114 This key indicates the number of insects or particles in the swarm. The
115 default is 100, which is a usual default for this algorithm.
117 Example : ``{"NumberOfInsects":100}``
120 This key indicates the part of the insect velocity which is imposed by the
121 swarm. It is a positive floating point value. The default value is 1.
123 Example : ``{"SwarmVelocity":1.}``
126 This key indicates the recall rate at the best swarm insect. It is a
127 floating point value between 0 and 1. The default value is 0.5.
129 Example : ``{"GroupRecallRate":0.5}``
132 This key indicates the quality criterion, minimized to find the optimal
133 state estimate. The default is the usual data assimilation criterion named
134 "DA", the augmented weighted least squares. The possible criteria has to be
135 in the following list, where the equivalent names are indicated by the sign
136 "=": ["AugmentedWeightedLeastSquares"="AWLS"="DA",
137 "WeightedLeastSquares"="WLS", "LeastSquares"="LS"="L2",
138 "AbsoluteValue"="L1", "MaximumError"="ME"].
140 Example : ``{"QualityCriterion":"DA"}``
143 This key allows to define upper and lower bounds for *increments* on every
144 state variable being optimized (and not on state variables themselves).
145 Bounds have to be given by a list of list of pairs of lower/upper bounds for
146 each increment on variable, with extreme values every time there is no bound
147 (``None`` is not allowed when there is no bound). This key is required and
148 there is no default values.
150 Example : ``{"BoxBounds":[[-0.5,0.5], [0.01,2.], [0.,1.e99], [-1.e99,1.e99]]}``
153 This key allow to give an integer in order to fix the seed of the random
154 generator used to generate the ensemble. A convenient value is for example
155 1000. By default, the seed is left uninitialized, and so use the default
156 initialization from the computer.
158 Example : ``{"SetSeed":1000}``
160 StoreSupplementaryCalculations
161 This list indicates the names of the supplementary variables that can be
162 available at the end of the algorithm. It involves potentially costly
163 calculations or memory consumptions. The default is a void list, none of
164 these variables being calculated and stored by default. The possible names
165 are in the following list: ["BMA", "CostFunctionJ", "CurrentState", "OMA",
166 "OMB", "Innovation", "SimulatedObservationAtBackground",
167 "SimulatedObservationAtCurrentState", "SimulatedObservationAtOptimum"].
169 Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
171 Information and variables available at the end of the algorithm
172 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
174 At the output, after executing the algorithm, there are variables and
175 information originating from the calculation. The description of
176 :ref:`section_ref_output_variables` show the way to obtain them by the method
177 named ``get`` of the variable "*ADD*" of the post-processing. The input
178 variables, available to the user at the output in order to facilitate the
179 writing of post-processing procedures, are described in the
180 :ref:`subsection_r_o_v_Inventaire`.
182 The unconditional outputs of the algorithm are the following:
185 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
186 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
188 Example : ``Xa = ADD.get("Analysis")[-1]``
191 *List of values*. Each element is a value of the error function :math:`J`.
193 Example : ``J = ADD.get("CostFunctionJ")[:]``
196 *List of values*. Each element is a value of the error function :math:`J^b`,
197 that is of the background difference part.
199 Example : ``Jb = ADD.get("CostFunctionJb")[:]``
202 *List of values*. Each element is a value of the error function :math:`J^o`,
203 that is of the observation difference part.
205 Example : ``Jo = ADD.get("CostFunctionJo")[:]``
207 The conditional outputs of the algorithm are the following:
210 *List of vectors*. Each element is a vector of difference between the
211 background and the optimal state.
213 Example : ``bma = ADD.get("BMA")[-1]``
216 *List of vectors*. Each element is a usual state vector used during the
217 optimization algorithm procedure.
219 Example : ``Xs = ADD.get("CurrentState")[:]``
222 *List of vectors*. Each element is an innovation vector, which is in static
223 the difference between the optimal and the background, and in dynamic the
226 Example : ``d = ADD.get("Innovation")[-1]``
229 *List of vectors*. Each element is a vector of difference between the
230 observation and the optimal state in the observation space.
232 Example : ``oma = ADD.get("OMA")[-1]``
235 *List of vectors*. Each element is a vector of difference between the
236 observation and the background state in the observation space.
238 Example : ``omb = ADD.get("OMB")[-1]``
240 SimulatedObservationAtBackground
241 *List of vectors*. Each element is a vector of observation simulated from
242 the background :math:`\mathbf{x}^b`.
244 Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
246 SimulatedObservationAtCurrentState
247 *List of vectors*. Each element is an observed vector at the current state,
248 that is, in the observation space.
250 Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
252 SimulatedObservationAtOptimum
253 *List of vectors*. Each element is a vector of observation simulated from
254 the analysis or optimal state :math:`\mathbf{x}^a`.
256 Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
261 References to other sections:
262 - :ref:`section_ref_algorithm_DerivativeFreeOptimization`
264 Bibliographical references: