Artificial Bee Colony solver
Project description
BeeColPy
BeeColPy is a module for function optimization through artificial bee colony algorithm, a method developed by Karaboga [1], a variant of classical particle swarm optimization.
Websites:
Source code: https://github.com/renard162/BeeColPy/
Introduction: https://en.wikipedia.org/wiki/Artificial_bee_colony_algorithm
Installation
Dependencies
BeeColPy requires:
- Python (>= 3.0)
- NumPy (>= 1.1.0)
BeeColPy do not support Python 2.7.
User installation
pip install beecolpy
Usage Instructions
For cost functions with continuous domain:
#Step-by-step:
#Create object and set the solver parameters:
abc_obj = abc(function, boundaries, colony_size=40, scouts=0.5,
iterations=50, min_max='min', nan_protection=True)
#Execute algorithm:
abc_obj.fit()
#Get solution obtained after fit() execution:
solution = abc_obj.get_solution()
"""
Obs.: Each time fit() was executed, the algorithm iterate 'iterations' times
resuming from last fit() execution.
"""
"""
Parameters
----------
function : Name
A name of a function to minimize/maximize.
Example: if the function is:
def my_func(x): return x[0]**2 + x[1]**2 + 5*x[1]
Put "my_func" as parameter.
boundaries : List of Tuples
A list of tuples containing the lower and upper boundaries of each
dimension of function domain.
Obs.: The number of boundaries determines the dimension of function.
Example: [(-5,5), (-20,20)]
[colony_size] : Int --optional-- (default: 40)
A value that determines the number of bees in algorithm. Half of this
amount determines the number of points analyzed (food sources).
According articles, half of this number determines the amount of
Employed bees and other half is Onlooker bees.
[scouts] : Float --optional-- (default: 0.5)
Determines the limit of tries for scout bee discard a food source and
replace for a new one.
- If scouts = 0 : Scout_limit = colony_size * dimension
- If scouts = (0 to 1) : Scout_limit = colony_size * dimension * scouts
Obs.: scout = 0.5 is used in [3] as benchmark.
- If scout = (1 to iterations) : Scout_limit = scout
- If scout >= iterations: Scout event never occurs
Obs.: Scout_limit is rounded down in all cases.
[iterations] : Int --optional-- (default: 50)
The number of iterations executed by algorithm.
[min_max] : String --optional-- (default: 'min')
Determines if algorithm will minimize or maximize the function.
- If min_max = 'min' : Try to localize the minimum of function.
- If min_max = 'max' : Try to localize the maximum of function.
[nan_protection] : Boolean --optional-- (default: True)
If true, re-generate food sources that get NaN value as cost during
initialization or during scout events. This option usually helps the
algorithm stability because, in rare cases, NaN values can lock the
algorithm in a infinite loop.
Obs.: NaN protection can drastically increases calculation time if
analysed function has too many values of domain returning NaN.
Methods
----------
fit()
Execute the algorithm with defined parameters.
Obs.: Returns a list with values found as minimum/maximum coordinate.
get_solution()
Returns the value obtained after fit() the method.
Obs.: If fit() is not executed, return the position of
best initial condition.
get_status()
Returns a tuple with:
- Number of complete iterations executed
- Number of scout events during iterations
- Number of times that NaN protection was activated
get_agents()
Returns a list with the position of each food source during
each iteration.
"""
For cost function with binary domain:
#Step-by-step:
#Create object and set the solver parameters:
bin_abc_obj = bin_abc(function, bits_count, method='am',
colony_size=40, scouts=0.5, iterations=50,
best_model_iterations=0,
min_max='min', nan_protection=True,
transfer_function='sigmoid',
best_model_iterations=0)
#Execute algorithm:
bin_abc_obj.fit()
#Get solution after execute fit() without execute it again:
solution = bin_abc_obj.get_solution()
"""
Obs.: Each time fit() was executed, the algorithm iterate 'iterations' times
resuming from last fit() execution.
"""
"""
Parameters
----------
function : Name
A name of a function to minimize/maximize.
Example: if the function is:
def my_func(x): return x[0] or (x[1] and x[2])
Put "my_func" as parameter.
-=x=-
bits_count : Int
The number of bits that compose the output vector.
boundaries : List of Tuples
A list of tuples containing the lower and upper boundaries that will be
applied over sigmoid function to determine the probability to bit become 1.
Example: [(-5,5), (-20,20)]
Obs.: - If boundaries are set, then it's take the priority over the bits_count.
- If boundaries are not set, then the boundaries became (-2,2) to each bit
in AMABC method or (-10,10) to each bit in BABC method.
-=x=-
[method] : String --optional-- (default: 'am')
Select the apllied solver:
- If method = 'am' : Applied Angle Modulated ABC (AMABC).
- If method = 'bin' : Applied Angle Modulated ABC (BABC).
[colony_size] : Int --optional-- (default: 40)
A value that determines the number of bees in algorithm. Half of this
amount determines the number of points analyzed (food sources).
According articles, half of this number determines the amount of
Employed bees and other half is Onlooker bees.
[scouts] : Float --optional-- (default: 0.5)
Determines the limit of tries for scout bee discard a food source and
replace for a new one.
- If scouts = 0 : Scout_limit = colony_size * dimension
- If scouts = (0 to 1) : Scout_limit = colony_size * dimension * scouts
Obs.: scout = 0.5 is used in [3] as benchmark.
- If scout = (1 to iterations) : Scout_limit = scout
- If scout >= iterations: Scout event never occurs
Obs.1: Scout_limit is rounded down in all cases.
Obs.2: In Binary form, the scouts tends to be more relevant than in
continuous form. If your problem are badly solved, try to reduce
the scouts value.
[iterations] : Int --optional-- (default: 50)
The number of iterations executed by algorithm.
[min_max] : String --optional-- (default: 'min')
Determines if algorithm will minimize or maximize the function.
- If min_max = 'min' : Try to localize the minimum of function.
- If min_max = 'max' : Try to localize the maximum of function.
[nan_protection] : Boolean or Int --optional-- (default (boolean): True)
With "method='am'", this variable are used as a boolean.
With "method='bin'", this variable determines the number of times the
function are recalculated when it returns a NaN. (default (int): 3)
If true or greater than 0, re-generate food sources that get NaN value
as cost during initialization or during scout events. This option
usually helps the algorithm stability because, in rare cases, NaN
values can lock the algorithm in a infinite loop.
Obs.: NaN protection can drastically increases calculation time if
analysed function has too many values of domain returning NaN.
[transfer_function] : String --optional-- (default: 'sigmoid')
Only used with "method='bin'". Defines the transfer function used to
calculate the probability for each bit becomes '1'.
The possibilities are explained on article [6]:
- If transfer_function = 'sigmoid' : S(x) = 1/[1 + exp(-x)]
- If transfer_function = 'sigmoid-2x' : S(x) = 1/[1 + exp(-2*x)]
- If transfer_function = 'sigmoid-x/2' : S(x) = 1/[1 + exp(-x/2)]
- If transfer_function = 'sigmoid-x/3' : S(x) = 1/[1 + exp(-x/3)]
[best_model_iterations] : int --optional-- (default: iterations count)
Only used with "method='bin'". Due stochastic aspect of Binary form of
particle based metaheuristic, after execution of ABC, the cost function
will be calculated "best_model_iterations" times and the "best" result
will be returned.
- If best_model_iterations = 0 : Tries "iterations" times. (default)
- If best_model_iterations = N : Tries "N" times.
Methods
----------
fit()
Execute the algorithm with defined parameters.
Obs.: Returns a list with values found as minimum/maximum coordinate.
get_solution()
Returns the value obtained after fit() the method.
Obs.: If fit() is not executed, return "None"
get_status()
Returns a tuple with:
- Number of complete iterations executed
- Number of scout events during iterations
- Number of times that NaN protection was activated
get_agents()
Returns a list with the position of each food source during
each iteration.
Obs.: In binary form, this method returns the position of each food source after
transformation "binary -> continuous". I.e. returns the values applied on angle
modulation function in AMABC or the values applied on transfer function in BABC.
"""
Example
"""
To find the minimum of sphere function on interval (-10 to 10) with
2 dimensions in domain using default options:
"""
from beecolpy import abc
def sphere(x):
total = 0
for i in range(len(x)):
total += x[i]**2
return total
abc_obj = abc(sphere, [(-10,10), (-10,10)]) #Load data
abc_obj.fit() #Execute the algorithm
#If you want to get the obtained solution after execute the fit() method:
solution = abc_obj.get_solution()
#If you want to get the number of iterations executed, number of times that
#scout event occur and number of times that NaN protection actuated:
iterations = abc_obj.get_status()[0]
scout = abc_obj.get_status()[1]
nan_events = abc_obj.get_status()[2]
#If you want to get a list with position of all points (food sources) used in each iteration:
food_sources = abc_obj.get_agents()
Author
Samuel Carlos Pessoa Oliveira - samuelcpoliveira@gmail.com
License
This project is licensed under the MIT License - see the LICENSE.md file for details.
Bibliography
[1] Karaboga, D. and Basturk, B., 2007 A powerful and efficient algorithm for numerical function optimization: artificial bee colony ABC) algorithm. Journal of global optimization, 39(3), pp.459-471. Doi: https://doi.org/10.1007/s10898-007-9149-x
[2] Liu, T., Zhang, L. and Zhang, J., 2013 Study of binary artificial bee colony algorithm based on particle swarm optimization. Journal of Computational Information Systems, 9(16), pp.6459-6466. Link: https://api.semanticscholar.org/CorpusID:8789571
[3] Anuar, S., Selamat, A. and Sallehuddin, R., 2016 A modified scout bee for artificial bee colony algorithm and its performance on optimization problems. Journal of King Saud University-Computer and Information Sciences, 28(4), pp. 95-406. Doi: https://doi.org/10.1016/j.jksuci.2016.03.001
[4] Kennedy, J. and Eberhart, R.C., 1997, October. A discrete binary version of the particle swarm algorithm. In 1997 IEEE International conference on systems, man, and cybernetics. Computational cybernetics and simulation (Vol. 5, pp. 4104-4108). IEEE. Doi: https://doi.org/10.1109/ICSMC.1997.637339
[5] Pampará, G. and Engelbrecht, A.P., 2011, April. Binary artificial bee colony optimization. In 2011 IEEE Symposium on Swarm Intelligence (pp. 1-8). IEEE. Doi: https://doi.org/10.1109/SIS.2011.5952562
[6] Mirjalili, S., Hashim, S., Taherzadeh, G., Mirjalili, S.Z. and Salehi, S., 2011. A study of different transfer functions for binary version of particle swarm optimization. In International Conference on Genetic and Evolutionary Methods (Vol. 1, No. 1, pp. 2-7). Link: http://hdl.handle.net/10072/48831
[7] Huang, S.C., 2015. Polygonal approximation using an artificial bee colony algorithm. Mathematical Problems in Engineering, 2015. Doi: https://doi.org/10.1155/2015/375926
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