ITK
6.0.0
Insight Toolkit
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#include <itkInitializationBiasedParticleSwarmOptimizer.h>
Implementation of a biased/regularized Particle Swarm Optimization (PSO) algorithm.
This PSO algorithm was originally described in: M. P. Wachowiak, R. Smolikova, Y. Zheng, J. M. Zurada, A. S. Elmaghraby, "An approach to multimodal biomedical image registration utilizing particle swarm optimization", IEEE Transactions on Evolutionary Computing, vol. 8(3): 289-301, 2004.
The algorithm uses a stochastic optimization approach. Optimization is performed by maintaining a swarm (flock) of particles that traverse the parameter space, searching for the optimal function value. Associated with each particle are its location and speed, in parameter space. A particle's next location is determined by its current location, its current speed, the location of the best function value it previously encountered, the location of the best function value the particles in its neighborhood previously encountered and the initial position the user specified.
The assumption is that the user's initial parameter settings are close to the minimum, which is often the case for registration. The initial parameter values are incorporated into the PSO's update rules, biasing the search in their direction. The swarms update equations are thus:
\(v_i(t+1) = wv_i(t) + c_1u_1(p_i-x_i(t)) + c_2u_2(p_g-x_i(t)) + c_3u_3(x_{init} - x_i(t))\) \(x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\)
where \(u_i\) are \(~U(0,1)\) and \(w,c_1,c_2, c_3\) are user selected weights, and c_3 is linearly decreased per iteration so that it is in \(c_3=initial, 0\).
Swarm initialization is performed within the user supplied parameter bounds using a uniform distribution or a normal distribution centered on the initial parameter values supplied by the user, \(x_{init}\). The search terminates when the maximal number of iterations has been reached or when the change in the best value in the past \(g\) generations is below a threshold and the swarm has collapsed (i.e. particles are close to each other in parameter space).
Definition at line 73 of file itkInitializationBiasedParticleSwarmOptimizer.h.
Static Public Member Functions | |
static Pointer | New () |
Static Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer | |
static Pointer | New () |
Static Public Member Functions inherited from itk::NonLinearOptimizer | |
static Pointer | New () |
Static Public Member Functions inherited from itk::Optimizer | |
static Pointer | New () |
Static Public Member Functions inherited from itk::Object | |
static bool | GetGlobalWarningDisplay () |
static void | GlobalWarningDisplayOff () |
static void | GlobalWarningDisplayOn () |
static Pointer | New () |
static void | SetGlobalWarningDisplay (bool val) |
Static Public Member Functions inherited from itk::LightObject | |
static void | BreakOnError () |
static Pointer | New () |
Protected Member Functions | |
InitializationBiasedParticleSwarmOptimizer () | |
void | PrintSelf (std::ostream &os, Indent indent) const override |
void | UpdateSwarm () override |
~InitializationBiasedParticleSwarmOptimizer () override=default | |
Protected Member Functions inherited from itk::ParticleSwarmOptimizerBase | |
void | FileInitialization () |
virtual void | Initialize () |
ParticleSwarmOptimizerBase () | |
void | PrintParamtersType (const ParametersType &x, std::ostream &os) const |
void | PrintSelf (std::ostream &os, Indent indent) const override |
void | RandomInitialization () |
virtual void | UpdateSwarm ()=0 |
virtual void | ValidateSettings () |
~ParticleSwarmOptimizerBase () override | |
Protected Member Functions inherited from itk::SingleValuedNonLinearOptimizer | |
void | PrintSelf (std::ostream &os, Indent indent) const override |
SingleValuedNonLinearOptimizer () | |
~SingleValuedNonLinearOptimizer () override=default | |
Protected Member Functions inherited from itk::NonLinearOptimizer | |
NonLinearOptimizer ()=default | |
~NonLinearOptimizer () override | |
Protected Member Functions inherited from itk::Optimizer | |
Optimizer () | |
void | PrintSelf (std::ostream &os, Indent indent) const override |
virtual void | SetCurrentPosition (const ParametersType ¶m) |
~Optimizer () override=default | |
Protected Member Functions inherited from itk::Object | |
Object () | |
bool | PrintObservers (std::ostream &os, Indent indent) const |
void | PrintSelf (std::ostream &os, Indent indent) const override |
virtual void | SetTimeStamp (const TimeStamp &timeStamp) |
~Object () override | |
Protected Member Functions inherited from itk::LightObject | |
virtual LightObject::Pointer | InternalClone () const |
LightObject () | |
virtual void | PrintHeader (std::ostream &os, Indent indent) const |
virtual void | PrintSelf (std::ostream &os, Indent indent) const |
virtual void | PrintTrailer (std::ostream &os, Indent indent) const |
virtual | ~LightObject () |
Definition at line 84 of file itkInitializationBiasedParticleSwarmOptimizer.h.
Definition at line 82 of file itkInitializationBiasedParticleSwarmOptimizer.h.
Definition at line 81 of file itkInitializationBiasedParticleSwarmOptimizer.h.
using itk::InitializationBiasedParticleSwarmOptimizer::Self = InitializationBiasedParticleSwarmOptimizer |
Standard "Self" type alias.
Definition at line 79 of file itkInitializationBiasedParticleSwarmOptimizer.h.
Definition at line 80 of file itkInitializationBiasedParticleSwarmOptimizer.h.
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The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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overridevirtual |
Reimplemented from itk::Object.
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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Method for creation through the object factory.
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overrideprotectedvirtual |
Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.
Reimplemented from itk::Object.
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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virtual |
The Particle swarm optimizer uses the following update formula:
\[c_3 = c_{3initial}(1.0 - IterationIndex/MaximalNumberOfIterations)\]
\[v_i(t+1) = w*v_i(t) + c_1*uniform(0,1)*(p_i-x_i(t)) + c_2*uniform(0,1)*(p_g-x_i(t)) + c_3*uniform(0,1)*(x_{init}-x_i(t))\]
\[x_i(t+1) = clampToBounds(x_i(t) + v_i(t+1))\]
where \(w\) - inertia constant \(c_1\) - personal coefficient \(c_2\) - global coefficient \(c_3\) - initial location coefficient \(p_i\) - parameters yielding the best function value obtained by this particle \(p_g\) - parameters yielding the best function value obtained by all particles \(x_{init}\) - initial parameter values provided by user
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Implement your update rule in this function.
Implements itk::ParticleSwarmOptimizerBase.
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Definition at line 129 of file itkInitializationBiasedParticleSwarmOptimizer.h.
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Definition at line 127 of file itkInitializationBiasedParticleSwarmOptimizer.h.
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private |
Definition at line 130 of file itkInitializationBiasedParticleSwarmOptimizer.h.
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private |
Definition at line 128 of file itkInitializationBiasedParticleSwarmOptimizer.h.