Multidimensional minimization by the differential evolution method. More...
#include <diff_evo.h>
This class minimizes a function using differential evolution. This method is a genetic algorithm and as such works well for non continuous problems, since it does not rely on a gradient of the function that is being mind.
The method starts by initializing a random population of candidate parameters. To do this the user needs to define a function to create these random parameters, which can be provided using set_init_function().
After the initial population is created the algorithm will repeat a number of standard steps until a solution is found or the maximum number of iterations is reached. Based on Storn97.
If the population converges prematurely, then diff_evo::f and pop_size should be increased.
Definition at line 66 of file diff_evo.h.
Public Types | |
typedef boost::numeric::ublas::vector< double > | ubvector |
Public Member Functions | |
virtual void | set_init_function (init_funct_t &function) |
Set the function that is used to produce random init variables. More... | |
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 x of size nvar . More... | |
virtual void | print_iter (size_t nvar, double fmin, int iter, vec_t &best_fit) |
Print out iteration information. More... | |
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mmin_base (const mmin_base< func_t, func_t, vec_t > &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, vec_t &x, double &fmin, func_t &func, func_t &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< func_t, func_t, vec_t > & | operator= (const mmin_base< func_t, func_t, vec_t > &mb) |
Copy constructor from operator=. | |
Public Attributes | |
size_t | pop_size |
Population size (default 0) More... | |
size_t | nconv |
The number of generations without a better fit before we assume that the algorithm has converged (default 25) | |
double | f |
Differential weight (default 0.75) More... | |
double | cr |
Crossover probability (default 0.8) More... | |
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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". | |
Protected Member Functions | |
virtual int | initialize_population (size_t nvar, vec_t &x0) |
Initialize a population of random agents. | |
virtual std::vector< int > | pick_unique_agents (int nr, size_t x) |
Pick number of unique agent id's. More... | |
Protected Attributes | |
vec_t | population |
Vector containing the population. More... | |
ubvector | fmins |
Vector that keeps track of fmins values. | |
init_funct_t * | rand_init_funct |
Function that is used to produce random init variables. More... | |
rng_gsl | gr |
Random number generator. | |
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std::ostream * | outs |
Stream for verbose output. | |
std::istream * | ins |
Stream for verbose input. | |
Private Member Functions | |
diff_evo (const diff_evo< func_t, vec_t, init_funct_t > &) | |
diff_evo< func_t, vec_t, init_funct_t > & | operator= (const diff_evo< func_t, vec_t, init_funct_t > &) |
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inlinevirtual |
Initialize all agents x with random positions in the search-space. Until a termination criterion is met (e.g. number of iterations performed, or adequate fitness reached), repeat the following: For each agent x in the population do: Pick three agents a, b, and c from the population at random, they must be distinct from each other as well as from agent x Pick a random index {1, ..., n}, where the highest possible value n is the dimensionality of the problem to be optimized. Compute the agent's potentially new position y = [y1, ..., yn] by iterating over each i {1, ..., n} as follows: Pick ri~U(0,1) uniformly from the open range (0,1) If (i=R) or (ri<CR) let yi = ai + F(bi - ci), otherwise let yi = xi If (f(y) < f(x)) then replace the agent in the population with the improved candidate solution, that is, set x = y in the population.
Pick the agent from the population that has the lowest fmin and return it as the best found candidate solution.
Implements o2scl::mmin_base< func_t, func_t, vec_t >.
Reimplemented in o2scl::diff_evo_adapt< func_t, vec_t, init_funct_t >.
Definition at line 151 of file diff_evo.h.
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inlineprotectedvirtual |
Unique from x and each other
Uses the Fisher-Yates algorithm.
Definition at line 343 of file diff_evo.h.
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inlinevirtual |
Reimplemented in o2scl::diff_evo_adapt< func_t, vec_t, init_funct_t >.
Definition at line 275 of file diff_evo.h.
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inlinevirtual |
REQUIRED
The init function is called in the beginning to fill the population with random individuals, so it is best to make this cover the part of the parameter space you are interested in. The method will find solutions outside this parameter space, but choosing a good init function will help finding solutions faster.
Definition at line 125 of file diff_evo.h.
double o2scl::diff_evo< func_t, vec_t, init_funct_t >::cr |
Usually between 0 and 1.
Definition at line 99 of file diff_evo.h.
double o2scl::diff_evo< func_t, vec_t, init_funct_t >::f |
A parameter which controls the amplification of the differential variation. Usually between 0 and 2.
Definition at line 93 of file diff_evo.h.
size_t o2scl::diff_evo< func_t, vec_t, init_funct_t >::pop_size |
Should be at least 4. Typically between and
where
is the dimensionality of the problem.
If this is 0 (the default), then it is set by mmin to be equal to .
Definition at line 81 of file diff_evo.h.
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protected |
For now using one long vector with all agents after each other
Definition at line 302 of file diff_evo.h.
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protected |
This function is used to fill the population with random agents
Definition at line 311 of file diff_evo.h.
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