Multidimensional minimization by simulated annealing (GSL) More...
#include <anneal_gsl.h>
Detailed Description
template<class func_t = multi_funct, class vec_t = boost::numeric::ublas::vector<double>, class rng_t = rng_gsl>
class o2scl::anneal_gsl< func_t, vec_t, rng_t >
This class is a modification of simulated annealing as implemented in GSL in the function gsl_siman_solve(). It acts as a generic multidimensional minimizer for any function given a generic temperature schedule specified by the user.
There are a large variety of strategies for choosing the temperature evolution. To offer the user the largest possible flexibility, the temperature evolution is controlled by a the virtual functions start() and next() which can be freely changed by creating a child class which overwrites these functions.
The simulated annealing algorithm proposes a displacement of one coordinate of the previous point by
![\[ x_{i,\mathrm{new}} = \mathrm{step\_size}_i (2 u_i - 1) + x_{i,\mathrm{old}} \]](form_1.png)
where the 
are random numbers between 0 and 1. The displacement is accepted or rejected based on the Metropolis method. The random number generator is set in the parent, anneal.
The default behavior is as follows: Initially, the step sizes are chosen to be 1.0 (or whatever was recently specified in set_step() ) and the temperature to be T_start (default 1.0). Each iteration decreases the temperature by a factor of T_dec (default 1.5) for each step, and the minimizer is finished when the next decrease would bring the temperature below o2scl::mmin_base::tol_abs. If none of the mmin_base::ntrial steps in a particular iteration changes the value of the minimum, and the step sizes are greater than min_step_ratio (default 100) times o2scl::mmin_base::tol_abs, then the step sizes are decreased by a factor of step_dec (default 1.5) for the next iteration.
If o2scl::mmin_base::verbose is greater than zero, then mmin() will print out information and/or request a keypress after the function iterations for each temperature.
An example demonstrating the usage of this class is given in examples/ex_anneal.cpp and in the Simulated annealing example .
- Idea for Future:
- Implement a more general simulated annealing routine which would allow the solution of discrete problems like the Traveling Salesman problem.
Definition at line 144 of file anneal_gsl.h.
Public Types | |
| typedef boost::numeric::ublas::vector< double > | ubvector |
Public Member Functions | |
| virtual int | mmin (size_t nvar, vec_t &x0, double &fmin, func_t &func) |
Calculate the minimum fmin of func w.r.t the array x0 of size nvar. | |
| virtual const char * | type () |
| Return string denoting type ("anneal_gsl") | |
| template<class vec2_t > | |
| int | set_step (size_t nv, vec2_t &stepv) |
| Set the step sizes. | |
| anneal_gsl (const anneal_gsl< func_t, vec_t, rng_t > &ag) | |
| Copy constructor. | |
| anneal_gsl< func_t, vec_t, rng_t > & | operator= (const anneal_gsl< func_t, vec_t, rng_t > &ag) |
| Copy constructor from operator=. | |
 Public Member Functions inherited from o2scl::anneal_base< multi_funct, boost::numeric::ublas::vector< double >, rng_gsl > | |
| anneal_base (const anneal_base< multi_funct, boost::numeric::ublas::vector< double >, rng_gsl > &ab) | |
| Copy constructor. | |
| virtual int | mmin (size_t nvar, boost::numeric::ublas::vector< double > &x, double &fmin, multi_funct &func)=0 |
Calculate the minimum fmin of func w.r.t the array x of size nvar. | |
| virtual int | print_iter (size_t nv, boost::numeric::ublas::vector< double > &x, double y, int iter, double tptr, std::string comment) |
| Print out iteration information. More... | |
| anneal_base< multi_funct, boost::numeric::ublas::vector< double >, rng_gsl > & | operator= (const anneal_base< multi_funct, boost::numeric::ublas::vector< double >, rng_gsl > &ab) |
| Copy constructor from operator=. | |
| Public Member Functions inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > | |
| mmin_base (const mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > &mb) | |
| Copy constructor. | |
| int | set_verbose_stream (std::ostream &out, std::istream &in) |
| Set streams for verbose I/O. More... | |
| virtual int | mmin_de (size_t nvar, boost::numeric::ublas::vector< double > &x, double &fmin, multi_funct &func, multi_funct &dfunc) |
Calculate the minimum min of func w.r.t. the array x of size nvar with gradient dfunc. | |
| int | print_iter (size_t nv, vec2_t &x, double y, int iter, double value, double limit, std::string comment) |
| Print out iteration information. More... | |
| const char * | type () |
| Return string denoting type ("mmin_base") | |
| mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > & | operator= (const mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > &mb) |
| Copy constructor from operator=. | |
Public Attributes | |
| double | boltz |
| Boltzmann factor (default 1.0). | |
| double | T_start |
| Initial temperature (default 1.0) | |
| double | T_dec |
| Factor to decrease temperature by (default 1.5) | |
| double | step_dec |
| Factor to decrease step size by (default 1.5) | |
| double | min_step_ratio |
| Ratio between minimum step size and tol_abs (default 100.0) | |
| Public Attributes inherited from o2scl::anneal_base< multi_funct, boost::numeric::ublas::vector< double >, rng_gsl > | |
| rng_gsl | rng |
| The default random number generator. | |
| o2scl::prob_dens_uniform | dist |
| The random distribution object. | |
| Public Attributes inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > | |
| int | verbose |
| Output control. | |
| int | ntrial |
| Maximum number of iterations. | |
| double | tol_rel |
| Function value tolerance. | |
| double | tol_abs |
| The independent variable tolerance. | |
| int | last_ntrial |
| The number of iterations for in the most recent minimization. | |
| bool | err_nonconv |
| If true, call the error handler if the routine does not "converge". | |
Storage for points in parameter space | |
| double | step_norm |
| Normalization for step. | |
| ubvector | step_vec |
| Vector of step sizes. | |
| virtual int | next (size_t nvar, vec_t &x_old, double min_old, vec_t &x_new, double min_new, double &T, size_t n_moves, vec_t &best_x, double best_E, bool &finished) |
| Determine how to change the minimization for the next iteration. | |
| virtual int | start (size_t nvar, double &T) |
| Setup initial temperature and stepsize. | |
| virtual int | step (vec_t &sx, int nvar) |
| Make a step to a new attempted minimum. | |
Additional Inherited Members | |
| Protected Attributes inherited from o2scl::mmin_base< multi_funct, multi_funct, boost::numeric::ublas::vector< double > > | |
| std::ostream * | outs |
| Stream for verbose output. | |
| std::istream * | ins |
| Stream for verbose input. | |
The documentation for this class was generated from the following file:
- /home/awsteiner/wcs/o2scl/src/anneal/anneal_gsl.h