def pikaia (ff, n, ff_extra_args = (), \
individuals = 100, \
generations = 500, \
digits = 6, \
crossover = 0.85, \
mutation = 2, \
initrate = 0.005, \
minrate = 0.0005, \
maxrate = 0.25, \
fitnessdiff = 1.0, \
reproduction = 3, \
elitism = 0, \
verbosity = 0):
"""
Pikaia version 1.2 - genetic algorithm based optimizer.
Wrapped with f2py by Marek Wojciechowski
<*****@*****.**>
Original fortran code: Paul Charbonneau & Barry Knapp
<*****@*****.**>
<*****@*****.**>
Simplest usage:
from pikaia import pikaia
x = pikaia(ff, n)
Function ff is a user-supplied scalar function of n vari-
ables, which must have the calling sequence f = ff(x, [n], [args]),
where x is a real parameter array of length n and [args] are
optional parameters. This function must
be written so as to bound all parameters to the interval [0,1];
that is, the user must determine a priori bounds for the para-
meter space, and ff must use these bounds to perform the appro-
priate scalings to recover true parameter values in the
a priori ranges.
By convention, ff should return higher values for more optimal
parameter values (i.e., individuals which are more "fit").
For example, in fitting a function through data points, ff
could return the inverse of chi**2.
Additional ff parameters [args] can be passed to pikaia routine
via keyword argument ff_extra_args which have to be a tuple
of variables.
Returning array x is the "fittest" (optimal) solution found,
i.e., the solution which maximizes fitness function ff.
Algorithm control parameters are set via keyword arguments:
individuals - number of individuals in a population (default
is 100)
generations - number of generations over which solution is
to evolve (default is 500)
digits - number of significant digits (i.e., number of
genes) retained in chromosomal encoding (default
is 6) (Note: This number is limited by the
machine floating point precision. Most 32-bit
floating point representations have only 6 full
digits of precision. To achieve greater preci-
sion this routine could be converted to double
precision, but note that this would also require
a double precision random number generator, which
likely would not have more than 9 digits of
precision if it used 4-byte integers internally.)
crossover - crossover probability; must be <= 1.0 (default
is 0.85). If crossover takes place, either one
or two splicing points are used, with equal
probabilities
mutation - 1/2/3/4/5 (default is 2)
1=one-point mutation, fixed rate
2=one-point, adjustable rate based on fitness
3=one-point, adjustable rate based on distance
4=one-point+creep, fixed rate
5=one-point+creep, adjustable rate based on fitness
6=one-point+creep, adjustable rate based on distance
initrate - initial mutation rate; should be small (default
is 0.005) (Note: the mutation rate is the proba-
bility that any one gene locus will mutate in
any one generation.)
minrate - minimum mutation rate; must be >= 0.0 (default
is 0.0005)
maxrate - maximum mutation rate; must be <= 1.0 (default
is 0.25)
fitnessdiff - relative fitness differential; range from 0
(none) to 1 (maximum). (default is 1.)
reproduction - reproduction plan; 1/2/3=Full generational
replacement/Steady-state-replace-random/Steady-
state-replace-worst (default is 3)
elitism - elitism flag; 0/1=off/on (default is 0)
(Applies only to reproduction plans 1 and 2)
verbosity - printed output 0/1/2=None/Minimal/Verbose
(default is 0)
Thus more complex usage:
x = pikaia( ff, n, ff_extra_args = (1, 0.5), \
individuals = 200, \
generations = 50, \
verbosity = 1 )
"""
# Initialize pikaia random number generator
from random import randint
_pikaia.rninit(randint(1, 999999999))
del randint
# Restore control array
ctrl = [ individuals, generations, digits, crossover, mutation, initrate, \
minrate, maxrate, fitnessdiff, reproduction, elitism, verbosity ]
# Optimize
x, f, status = _pikaia.pikaia(ff, n, ctrl, ff_extra_args)
return x
def pikaia (ff, n, ff_extra_args = (), \
individuals = 100, \
generations = 500, \
digits = 6, \
crossover = 0.85, \
mutation = 2, \
initrate = 0.005, \
minrate = 0.0005, \
maxrate = 0.25, \
fitnessdiff = 1.0, \
reproduction = 3, \
elitism = 0, \
verbosity = 0):
"""
Pikaia version 1.2 - genetic algorithm based optimizer.
Simplest usage::
from pikaia import pikaia
x = pikaia(ff, n)
:Parameters:
ff : callable
Scalar function of the signature ff(x, [n, args]),
where *x* is a real array of length *n* and *args*
are extra parameters. Pikaia optimizer assumes *x*
elements are bounded to the interval (0, 1), thus
*ff* have to aware of this, ie. probably you need
some internal scaling inside *ff*.
By convention, ff should return higher values for more
optimal parameter values (i.e., individuals which are
more "fit"). For example, in fitting a function
through data points, *ff* could return the inverse of
chi**2.
n : int
Length of *x*. Note that you do not need
starting point.
ff_extra_args: tuple
Extra arguments passed to *ff*.
individuals : int
Number of individuals in a population (default is 100)
generations : int
Number of generations over which solution is
to evolve (default is 500)
digits : int
Number of significant digits (i.e., number of
genes) retained in chromosomal encoding (default
is 6). (Note: This number is limited by the
machine floating point precision. Most 32-bit
floating point representations have only 6 full
digits of precision. To achieve greater precision
this routine could be converted to double
precision, but note that this would also require
a double precision random number generator, which
likely would not have more than 9 digits of
precision if it used 4-byte integers internally.)
crossover : float
Crossover probability; must be <= 1.0 (default
is 0.85). If crossover takes place, either one
or two splicing points are used, with equal
probabilities.
mutation : {1, 2, 3, 4, 5, 6}
===== =====================================================
digit description
===== =====================================================
1 one-point mutation, fixed rate
2 one-point, adjustable rate based on fitness (default)
3 one-point, adjustable rate based on distance
4 one-point+creep, fixed rate
5 one-point+creep, adjustable rate based on fitness
6 one-point+creep, adjustable rate based on distance
===== =====================================================
initrate : float
Initial mutation rate. Should be small (default
is 0.005) (Note: the mutation rate is the probability
that any one gene locus will mutate in any one generation.)
minrate : float
Minimum mutation rate. Must be >= 0.0 (default is 0.0005)
maxrate : float
Maximum mutation rate. Must be <= 1.0 (default is 0.25)
fitnessdiff : float
Relative fitness differential. Range from 0 (none)
to 1 (maximum) (default is 1).
reproduction : {1, 2, 3}
Reproduction plan; 1/2/3 = Full generationalreplacement/Steady-
state-replace-random/Steady-state-replace-worst (default is 3)
elitism : {0, 1}
Elitism flag; 0/1=off/on (default is 0)
(Applies only to reproduction plans 1 and 2)
verbosity : {0, 1, 2}
Printed output 0/1/2=None/Minimal/Verbose (default is 0)
:Returns:
x : array (float32)
The 'fittest' (optimal) solution found, i.e., the solution
which maximizes fitness function *ff*.
:Examples:
>>> from pikaia import pikaia
>>> def ff(x): return -sum(x**2)
>>> pikaia(ff, 4, individuals=50, generations=200)
array([ 1.23000005e-04, 7.69999970e-05, 2.99999992e-05,
2.80000004e-05], dtype=float32)
.. note::
Original fortran code of pikaia is written by:
Paul Charbonneau & Barry Knapp ([email protected],
[email protected])
Wrapped with f2py by Marek Wojciechowski ([email protected])
"""
# Initialize pikaia random number generator
from random import randint
_pikaia.rninit(randint(1, 999999999))
del randint
# Restore control array
ctrl = [ individuals, generations, digits, crossover, mutation, initrate, \
minrate, maxrate, fitnessdiff, reproduction, elitism, verbosity ]
# Optimize
x, f, status = _pikaia.pikaia(ff, n, ctrl, ff_extra_args)
return x
def pikaia (ff, n, ff_extra_args = (), \
individuals = 100, \
generations = 500, \
digits = 6, \
crossover = 0.85, \
mutation = 2, \
initrate = 0.005, \
minrate = 0.0005, \
maxrate = 0.25, \
fitnessdiff = 1.0, \
reproduction = 3, \
elitism = 0, \
verbosity = 0):
"""
Pikaia version 1.2 - genetic algorithm based optimizer.
Simplest usage::
from pikaia import pikaia
x = pikaia(ff, n)
:Parameters:
ff : callable
Scalar function of the signature ff(x, [n, args]),
where *x* is a real array of length *n* and *args*
are extra parameters. Pikaia optimizer assumes *x*
elements are bounded to the interval (0, 1), thus
*ff* have to aware of this, ie. probably you need
some internal scaling inside *ff*.
By convention, ff should return higher values for more
optimal parameter values (i.e., individuals which are
more "fit"). For example, in fitting a function
through data points, *ff* could return the inverse of
chi**2.
n : int
Length of *x*. Note that you do not need
starting point.
ff_extra_args: tuple
Extra arguments passed to *ff*.
individuals : int
Number of individuals in a population (default is 100)
generations : int
Number of generations over which solution is
to evolve (default is 500)
digits : int
Number of significant digits (i.e., number of
genes) retained in chromosomal encoding (default
is 6). (Note: This number is limited by the
machine floating point precision. Most 32-bit
floating point representations have only 6 full
digits of precision. To achieve greater precision
this routine could be converted to double
precision, but note that this would also require
a double precision random number generator, which
likely would not have more than 9 digits of
precision if it used 4-byte integers internally.)
crossover : float
Crossover probability; must be <= 1.0 (default
is 0.85). If crossover takes place, either one
or two splicing points are used, with equal
probabilities.
mutation : {1, 2, 3, 4, 5, 6}
===== =====================================================
digit description
===== =====================================================
1 one-point mutation, fixed rate
2 one-point, adjustable rate based on fitness (default)
3 one-point, adjustable rate based on distance
4 one-point+creep, fixed rate
5 one-point+creep, adjustable rate based on fitness
6 one-point+creep, adjustable rate based on distance
===== =====================================================
initrate : float
Initial mutation rate. Should be small (default
is 0.005) (Note: the mutation rate is the probability
that any one gene locus will mutate in any one generation.)
minrate : float
Minimum mutation rate. Must be >= 0.0 (default is 0.0005)
maxrate : float
Maximum mutation rate. Must be <= 1.0 (default is 0.25)
fitnessdiff : float
Relative fitness differential. Range from 0 (none)
to 1 (maximum) (default is 1).
reproduction : {1, 2, 3}
Reproduction plan; 1/2/3 = Full generationalreplacement/Steady-
state-replace-random/Steady-state-replace-worst (default is 3)
elitism : {0, 1}
Elitism flag; 0/1=off/on (default is 0)
(Applies only to reproduction plans 1 and 2)
verbosity : {0, 1, 2, 3}
Printed output 0/1/2,3=None/Minimal/Verbose + monitoring files:
verbosity >= 2:
pikaia_ind_{best,mean,worst}.txt
* generation
* individual vector (decoded, e.g. the float values in
[0,1])
pikaia_fit.txt
* generation
* fitness best
* fitness mean
* fitness worst
* pmut (mutation rate)
* nnew (number of newly created individuals)
verbosity == 3:
pikaia_ind_all.txt
* generation
* individual vector 1, individual vector 2, ...
-> all individuals in one line (number of
columns = number of
dimensions * number of individuals)
(See examples/pikaia.py for how to use this file.)
(default is 0)
:Returns:
x : array (float32)
The 'fittest' (optimal) solution found, i.e., the solution
which maximizes fitness function *ff*.
:Examples:
>>> from pikaia import pikaia
>>> def ff(x): return -sum(x**2)
>>> pikaia(ff, 4, individuals=50, generations=200)
array([ 1.23000005e-04, 7.69999970e-05, 2.99999992e-05,
2.80000004e-05], dtype=float32)
.. note::
Original fortran code of pikaia is written by:
Paul Charbonneau & Barry Knapp ([email protected],
[email protected])
Wrapped with f2py by Marek Wojciechowski ([email protected])
"""
# Initialize pikaia random number generator
from random import randint
_pikaia.rninit(randint(1, 999999999))
del randint
# Restore control array
ctrl = [ individuals, generations, digits, crossover, mutation, initrate, \
minrate, maxrate, fitnessdiff, reproduction, elitism, verbosity ]
# Optimize
x, f, status = _pikaia.pikaia(ff, n, ctrl, ff_extra_args)
return x