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SA< FunctionType, CoolingScheduleType > Class Template Reference

Simulated Annealing is an stochastic optimization algorithm which is able to deliver near-optimal results quickly without knowing the gradient of the function being optimized. More...

Public Member Functions

 SA (FunctionType &function, CoolingScheduleType &coolingSchedule, const size_t maxIterations=1000000, const double initT=10000., const size_t initMoves=1000, const size_t moveCtrlSweep=100, const double tolerance=1e-5, const size_t maxToleranceSweep=3, const double maxMoveCoef=20, const double initMoveCoef=0.3, const double gain=0.3)
 Construct the SA optimizer with the given function and parameters. More...
 
const FunctionType & Function () const
 Get the instantiated function to be optimized. More...
 
FunctionType & Function ()
 Modify the instantiated function. More...
 
double Gain () const
 Get the gain. More...
 
double & Gain ()
 Modify the gain. More...
 
size_t InitMoves () const
 Get the initial moves. More...
 
size_t & InitMoves ()
 Modify the initial moves. More...
 
size_t MaxIterations () const
 Get the maximum number of iterations. More...
 
size_t & MaxIterations ()
 Modify the maximum number of iterations. More...
 
arma::mat MaxMove () const
 Get the maximum move size of each parameter. More...
 
arma::mat & MaxMove ()
 Modify the maximum move size of each parameter. More...
 
size_t MaxToleranceSweep () const
 Get the maxToleranceSweep. More...
 
size_t & MaxToleranceSweep ()
 Modify the maxToleranceSweep. More...
 
size_t MoveCtrlSweep () const
 Get sweeps per move control. More...
 
size_t & MoveCtrlSweep ()
 Modify sweeps per move control. More...
 
arma::mat MoveSize () const
 Get move size of each parameter. More...
 
arma::mat & MoveSize ()
 Modify move size of each parameter. More...
 
double Optimize (arma::mat &iterate)
 Optimize the given function using simulated annealing. More...
 
double Temperature () const
 Get the temperature. More...
 
double & Temperature ()
 Modify the temperature. More...
 
double Tolerance () const
 Get the tolerance. More...
 
double & Tolerance ()
 Modify the tolerance. More...
 

Detailed Description

template<typename FunctionType, typename CoolingScheduleType = ExponentialSchedule>
class mlpack::optimization::SA< FunctionType, CoolingScheduleType >

Simulated Annealing is an stochastic optimization algorithm which is able to deliver near-optimal results quickly without knowing the gradient of the function being optimized.

It has unique hill climbing capability that makes it less vulnerable to local minima. This implementation uses exponential cooling schedule and feedback move control by default, but the cooling schedule can be changed via a template parameter.

The algorithm keeps the temperature at initial temperature for initMove steps to get rid of the dependency on the initial condition. After that, it cools every step until the system is considered frozen or maxIterations is reached.

At each step, SA only perturbs one parameter at a time. When SA has perturbed all parameters in a problem, a sweep has been completed. Every moveCtrlSweep sweeps, the algorithm does feedback move control to change the average move size depending on the responsiveness of each parameter. Parameter gain controls the proportion of the feedback control.

The system is considered "frozen" when its score fails to change more then tolerance for maxToleranceSweep consecutive sweeps.

For SA to work, the FunctionType parameter must implement the following two methods:

double Evaluate(const arma::mat& coordinates); arma::mat& GetInitialPoint();

and the CoolingScheduleType parameter must implement the following method:

double NextTemperature(const double currentTemperature, const double currentValue);

which returns the next temperature given current temperature and the value of the function being optimized.

Template Parameters
FunctionTypeobjective function type to be minimized.
CoolingScheduleTypetype for cooling schedule

Definition at line 65 of file sa.hpp.

Constructor & Destructor Documentation

SA ( FunctionType &  function,
CoolingScheduleType &  coolingSchedule,
const size_t  maxIterations = 1000000,
const double  initT = 10000.,
const size_t  initMoves = 1000,
const size_t  moveCtrlSweep = 100,
const double  tolerance = 1e-5,
const size_t  maxToleranceSweep = 3,
const double  maxMoveCoef = 20,
const double  initMoveCoef = 0.3,
const double  gain = 0.3 
)

Construct the SA optimizer with the given function and parameters.

Parameters
functionFunction to be minimized.
coolingScheduleInstantiated cooling schedule.
maxIterationsMaximum number of iterations allowed (0 indicates no limit).
initTInitial temperature.
initMovesNumber of initial iterations without changing temperature.
moveCtrlSweepSweeps per feedback move control.
toleranceTolerance to consider system frozen.
maxToleranceSweepMaximum sweeps below tolerance to consider system frozen.
maxMoveCoefMaximum move size.
initMoveCoefInitial move size.
gainProportional control in feedback move control.

Member Function Documentation

const FunctionType& Function ( ) const
inline

Get the instantiated function to be optimized.

Definition at line 107 of file sa.hpp.

FunctionType& Function ( )
inline

Modify the instantiated function.

Definition at line 109 of file sa.hpp.

double Gain ( ) const
inline

Get the gain.

Definition at line 137 of file sa.hpp.

double& Gain ( )
inline

Modify the gain.

Definition at line 139 of file sa.hpp.

size_t InitMoves ( ) const
inline

Get the initial moves.

Definition at line 117 of file sa.hpp.

size_t& InitMoves ( )
inline

Modify the initial moves.

Definition at line 119 of file sa.hpp.

size_t MaxIterations ( ) const
inline

Get the maximum number of iterations.

Definition at line 142 of file sa.hpp.

size_t& MaxIterations ( )
inline

Modify the maximum number of iterations.

Definition at line 144 of file sa.hpp.

arma::mat MaxMove ( ) const
inline

Get the maximum move size of each parameter.

Definition at line 147 of file sa.hpp.

arma::mat& MaxMove ( )
inline

Modify the maximum move size of each parameter.

Definition at line 149 of file sa.hpp.

size_t MaxToleranceSweep ( ) const
inline

Get the maxToleranceSweep.

Definition at line 132 of file sa.hpp.

size_t& MaxToleranceSweep ( )
inline

Modify the maxToleranceSweep.

Definition at line 134 of file sa.hpp.

size_t MoveCtrlSweep ( ) const
inline

Get sweeps per move control.

Definition at line 122 of file sa.hpp.

size_t& MoveCtrlSweep ( )
inline

Modify sweeps per move control.

Definition at line 124 of file sa.hpp.

arma::mat MoveSize ( ) const
inline

Get move size of each parameter.

Definition at line 152 of file sa.hpp.

arma::mat& MoveSize ( )
inline

Modify move size of each parameter.

Definition at line 154 of file sa.hpp.

double Optimize ( arma::mat &  iterate)

Optimize the given function using simulated annealing.

The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned.

Parameters
iterateStarting point (will be modified).
Returns
Objective value of the final point.
double Temperature ( ) const
inline

Get the temperature.

Definition at line 112 of file sa.hpp.

double& Temperature ( )
inline

Modify the temperature.

Definition at line 114 of file sa.hpp.

double Tolerance ( ) const
inline

Get the tolerance.

Definition at line 127 of file sa.hpp.

double& Tolerance ( )
inline

Modify the tolerance.

Definition at line 129 of file sa.hpp.


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