..
- Copyright (C) 2008-2017 EDF R&D
+ Copyright (C) 2008-2018 EDF R&D
This file is part of SALOME ADAO module.
Description
+++++++++++
-This algorithm realizes an estimation of the state of a dynamic system by
-minimization of a cost function :math:`J` by using a particle swarm. It is a
-method that doesn't use the derivatives of the cost function. It fall in the
-same category than the :ref:`section_ref_algorithm_DerivativeFreeOptimization`.
+This algorithm realizes an estimation of the state of a system by minimization
+of a cost function :math:`J` by using an evolutionary strategy of particle
+swarm. It is a method that does not use the derivatives of the cost function.
+It falls in the same category than the
+:ref:`section_ref_algorithm_DerivativeFreeOptimization` or the
+:ref:`section_ref_algorithm_DifferentialEvolution`.
This is an optimization method allowing for global minimum search of a general
error function :math:`J` of type :math:`L^1`, :math:`L^2` or :math:`L^{\infty}`,
with or without weights. The default error function is the augmented weighted
-least squares function, classicaly used in data assimilation.
+least squares function, classically used in data assimilation.
Optional and required commands
++++++++++++++++++++++++++++++
-.. index:: single: AlgorithmParameters
-.. index:: single: Background
-.. index:: single: BackgroundError
-.. index:: single: Observation
-.. index:: single: ObservationError
-.. index:: single: ObservationOperator
-.. index:: single: MaximumNumberOfSteps
-.. index:: single: MaximumNumberOfFunctionEvaluations
-.. index:: single: NumberOfInsects
-.. index:: single: SwarmVelocity
-.. index:: single: GroupRecallRate
-.. index:: single: QualityCriterion
-.. index:: single: BoxBounds
-.. index:: single: SetSeed
-.. index:: single: StoreSupplementaryCalculations
-
The general required commands, available in the editing user interface, are the
following:
- Background
- *Required command*. This indicates the background or initial vector used,
- previously noted as :math:`\mathbf{x}^b`. Its value is defined as a
- "*Vector*" or a *VectorSerie*" type object.
-
- BackgroundError
- *Required command*. This indicates the background error covariance matrix,
- previously noted as :math:`\mathbf{B}`. Its value is defined as a "*Matrix*"
- type object, a "*ScalarSparseMatrix*" type object, or a
- "*DiagonalSparseMatrix*" type object.
-
- Observation
- *Required command*. This indicates the observation vector used for data
- assimilation or optimization, previously noted as :math:`\mathbf{y}^o`. It
- is defined as a "*Vector*" or a *VectorSerie* type object.
-
- ObservationError
- *Required command*. This indicates the observation error covariance matrix,
- previously noted as :math:`\mathbf{R}`. It is defined as a "*Matrix*" type
- object, a "*ScalarSparseMatrix*" type object, or a "*DiagonalSparseMatrix*"
- type object.
-
- ObservationOperator
- *Required command*. This indicates the observation operator, previously
- noted :math:`H`, which transforms the input parameters :math:`\mathbf{x}` to
- results :math:`\mathbf{y}` to be compared to observations
- :math:`\mathbf{y}^o`. Its value is defined as a "*Function*" type object or
- a "*Matrix*" type one. In the case of "*Function*" type, different
- functional forms can be used, as described in the section
- :ref:`section_ref_operator_requirements`. If there is some control :math:`U`
- included in the observation, the operator has to be applied to a pair
- :math:`(X,U)`.
+ .. include:: snippets/Background.rst
+
+ .. include:: snippets/BackgroundError.rst
+
+ .. include:: snippets/Observation.rst
+
+ .. include:: snippets/ObservationError.rst
+
+ .. include:: snippets/ObservationOperator.rst
The general optional commands, available in the editing user interface, are
indicated in :ref:`section_ref_assimilation_keywords`. Moreover, the parameters
command.
The options of the algorithm are the following:
+.. index:: single: NumberOfInsects
+.. index:: single: SwarmVelocity
+.. index:: single: GroupRecallRate
+.. index:: single: QualityCriterion
+.. index:: single: BoxBounds
- MaximumNumberOfSteps
- This key indicates the maximum number of iterations allowed for iterative
- optimization. The default is 50, which is an arbitrary limit. It is then
- recommended to adapt this parameter to the needs on real problems.
-
- Example : ``{"MaximumNumberOfSteps":100}``
+ .. include:: snippets/MaximumNumberOfSteps_50.rst
- MaximumNumberOfFunctionEvaluations
- This key indicates the maximum number of evaluation of the cost function to
- be optimized. The default is 15000, which is an arbitrary limit. It is then
- recommended to adapt this parameter to the needs on real problems. For some
- optimizers, the effective number of function evaluations can be slightly
- different of the limit due to algorithm internal control requirements.
+ .. include:: snippets/MaximumNumberOfFunctionEvaluations.rst
- Example : ``{"MaximumNumberOfFunctionEvaluations":50}``
+ .. include:: snippets/QualityCriterion.rst
NumberOfInsects
This key indicates the number of insects or particles in the swarm. The
default is 100, which is a usual default for this algorithm.
- Example : ``{"NumberOfInsects":100}``
+ Example :
+ ``{"NumberOfInsects":100}``
SwarmVelocity
- This key indicates the part of the insect velocity which is imposed by the
+ This key indicates the part of the insect velocity which is imposed by the
swarm. It is a positive floating point value. The default value is 1.
- Example : ``{"SwarmVelocity":1.}``
+ Example :
+ ``{"SwarmVelocity":1.}``
GroupRecallRate
This key indicates the recall rate at the best swarm insect. It is a
floating point value between 0 and 1. The default value is 0.5.
- Example : ``{"GroupRecallRate":0.5}``
-
- QualityCriterion
- This key indicates the quality criterion, minimized to find the optimal
- state estimate. The default is the usual data assimilation criterion named
- "DA", the augmented weighted least squares. The possible criteria has to be
- in the following list, where the equivalent names are indicated by the sign
- "=": ["AugmentedWeightedLeastSquares"="AWLS"="DA",
- "WeightedLeastSquares"="WLS", "LeastSquares"="LS"="L2",
- "AbsoluteValue"="L1", "MaximumError"="ME"].
-
- Example : ``{"QualityCriterion":"DA"}``
+ Example :
+ ``{"GroupRecallRate":0.5}``
BoxBounds
This key allows to define upper and lower bounds for *increments* on every
(``None`` is not allowed when there is no bound). This key is required and
there is no default values.
- Example : ``{"BoxBounds":[[-0.5,0.5], [0.01,2.], [0.,1.e99], [-1.e99,1.e99]]}``
+ Example :
+ ``{"BoxBounds":[[-0.5,0.5], [0.01,2.], [0.,1.e99], [-1.e99,1.e99]]}``
- SetSeed
- This key allow to give an integer in order to fix the seed of the random
- generator used to generate the ensemble. A convenient value is for example
- 1000. By default, the seed is left uninitialized, and so use the default
- initialization from the computer.
-
- Example : ``{"SetSeed":1000}``
+ .. include:: snippets/SetSeed.rst
StoreSupplementaryCalculations
+ .. index:: single: StoreSupplementaryCalculations
+
This list indicates the names of the supplementary variables that can be
available at the end of the algorithm. It involves potentially costly
calculations or memory consumptions. The default is a void list, none of
"SimulatedObservationAtBackground", "SimulatedObservationAtCurrentState",
"SimulatedObservationAtOptimum"].
- Example : ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
+ Example :
+ ``{"StoreSupplementaryCalculations":["BMA", "Innovation"]}``
Information and variables available at the end of the algorithm
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
The unconditional outputs of the algorithm are the following:
- Analysis
- *List of vectors*. Each element is an optimal state :math:`\mathbf{x}*` in
- optimization or an analysis :math:`\mathbf{x}^a` in data assimilation.
-
- Example : ``Xa = ADD.get("Analysis")[-1]``
-
- CostFunctionJ
- *List of values*. Each element is a value of the error function :math:`J`.
-
- Example : ``J = ADD.get("CostFunctionJ")[:]``
-
- CostFunctionJb
- *List of values*. Each element is a value of the error function :math:`J^b`,
- that is of the background difference part.
+ .. include:: snippets/Analysis.rst
- Example : ``Jb = ADD.get("CostFunctionJb")[:]``
+ .. include:: snippets/CostFunctionJ.rst
- CostFunctionJo
- *List of values*. Each element is a value of the error function :math:`J^o`,
- that is of the observation difference part.
+ .. include:: snippets/CostFunctionJb.rst
- Example : ``Jo = ADD.get("CostFunctionJo")[:]``
+ .. include:: snippets/CostFunctionJo.rst
The conditional outputs of the algorithm are the following:
- BMA
- *List of vectors*. Each element is a vector of difference between the
- background and the optimal state.
-
- Example : ``bma = ADD.get("BMA")[-1]``
-
- CurrentState
- *List of vectors*. Each element is a usual state vector used during the
- optimization algorithm procedure.
-
- Example : ``Xs = ADD.get("CurrentState")[:]``
-
- Innovation
- *List of vectors*. Each element is an innovation vector, which is in static
- the difference between the optimal and the background, and in dynamic the
- evolution increment.
-
- Example : ``d = ADD.get("Innovation")[-1]``
-
- OMA
- *List of vectors*. Each element is a vector of difference between the
- observation and the optimal state in the observation space.
-
- Example : ``oma = ADD.get("OMA")[-1]``
-
- OMB
- *List of vectors*. Each element is a vector of difference between the
- observation and the background state in the observation space.
+ .. include:: snippets/BMA.rst
- Example : ``omb = ADD.get("OMB")[-1]``
+ .. include:: snippets/CurrentState.rst
- SimulatedObservationAtBackground
- *List of vectors*. Each element is a vector of observation simulated from
- the background :math:`\mathbf{x}^b`.
+ .. include:: snippets/Innovation.rst
- Example : ``hxb = ADD.get("SimulatedObservationAtBackground")[-1]``
+ .. include:: snippets/OMA.rst
- SimulatedObservationAtCurrentState
- *List of vectors*. Each element is an observed vector at the current state,
- that is, in the observation space.
+ .. include:: snippets/OMB.rst
- Example : ``Ys = ADD.get("SimulatedObservationAtCurrentState")[-1]``
+ .. include:: snippets/SimulatedObservationAtBackground.rst
- SimulatedObservationAtOptimum
- *List of vectors*. Each element is a vector of observation simulated from
- the analysis or optimal state :math:`\mathbf{x}^a`.
+ .. include:: snippets/SimulatedObservationAtCurrentState.rst
- Example : ``hxa = ADD.get("SimulatedObservationAtOptimum")[-1]``
+ .. include:: snippets/SimulatedObservationAtOptimum.rst
See also
++++++++
References to other sections:
- :ref:`section_ref_algorithm_DerivativeFreeOptimization`
+ - :ref:`section_ref_algorithm_DifferentialEvolution`
Bibliographical references:
- [WikipediaPSO]_
