2 Copyright (C) 2008-2017 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
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12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
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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 than 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: MaximumNumberOfFunctionEvaluations
54 .. index:: single: NumberOfInsects
55 .. index:: single: SwarmVelocity
56 .. index:: single: GroupRecallRate
57 .. index:: single: QualityCriterion
58 .. index:: single: BoxBounds
59 .. index:: single: SetSeed
60 .. index:: single: StoreSupplementaryCalculations
62 The general required commands, available in the editing user interface, are the
66 *Required command*. This indicates the background or initial vector used,
67 previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
68 "*Vector*" or a *VectorSerie*" type object.
71 *Required command*. This indicates the background error covariance matrix,
72 previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
73 type object, a "*ScalarSparseMatrix*" type object, or a
74 "*DiagonalSparseMatrix*" type object.
77 *Required command*. This indicates the observation vector used for data
78 assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
79 is defined as a "*Vector*" or a *VectorSerie* type object.
82 *Required command*. This indicates the observation error covariance matrix,
83 previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
84 object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
88 *Required command*. This indicates the observation operator, previously
89 noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
90 results :math:`\mathbf{y}` to be compared to observations
91 :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
92 a "*Matrix*" type one. In the case of "*Function*" type, different
93 functional forms can be used, as described in the section
94 :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
95 included in the observation, the operator has to be applied to a pair
98 The general optional commands, available in the editing user interface, are
99 indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
100 of the command "*AlgorithmParameters*" allows to choose the specific options,
101 described hereafter, of the algorithm. See
102 :ref:`section_ref_options_Algorithm_Parameters` for the good use of this
105 The options of the algorithm are the following:
108 This key indicates the maximum number of iterations allowed for iterative
109 optimization. The default is 50, which is an arbitrary limit. It is then
110 recommended to adapt this parameter to the needs on real problems.
112 Example : ``{"MaximumNumberOfSteps":100}``
114 MaximumNumberOfFunctionEvaluations
115 This key indicates the maximum number of evaluation of the cost function to
116 be optimized. The default is 15000, which is an arbitrary limit. It is then
117 recommended to adapt this parameter to the needs on real problems. For some
118 optimizers, the effective number of function evaluations can be slightly
119 different of the limit due to algorithm internal control requirements.
121 Example : ``{"MaximumNumberOfFunctionEvaluations":50}``
124 This key indicates the number of insects or particles in the swarm. The
125 default is 100, which is a usual default for this algorithm.
127 Example : ``{"NumberOfInsects":100}``
130 This key indicates the part of the insect velocity which is imposed by the
131 swarm. It is a positive floating point value. The default value is 1.
133 Example : ``{"SwarmVelocity":1.}``
136 This key indicates the recall rate at the best swarm insect. It is a
137 floating point value between 0 and 1. The default value is 0.5.
139 Example : ``{"GroupRecallRate":0.5}``
142 This key indicates the quality criterion, minimized to find the optimal
143 state estimate. The default is the usual data assimilation criterion named
144 "DA", the augmented weighted least squares. The possible criteria has to be
145 in the following list, where the equivalent names are indicated by the sign
146 "=": ["AugmentedWeightedLeastSquares"="AWLS"="DA",
147 "WeightedLeastSquares"="WLS", "LeastSquares"="LS"="L2",
148 "AbsoluteValue"="L1", "MaximumError"="ME"].
150 Example : ``{"QualityCriterion":"DA"}``
153 This key allows to define upper and lower bounds for *increments* on every
154 state variable being optimized (and not on state variables themselves).
155 Bounds have to be given by a list of list of pairs of lower/upper bounds for
156 each increment on variable, with extreme values every time there is no bound
157 (``None`` is not allowed when there is no bound). This key is required and
158 there is no default values.
160 Example : ``{"BoxBounds":[[-0.5,0.5], [0.01,2.], [0.,1.e99], [-1.e99,1.e99]]}``
163 This key allow to give an integer in order to fix the seed of the random
164 generator used to generate the ensemble. A convenient value is for example
165 1000. By default, the seed is left uninitialized, and so use the default
166 initialization from the computer.
168 Example : ``{"SetSeed":1000}``
170 StoreSupplementaryCalculations
171 This list indicates the names of the supplementary variables that can be
172 available at the end of the algorithm. It involves potentially costly
173 calculations or memory consumptions. The default is a void list, none of
174 these variables being calculated and stored by default. The possible names
175 are in the following list: ["BMA", "CostFunctionJ", "CostFunctionJb",
176 "CostFunctionJo", "CurrentState", "OMA", "OMB", "Innovation",
177 "SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState",
178 "SimulatedObservationAtOptimum"].
180 Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
182 Information and variables available at the end of the algorithm
183 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
185 At the output, after executing the algorithm, there are variables and
186 information originating from the calculation. The description of
187 :ref:`section_ref_output_variables` show the way to obtain them by the method
188 named ``get`` of the variable "*ADD*" of the post-processing. The input
189 variables, available to the user at the output in order to facilitate the
190 writing of post-processing procedures, are described in the
191 :ref:`subsection_r_o_v_Inventaire`.
193 The unconditional outputs of the algorithm are the following:
196 *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
197 optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
199 Example : ``Xa = ADD.get("Analysis")[-1]``
202 *List of values*. Each element is a value of the error function :math:`J`.
204 Example : ``J = ADD.get("CostFunctionJ")[:]``
207 *List of values*. Each element is a value of the error function :math:`J^b`,
208 that is of the background difference part.
210 Example : ``Jb = ADD.get("CostFunctionJb")[:]``
213 *List of values*. Each element is a value of the error function :math:`J^o`,
214 that is of the observation difference part.
216 Example : ``Jo = ADD.get("CostFunctionJo")[:]``
218 The conditional outputs of the algorithm are the following:
221 *List of vectors*. Each element is a vector of difference between the
222 background and the optimal state.
224 Example : ``bma = ADD.get("BMA")[-1]``
227 *List of vectors*. Each element is a usual state vector used during the
228 optimization algorithm procedure.
230 Example : ``Xs = ADD.get("CurrentState")[:]``
233 *List of vectors*. Each element is an innovation vector, which is in static
234 the difference between the optimal and the background, and in dynamic the
237 Example : ``d = ADD.get("Innovation")[-1]``
240 *List of vectors*. Each element is a vector of difference between the
241 observation and the optimal state in the observation space.
243 Example : ``oma = ADD.get("OMA")[-1]``
246 *List of vectors*. Each element is a vector of difference between the
247 observation and the background state in the observation space.
249 Example : ``omb = ADD.get("OMB")[-1]``
251 SimulatedObservationAtBackground
252 *List of vectors*. Each element is a vector of observation simulated from
253 the background :math:`\mathbf{x}^b`.
255 Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
257 SimulatedObservationAtCurrentState
258 *List of vectors*. Each element is an observed vector at the current state,
259 that is, in the observation space.
261 Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
263 SimulatedObservationAtOptimum
264 *List of vectors*. Each element is a vector of observation simulated from
265 the analysis or optimal state :math:`\mathbf{x}^a`.
267 Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
272 References to other sections:
273 - :ref:`section_ref_algorithm_DerivativeFreeOptimization`
275 Bibliographical references: