simulated_annealing_01

Simulated Annealing algorithm (see theory).

df_all, df_best, delta_time, report = simulated_annealing_01(settings)

This function does not perform more than one repetition. To perform multiple repetitions, use the metaheuristic_optimizer function.

Input variables

Name	Description	Type
settings	Algorithm settings: [0] setup, [1] initial population, [2] seeds	List
settings[0] \(=\) setup	Algorithm setup	Dictionary
setup keys
'number of population'	Number of population	Integer
'number of iterations'	Number of iterations	Integer
'number of dimensions'	Problem dimension	Integer
'x pop lower limit'	Lower limit of the design variables	List
'x upper lower limit'	Upper limit of the design variables	List
'none variable'	None variable. Default is None. User can use this variable in objective function	None, list, float, dictionary, str or any
'objective function'	Objective function. The Metapy user defined this function	Py function (def)
'algorithm parameters'	Algorithm parameters	Dictionary
'algorithm parameters' keys
'mutation'	Mutation parameters	Dictionary
'temp. control'	Temperature parameters	Dictionary
settings[1] \(=\) initial population	Users can inform the initial population or use initial population functions	List or METApy function
settings[2] \(=\) seed	Random seed. Use None for random seed	None or Integer

Output variables

df_all	All data of the population	Dataframe
df_best	Best data of the population	Dataframe
delta_time	Time of the algorithm execution in seconds	Float
report	Report of the algorithm execution	String

Mutation parameters

'mutation': {
             'cov (%)': 20,
             'pdf': 'gaussian'
            }

Name	Description	Type
'cov (%)'	Coefficient of variation in percentage	Float
'pdf'	Probability density function used in random generator. Options: 'gaussian' or 'uniform'	String

Temperature parameters

'temp. control': {
                  'temperature t_0': 15,
                  'temperature update': 'geometric',
                  'alpha': 0.9
                 }

Name	Description	Type
'temperature t_0'	Initial temperature. 'auto': Automatic starts cooling temperature. For specific value, use a float number (see theory)	Float or String
'temperature update'	Cooling schema (see theory): 'geometric' 'lundy' 'linear' 'exponential'	String
'alpha'	Cooling control (see theory)	Float

Example 1

Use the Simulated Annealing optimization method to optimize the 2D sphere function. Use a total of 100 iterations to perform the optimization. Consider the limits \(\mathbf{x}_L = [-5.0, -5.0]\) and \(\mathbf{x}_U = [5.0, 5.0]\) for the problem design variables. Consider the initial guess (two agents) \(\mathbf{pop}_0 = [-0.74, 1.25]\) and \(\mathbf{pop}_1 = [3.58, -3.33]\). Use \(cov = 20\%\), Gaussian random generator, \(T_0 = 15\) and geometric schedule (\(\alpha = 0.90\)).

"""Object Function: of_file.py"""  
def my_function(x, none_variable):
    x_0 = x[0]
    x_1 = x[1]
    of = x_0 ** 2 + x_1 ** 2
    return of

"""Run optimization: your_problem.py or your_problem.ipynb"""
# import libray
# pip install metapy-toolbox or pip install --upgrade metapy-toolbox
from metapy_toolbox import simulated_annealing_01
from of_file import my_function # External .py file with your objective function

# Algorithm setup
setup = {
            'number of iterations': 100,
            'number of population': 2,
            'number of dimensions': 2,
            'x pop lower limit': [-5, -5],
            'x pop upper limit': [5, 5],
            'none variable': None,
            'objective function': my_obj_function,
            'algorithm parameters': {
                                        'mutation': {
                                                     'cov (%)': 20,
                                                     'pdf': 'gaussian'
                                                    },
                                        'temp. control': {
                                                          'temperature t_0': 15,
                                                          'temperature update': 'geometric',
                                                          'alpha': 0.9
                                                         }
                                    },
        }

# Initial guess
init_pop = [[-0.74, 1.25],
            [3.58, -3.33]]
"""
# or random initial guess (real design variables)
from metapy_toolbox import initial_population_01
init_pop = initial_population_01(setup['number of population'],
                                setup['number of dimensions'],
                                setup['x pop lower limit'],
                                setup['x pop upper limit'])
"""

# Seed
seed = None

# Call function
settings = [setup, init_pop, seed]
df_all_results, df_resume, time_cost, report = simulated_annealing_01(settings)