SimTK::Optimizer Class Reference

API for SimTK Simmath's optimizers. More...

Classes
class	OptimizerRep

Public Member Functions
	Optimizer ()
	Optimizer (const OptimizerSystem &sys)
	Optimizer (const OptimizerSystem &sys, OptimizerAlgorithm algorithm)
	~Optimizer ()
void	setConvergenceTolerance (Real accuracy)
	Sets the relative accuracy used determine if the problem has converged. More...
void	setConstraintTolerance (Real tolerance)
	Sets the absolute tolerance used to determine whether constraint violation is acceptable. More...
void	setMaxIterations (int iter)
	Set the maximum number of iterations allowed of the optimization method's outer stepping loop. More...
void	setLimitedMemoryHistory (int history)
	Set the maximum number of previous hessians used in a limited memory hessian approximation. More...
void	setDiagnosticsLevel (int level)
	Set the level of debugging info displayed. More...
void	setOptimizerSystem (const OptimizerSystem &sys)
void	setOptimizerSystem (const OptimizerSystem &sys, OptimizerAlgorithm algorithm)
bool	setAdvancedStrOption (const char *option, const char *value)
	Set the value of an advanced option specified by a string. More...
bool	setAdvancedRealOption (const char *option, const Real value)
	Set the value of an advanced option specified by a real value. More...
bool	setAdvancedIntOption (const char *option, const int value)
	Set the value of an advanced option specified by an integer value. More...
bool	setAdvancedBoolOption (const char *option, const bool value)
	Set the value of an advanced option specified by an boolean value. More...
bool	setAdvancedVectorOption (const char *option, const Vector value)
	Set the value of an advanced option specified by an Vector value. More...
void	setDifferentiatorMethod (Differentiator::Method method)
	Set which numerical differentiation algorithm is to be used for the next useNumericalGradient() or useNumericalJacobian() call. More...
Differentiator::Method	getDifferentiatorMethod () const
	Return the differentiation method last supplied in a call to setDifferentiatorMethod(), not necessarily the method currently in use. More...
OptimizerAlgorithm	getAlgorithm () const
	Return the algorithm used for the optimization. More...
void	useNumericalGradient (bool flag, Real estimatedAccuracyOfObjective=SignificantReal)
	Enable numerical calculation of gradient, with optional estimation of the accuracy to which the objective function is calculated. More...
void	useNumericalJacobian (bool flag, Real estimatedAccuracyOfConstraints=SignificantReal)
	Enable numerical calculation of the constraint Jacobian, with optional estimation of the accuracy to which the constraint functions are calculated. More...
Real	optimize (Vector &)
	Compute optimization. More...
const OptimizerSystem &	getOptimizerSystem () const
	Return a reference to the OptimizerSystem currently associated with this Optimizer. More...
bool	isUsingNumericalGradient () const
	Indicate whether the Optimizer is currently set to use a numerical gradient. More...
bool	isUsingNumericalJacobian () const
	Indicate whether the Optimizer is currently set to use a numerical Jacobian. More...
Real	getEstimatedAccuracyOfObjective () const
	Return the estimated accuracy last specified in useNumericalGradient(). More...
Real	getEstimatedAccuracyOfConstraints () const
	Return the estimated accuracy last specified in useNumericalJacobian(). More...

Static Public Member Functions
static bool	isAlgorithmAvailable (OptimizerAlgorithm algorithm)
	BestAvailable, UnknownAlgorithm, and UserSuppliedAlgorithm are treated as never available. More...

Friends
class	OptimizerRep

Detailed Description

API for SimTK Simmath's optimizers.

An optimizer finds a minimum to an objective function. Usually, this minimum is a local minimum. Some algorithms, like CMAES, are designed to find the global minumum. The optimizer can be constrained to search for a minimum within a feasible region. The feasible region is defined in two ways: via limits on the parameters of the objective function; and, for algorithms other than CMAES, by supplying constraint functions that must be satisfied. The optimizer starts searching for a minimum beginning at a user supplied initial value for the set of parameters.

The objective function and constraints are specified by supplying the Optimizer with a concrete implemenation of an OptimizerSystem class. The OptimizerSystem can be passed to the Optimizer either through the Optimizer constructor or by calling the Optimizer::setOptimizerSystem method. The Optimizer class will select the best optimization algorithm to solve the problem based on the constraints supplied by the OptimizerSystem. A user can also override the optimization algorithm selected by the Optimizer by specifying the optimization algorithm.

Optimization algorithms and advanced options

See OptimizerAlgorithm for a brief description of the available algorithms. Most of these algorithms have options that are specific to the algorithm. These options are set via methods like Optimizer::setAdvancedStrOption. If you want to get going quickly, you can just use the default values of these options and ignore this section. As an example, an int option popsize would be set via:

opt.setAdvancedIntOption("popsize", 5);

For now, we only have detailed documentation for the CMAES algorithm.

CMAES

This is the c-cmaes algorithm written by Niko Hansen (https://github.com/cma-es/c-cmaes).

Some notes:

• This algorithm obeys parameter limits.
• This is a derivative-free optimization algorithm, so methods like the following have no effect:
  • Optimizer::useNumericalGradient
  • Optimizer::setDifferentiatorMethod
  • Optimizer::setLimitedMemoryHistory
  • OptimizerSystem::gradientFunc
  • OptimizerSystem::hessian
• This algorithm does not obey constraint functions, so methods like the following have no effect:
  • Optimizer::setConstraintTolerance
  • Optimizer::useNumericalJacobian
  • OptimizerSystem::constraintFunc
  • OptimizerSystem::constraintJacobian
  • OptimizerSystem::setNumEqualityConstraints
  • OptimizerSystem::setNumInequalityConstraints
  • OptimizerSystem::setNumLinearEqualityConstraints
  • OptimizerSystem::setNumLinearInequalityConstraints
• The effect of the diagnostics level is as follows:
  • 0: minimal output to console (warnings, errors), some files are written to the current directory (errcmaes.err error log).
  • 1: additional output to console.
  • 2: all files are written to the current directory.
  • 3: output to console, and all files are written to the current directory.

Encoding of Variables

Inappropriate initialization of the algorithm may lead to resampling of the parameter distribution. Since some parameters may be defined in a bounded region [a, b]. The CMA algorithm involves sampling a random distribution for the variables (parameters) in the optimization problem. If the sampled values do not lie within the variables' bounds, CMA must resample the distribution until the variables lie within the bounds. This resampling is undesirable, and may prevent the algorithm from functioning properly. There are two ways to avoid excessive resampling:To overcome this the problem the user can formulate the problem as follows:

1) Either define the bounds of the parameter and choose the appropriate stddev and initial value for each parameter (see init_stepsize) 2) Or to reformulate the problem, by rescaling the parameter space so that each parameter map in a region between e.g. [0, 1] and each parameter has an initial value of 0.5 and stddev of 0.2 (see comments below).

The specific formulation of a (real) optimization problem has a tremendous impact on the optimization performance. In particular, a reasonable parameter encoding is essential. All parameters should be rescaled such that they have presumably similar sensitivity (this makes the identity as initial covariance matrix the right choice). Usually, the best approach is to write a wrapper around the objective function that transforms the parameters before the actual function call. The wrapper scales, for example, in each parameter/coordinate the value [0; 10] into the typical actual domain of the parameter/coordinate.

The natural encoding of (some of) the parameters can also be "logarithmic". That is, for a parameter that must always be positive, with a ratio between typical upper and lower value being larger than 100, we might use 10x instead of x to call the objective function. More specifically, to achieve the parameter range [10^–4,10^–1], we use 10^–4×10^3x/10 with x in [0; 10]. Again, the idea is to have similar sensitivity: this makes sense if we expect the change from 10^–4 to 10^–3 to have an impact similar to the change from 10^–2 to 10^–1. In order to avoid the problem that changes of very small values have too less an impact, an alternative is to choose 10^–1 × (x/10)2 >= 0. In the case where only a lower bound at zero is necessary, a simple and natural transformation is x2 × default_x, such that x=1 represents the default (or initial) value and x remains unbounded during optimization.

In summary, to map the values [0;10] into [a;b] we have the alternative transformations a + (b-a) × x/10 or a + (b-a) × (x/10)2 >= a or a × (b/a)x/10 >= 0.

For more details see: https://www.lri.fr/~hansen/cmaes_inmatlab.html

Advanced options:

The default values for options whose name begins with "stop" are specified at https://github.com/CMA-ES/c-cmaes/blob/master/cmaes_initials.par

• popsize (int; default: depends on number of parameters) The population size (also known as lambda).

• init_stepsize (Vector/Real; default: 0.3) Initial stddev; After the encoding of variables, the initial solution point x0 and the initial standard deviation (step_size) sigma0 must be chosen. In a practical application, one often wants to start by trying to improve a given solution locally. In this case we choose a rather small sigma0 (say in [0.001, 0.1], given the x-values "live" in [0,10]). Thereby we can also check whether the initial solution is possibly a local optimum. When a global optimum is sought-after on rugged or multimodal landscapes, sigma0 should be chosen such that the final desirable location (or at least some of its domain of attraction) is not far outside of x0 ± 2sigma0 in each coordinate. (Remark that in Rn, if each boundary domain is in distance sigma, then the boundary corner is sigma*sqrt(n) away, which poses a slight dilemma for larger n.)

  A warning is emitted if this is not set and default value is used for each variable.

  Example setting the init_stepsize:

  Vector initStepSize(N, 0.3); opt.setAdvancedVectorOption("init_stepsize", initStepSize); "or" opt.setAdvancedRealOption("init_stepsize", 0.3);

• seed (int; default: 0, which uses clock time) Seed for the random number generator that is used to sample the population from a normal distribution. See note below.
• maxTimeFractionForEigendecomposition (real; default: 0.2) Controls the amount of time spent generating eigensystem decompositions.
• stopMaxFunEvals (int) Stop optimization after this number of evaluations of the objective function.
• stopFitness (real) Stop if function value is smaller than stopFitness.
• stopTolFunHist (real) Stop if function value differences of best values are smaller than stopTolFunHist.
• stopTolX (real) Stop if step sizes are smaller than stopTolX.
• stopTolUpXFactor (real) Stop if standard deviation increases by more than stopTolUpXFactor.
• parallel (str) To run the optimization with multiple threads, set this to "multithreading". Only use this if your OptimizerSystem is threadsafe: you can't reliably modify any mutable variables in your OptimizerSystem::objectiveFun().
• nthreads (int) If the parallel option is set to "multithreading", this is the number of threads to use (by default, this is the number of processors/threads on the machine).

If you want to generate identical results with repeated optimizations, you can set the seed option. In addition, you must set the maxTimeFractionForEigendecomposition option to be greater than or equal to 1.0.

opt.setAdvancedIntOption("seed", 42);
opt.setAdvancedRealOption("maxTimeFractionForEigendecomposition", 1);

Constructor & Destructor Documentation

Optimizer() [1/3]

SimTK::Optimizer::Optimizer

(

)

Optimizer() [2/3]

SimTK::Optimizer::Optimizer

(

const OptimizerSystem &

sys

)

Optimizer() [3/3]

SimTK::Optimizer::Optimizer	(	const OptimizerSystem &	sys,
		OptimizerAlgorithm	algorithm
	)

~Optimizer()

SimTK::Optimizer::~Optimizer

(

)

Member Function Documentation

isAlgorithmAvailable()

static bool SimTK::Optimizer::isAlgorithmAvailable ( OptimizerAlgorithm  algorithm )

static

BestAvailable, UnknownAlgorithm, and UserSuppliedAlgorithm are treated as never available.

setConvergenceTolerance()

void SimTK::Optimizer::setConvergenceTolerance

(

Real

accuracy

)

Sets the relative accuracy used determine if the problem has converged.

setConstraintTolerance()

void SimTK::Optimizer::setConstraintTolerance

(

Real

tolerance

)

Sets the absolute tolerance used to determine whether constraint violation is acceptable.

setMaxIterations()

void SimTK::Optimizer::setMaxIterations

(

int

iter

)

Set the maximum number of iterations allowed of the optimization method's outer stepping loop.

Most optimizers also have an inner loop ("line search") which is also iterative but is not affected by this setting. Inner loop convergence is typically prescribed by theory, and failure there is often an indication of an ill-formed problem.

setLimitedMemoryHistory()

void SimTK::Optimizer::setLimitedMemoryHistory

(

int

history

)

Set the maximum number of previous hessians used in a limited memory hessian approximation.

setDiagnosticsLevel()

void SimTK::Optimizer::setDiagnosticsLevel

(

int

level

)

Set the level of debugging info displayed.

setOptimizerSystem() [1/2]

void SimTK::Optimizer::setOptimizerSystem

(

const OptimizerSystem &

sys

)

setOptimizerSystem() [2/2]

void SimTK::Optimizer::setOptimizerSystem	(	const OptimizerSystem &	sys,
		OptimizerAlgorithm	algorithm
	)

setAdvancedStrOption()

bool SimTK::Optimizer::setAdvancedStrOption	(	const char *	option,
		const char *	value
	)

Set the value of an advanced option specified by a string.

setAdvancedRealOption()

bool SimTK::Optimizer::setAdvancedRealOption	(	const char *	option,
		const Real	value
	)

Set the value of an advanced option specified by a real value.

setAdvancedIntOption()

bool SimTK::Optimizer::setAdvancedIntOption	(	const char *	option,
		const int	value
	)

Set the value of an advanced option specified by an integer value.

setAdvancedBoolOption()

bool SimTK::Optimizer::setAdvancedBoolOption	(	const char *	option,
		const bool	value
	)

Set the value of an advanced option specified by an boolean value.

setAdvancedVectorOption()

bool SimTK::Optimizer::setAdvancedVectorOption	(	const char *	option,
		const Vector	value
	)

Set the value of an advanced option specified by an Vector value.

setDifferentiatorMethod()

void SimTK::Optimizer::setDifferentiatorMethod

(

Differentiator::Method

method

)

Set which numerical differentiation algorithm is to be used for the next useNumericalGradient() or useNumericalJacobian() call.

Choices are Differentiator::ForwardDifference (first order) or Differentiator::CentralDifference (second order) with central the default.

Warning

This has no effect if you have already called useNumericalGradient() or useNumericalJacobian(). Those must be called after setDifferentiatorMethod().

See also

SimTK::Differentiator

getDifferentiatorMethod()

Differentiator::Method SimTK::Optimizer::getDifferentiatorMethod

(

)

const

Return the differentiation method last supplied in a call to setDifferentiatorMethod(), not necessarily the method currently in use.

See setDifferentiatorMethod() for more information.

See also

SimTK::Differentiator

getAlgorithm()

OptimizerAlgorithm SimTK::Optimizer::getAlgorithm

(

)

const

Return the algorithm used for the optimization.

You may be interested in this value if you didn't specify an algorithm, or specified for Simbody to choose the BestAvailable algorithm. This method won't return BestAvailable, even if it's the 'algorithm' that you chose.

useNumericalGradient()

void SimTK::Optimizer::useNumericalGradient	(	bool	flag,
		Real	estimatedAccuracyOfObjective = SignificantReal
	)

Enable numerical calculation of gradient, with optional estimation of the accuracy to which the objective function is calculated.

For example, if you are calculate about 6 significant digits, supply the estimated accuracy as 1e-6. Providing the estimated accuracy improves the quality of the calculated derivative. If no accuracy is provided we'll assume the objective is calculated to near machine precision. The method used for calculating the derivative will be whatever was previously supplied in a call to setDifferentiatorMethod(), or the default which is to use central differencing (two function evaluations per gradient entry). See SimTK::Differentiator for more information.

See also

setDifferentiatorMethod(), SimTK::Differentiator

useNumericalJacobian()

void SimTK::Optimizer::useNumericalJacobian	(	bool	flag,
		Real	estimatedAccuracyOfConstraints = SignificantReal
	)

Enable numerical calculation of the constraint Jacobian, with optional estimation of the accuracy to which the constraint functions are calculated.

For example, if you are calculating about 6 significant digits, supply the estimated accuracy as 1e-6. Providing the estimated accuracy improves the quality of the calculated derivative. If no accuracy is provided we'll assume the constraints are calculated to near machine precision. The method used for calculating the derivative will be whatever was previously supplied in a call to setDifferentiatorMethod(), or the default which is to use central differencing (two function evaluations per Jacobian column. See SimTK::Differentiator for more information.

See also

setDifferentiatorMethod(), SimTK::Differentiator

optimize()

Real SimTK::Optimizer::optimize

(

Vector &

)

Compute optimization.

getOptimizerSystem()

const OptimizerSystem& SimTK::Optimizer::getOptimizerSystem

(

)

const

Return a reference to the OptimizerSystem currently associated with this Optimizer.

isUsingNumericalGradient()

bool SimTK::Optimizer::isUsingNumericalGradient

(

)

const

Indicate whether the Optimizer is currently set to use a numerical gradient.

isUsingNumericalJacobian()

bool SimTK::Optimizer::isUsingNumericalJacobian

(

)

const

Indicate whether the Optimizer is currently set to use a numerical Jacobian.

getEstimatedAccuracyOfObjective()

Real SimTK::Optimizer::getEstimatedAccuracyOfObjective

(

)

const

Return the estimated accuracy last specified in useNumericalGradient().

getEstimatedAccuracyOfConstraints()

Real SimTK::Optimizer::getEstimatedAccuracyOfConstraints

(

)

const

Return the estimated accuracy last specified in useNumericalJacobian().

Friends And Related Function Documentation

OptimizerRep

friend class OptimizerRep

friend

---

The documentation for this class was generated from the following file:

• Optimizer.h