PyPI package containing opposition learning operators and population initializers for evolutionary algorithms
Project description
Opposition learning operators and population initializers
Documentation: https://pasaopasen.github.io/opp-op-pop-init/
OPPosition learning OPerators and POPulation INITializers (from DPEA) is the python package containing opposition learning operators and population initializers for evolutionary algorithms.
- Opposition learning operators and population initializers
Installation
pip install OppOpPopInit
or
pip3 install OppOpPopInit
About opposition operators
In several evolutionary algorithms it can be useful to create the opposite of some part of current population to explore searching space better. Usually it uses at the begging of searching process (with first population initialization) and every few generations with decreasing probability F
. Also it's better to create oppositions of worse objects from populations. See this article for more information.
This package provides several operators for creating oppositions (opposition operators) and methods for creating start population using different distribution functions and opposition operators for each dimension!
Imports
What can u import from this package:
from OppOpPopInit import OppositionOperators # available opposition operators as static class
from OppOpPopInit import SampleInitializers # available population initializers as static class
# main function which creates random population
# using initializers and oppositors
from OppOpPopInit import init_population
Also there is a little module for plotting pictures like u can see below
import OppOpPopInit.plotting
Interface agreements
Borders
In the entire part of math optimization tasks the best skin of possible solutions is using 1D-vectors (x1, x2, ..., xn)
of variables where each variables x
can be from some area [xmin, xmax]
. geneticalgorithm2 package and this package are both geared towards this case.
So, many functions here takes arguments minimums
and maximums
which mean the lower and the upper bounds (borders) of available areas by each using dimension. minimums
and maximums
should be sequences of integer or real numbers or only one number, but they cannot be numbers both and they must have equal length if they are sequence both.
Format of creators and oppositors
Creators are functions which create random samples (depended on bounds). In code a creator can be any object who can be called like function with signature () -> np.ndarray
(Callable[[], np.ndarray]
).
Oppositors are functions which take np.ndarray
samples and return it's opposed form as np.ndarray
. So in code an oppositor if the object can be called like (np.ndarray) -> np.ndarray
(Callable[[np.ndarray], np.ndarray]
).
Available opposition operators
Checklist
*OppositionOperators.Continual.abs
*OppositionOperators.Continual.modular
*OppositionOperators.Continual.quasi
*OppositionOperators.Continual.quasi_reflect
*OppositionOperators.Continual.over
*OppositionOperators.Continual.Partial
-- for using several opposition operators for each subset of searching area.
*OppositionOperators.Discrete.integers_by_order
-- it's like abs
operator but for integer values
*OppositionOperators.CombinedOppositor
-- for using existing opposition operators for each dimension with continual or mixed task. See examplebelow
U can create your own oppositor using pattern:
def oppositor(sample: np.ndarray) -> np.ndarray:
# some code
return new_sample
There are also OppositionOperators.Discrete._index_by_order
and OppositionOperators.Discrete.value_by_order
constructors for very special discrete tasks with available sets of valid values (like [-1, 0, 1, 5, 15]
), but it's highly recommended to convert this task to indexes array task (and use OppositionOperators.Discrete.integers_by_order
) like below:
# available values
vals = np.array([1, 90. -45, 3, 0.7, 3.4, 12])
valid_array_example = np.array([1, 1, 1, 3, -45])
# function
def optimized_func(arr: np.ndarray) -> float:
#some code
return result
# recommented way for optimization algorithm
indexes = np.arange(vals.size)
def new_optimized_functio(new_arr):
arr = np.array([vals[i] for i in new_arr])
return optimized_func(arr)
# and forth u are using indexes format for your population
print(
new_optimized_functio(
np.array([0, 0, 1, 4])
)
)
Examples
abs
oppositor
modular
oppositor
quasi
oppositor
quasi_reflect
oppositor
over
oppositor
integers_by_order
oppositor
More examples
Partial/Combined oppositor
If u want to use some oppositor to one dimenstion subset (e. g. indexes 0, 1, 3) and other oppositors for other subsets (e. g. indexes 2, 4, 5) -- u need to create Partial
or Combined
oppositors. The difference between them is that u need existing oppositors to make combined oppositor with them and u need oppositor makers to make partial oppositor. So, Partial
oppositor is often easier to use but Combined
is more flexible.
To create Combined
oppositor use code like:
oppositor = OppositionOperators.CombinedOppositor(
[
(sequece of indexes to apply, oppositor_for_this_dimentions),
(sequece of indexes to apply, oppositor_for_this_dimentions),
...
(sequece of indexes to apply, oppositor_for_this_dimentions)
]
)
To create Partial
oppositor use code:
oppositor = OppositionOperators.PartialOppositor(
minimums=minimumns,
maximums=maximums,
indexes_to_opp_creator=[
(sequece of indexes to apply, oppositor_creator),
(sequece of indexes to apply, oppositor_creator)
]
)
Example:
import numpy as np
from OppOpPopInit import OppositionOperators
# 5 dim population
min_bound = np.array([-8, -3, -5.7, 0, 0])
max_bound = np.array([5, 4, 4, 9, 9])
# population points
points = np.array([
[1, 2, 3, 4, 7.5],
[1.6, -2, 3.9, 0.4, 5],
[1.1, 3.2, -3, 4, 5],
[4.1, 2, 3, -4, 0.5]
])
# saved indexes for oppositors
first_op_indexes = np.array([0, 2])
second_op_indexes = np.array([1, 3])
oppositor = OppositionOperators.CombinedOppositor(
[
(first_op_indexes, OppositionOperators.Continual.abs(
minimums=min_bound[first_op_indexes],
maximums=max_bound[first_op_indexes],
)),
(second_op_indexes, OppositionOperators.Continual.over(
minimums=min_bound[second_op_indexes],
maximums=max_bound[second_op_indexes],
))
]
)
# or
oppositor = OppositionOperators.PartialOppositor(
minimums=min_bound,
maximums=max_bound,
indexes_to_opp_creator=[
(first_op_indexes, OppositionOperators.Continual.abs),
(second_op_indexes, OppositionOperators.Continual.over)
]
)
# as u see, it's not necessary to oppose population by all dimensions, here we won't oppose by last dimension
oppositions = OppositionOperators.Reflect(points, oppositor)
print(oppositions)
# array([[-4. , 1.84589799, -4.7 , 5.04795851, 7.5 ],
# [-4.6 , -0.74399971, -5.6 , 7.49178902, 5. ],
# [-4.1 , 0.54619162, 1.3 , 6.14214043, 5. ],
# [-7.1 , -2.59648698, -4.7 , 0.95770904, 0.5 ]])
RandomPartialOppositor
One of the most amazing feature of this package is RandomPartialOppositor
. It lets u apply several oppositors to random subsets of dimension area and change these subsets after some counts after applying. It means that u can apply only one this oppositor to several samples and get result like u applyed several partial oppositors to parts of this samples.
Create RandomPartialOppositor
oppositor using this structure:
oppositor = OppositionOperators.RandomPartialOppositor(
[
(count_of_random_dimensions, repeate_config_during_steps, avalable_indexes, oppositor_creator),
(count_of_random_dimensions, repeate_config_during_steps, avalable_indexes, oppositor_creator),
...
(count_of_random_dimensions, repeate_config_during_steps, avalable_indexes, oppositor_creator)
],
minimums,
maximums
)
Reflect method
Use OppositionOperators.Reflect(samples, oppositor)
for oppose samples array using some oppositor. samples
argument here is 2D-array with size samples*dimension.
Reflection with selection best
There is OppositionOperators.ReflectWithSelectionBest(population_samples, oppositor, eval_func, samples_scores = None, more_is_better = False)
method for reflect population (with size N
) and select best N
objects from existing 2N
objects. It has parameters:
population_samples
: 2D numpy array; reflected population.oppositor
: function; applying oppositor.eval_func
: function; optimized function of population/task.samples_scores
:None
/1D numpy array, optional; scores for reflected population (if calculated -- it's not necessary to calculate it again). The default isNone
.more_is_better
: logical, optional; The goal -- is maximize the function. The default isFalse
.
See example
Population initializers
Simple random populations
Like oppositors operators
there are some constructors for creating creators of start population:
SampleInitializers.RandomInteger(minimums, maximums)
-- returns function which will return random integer vectors betweenminimums
andmaximums
SampleInitializers.Uniform(minimums, maximums)
-- returns function which will return random vectors betweenminimums
andmaximums
from uniform distributionSampleInitializers.Normal(minimums, maximums, sd = None)
-- returns function which will return random vectors betweenminimums
andmaximums
from normal distribution
U can create your initializer function:
def func() -> np.ndarray:
# code
return valid_sample_array
There is also SampleInitializers.Combined(minimums, maximums, indexes, creator_initializers)
for generate population with different constructors for each dimension subset!
Use creator
for initialize population with k
objects using SampleInitializers.CreateSamples(creator, k)
.
RandomInteger
Uniform
Normal
Mixed
Populations with oppositions
Use init_population(total_count, creator, oppositors = None)
to create population of size total_count
where some objects are constructed by creator
and other objects are constructed by applying each oppositor from oppositors
to start objects.
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