mutation_01_hill_movement

This function mutates a solution using a Gaussian or Uniform distribution. Hill Climbing movement.

x_i_new, of_i_new,\
    fit_i_new, neof = mutation_01_hill_movement(obj_function, x_i_old,
                                                    x_lower, x_upper,
                                                    n_dimensions,
                                                    pdf, cov,
                                                    none_variable=None)

Input variables

Name	Description	Type
obj_function	Objective function. The Metapy user defined this function	Py function (def)
x_i_old	Current design variables of the \(i\) agent	List
x_lower	Lower limit of the design variables	List
x_upper	Upper limit of the design variables	List
n_dimensions	Problem dimension	Integer
pdf	Probability density function used in random generator. Options: 'gaussian' or 'uniform'	String
cov	Coefficient of variation in percentage	Float
none_variable	None variable. Default is None. User can use this variable in objective function	None, list, float, dictionary, str or any

Output variables

Name	Description	Type
x_i_new	Update variables of the \(i\) agent	List
of_i_new	Update objective function value of the i agent	Float
fit_i_new	Update fitness value of the i agent	Float
neof	Number of evaluations of the objective function	Integer
report	Report about the mutation process	String

Theory

See Hill Climbing movement.

Example 1

Use the mutation_01_hill_movement function to generate a new solution from an existing solution, applying a coefficient of variation of 15% in current design variables. Use the range \(\mathbf{x}_L = [1.0, 1.0]\) and \(\mathbf{x}_L = [5.0, 5.0]\). Consider current solution \(\mathbf{x}_i = [2.0, 2.0]\). Use a uniform distribution to generate.

# Import
from metapy_toolbox import mutation_01_hill_movement # or import *

# Data
xL = [1, 1]
xU = [5, 5]
d = len(xL)
sigma = 15 # 15%
xI = [2, 2]
pdf = 'uniform'

# Objective function
def obj_function(x, _):
    """Example objective function"""
    x0 = x[0]
    x1 = x[1]
    of = x0 ** 2 + x1 ** 2
    return of

# Call function
xII, ofINew, fitINew, neof, report = mutation_01_hill_movement(obj_function, xI, xL, xU,
                                                               d, pdf, sigma)

# Output details
print('x New: ', xII)
print('of New: ', ofINew)
print('fit New: ', fitINew)
print('number of evalutions objective function: ', neof)

x New:  [2.2555966876941307, 2.1080630093627852]
of New:  9.531646068980415
fit New:  0.09495191857475814
number of evalutions objective function:  1

To check the movement report just apply the following instruction.

# Report details
arq = "report_example.txt"

# Writing report
with open(arq, "w") as file:
    file.write(report)

Open report_example.txt.

    current x = [2, 2]
    Dimension 0: mean = 2, sigma = 0.3, neighbor = 2.2555966876941307
    Dimension 1: mean = 2, sigma = 0.3, neighbor = 2.1080630093627852
    update x = [2.2555966876941307, 2.1080630093627852], of = 9.531646068980415, fit = 0.09495191857475814