#!/usr/bin/env python
# Created by "Thieu" at 16:44, 18/03/2020 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from copy import deepcopy
from mealpy.optimizer import Optimizer
[docs]class OriginalAEO(Optimizer):
"""
The original version of: Artificial Ecosystem-based Optimization (AEO)
Links:
1. https://doi.org/10.1007/s00521-019-04452-x
2. https://www.mathworks.com/matlabcentral/fileexchange/72685-artificial-ecosystem-based-optimization-aeo
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.system_based.AEO import OriginalAEO
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> model = OriginalAEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Zhao, W., Wang, L. and Zhang, Z., 2020. Artificial ecosystem-based optimization: a novel
nature-inspired meta-heuristic algorithm. Neural Computing and Applications, 32(13), pp.9383-9425.
"""
def __init__(self, problem, epoch=10000, pop_size=100, **kwargs):
"""
Args:
problem (dict): The problem dictionary
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = 2 * pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Production - Update the worst agent
# Eq. 2, 3, 1
a = (1.0 - epoch / self.epoch) * np.random.uniform()
x1 = (1 - a) * self.pop[-1][self.ID_POS] + a * np.random.uniform(self.problem.lb, self.problem.ub)
pos_new = self.amend_position(x1)
fit_new = self.get_fitness_position(pos_new)
self.pop[-1] = [pos_new, fit_new]
## Consumption - Update the whole population left
pop_new = []
for idx in range(0, self.pop_size - 1):
rand = np.random.random()
# Eq. 4, 5, 6
v1 = np.random.normal(0, 1)
v2 = np.random.normal(0, 1)
c = 0.5 * v1 / abs(v2) # Consumption factor
if idx == 0:
j = 1
else:
j = np.random.randint(0, idx)
### Herbivore
if rand < 1.0 / 3:
x_t1 = self.pop[idx][self.ID_POS] + c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) # Eq. 6
### Carnivore
elif 1.0 / 3 <= rand and rand <= 2.0 / 3:
x_t1 = self.pop[idx][self.ID_POS] + c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]) # Eq. 7
### Omnivore
else:
r2 = np.random.uniform()
x_t1 = self.pop[idx][self.ID_POS] + c * (r2 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS])
+ (1 - r2) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
pos_new = self.amend_position(x_t1)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new.append(deepcopy(self.pop[-1]))
pop_new = self.greedy_selection_population(self.pop, pop_new)
## find current best used in decomposition
_, best = self.get_global_best_solution(pop_new)
## Decomposition
### Eq. 10, 11, 12, 9
pop_child = []
for idx in range(0, self.pop_size):
r3 = np.random.uniform()
d = 3 * np.random.normal(0, 1)
e = r3 * np.random.randint(1, 3) - 1
h = 2 * r3 - 1
x_t1 = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * pop_new[idx][self.ID_POS])
pos_new = self.amend_position(x_t1)
pop_child.append([pos_new, None])
pop_child = self.update_fitness_population(pop_child)
self.pop = self.greedy_selection_population(pop_new, pop_child)
[docs]class IAEO(OriginalAEO):
"""
The original version of: Improved Artificial Ecosystem-based Optimization (IAEO)
Links:
1. https://doi.org/10.1016/j.ijhydene.2020.06.256
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.system_based.AEO import IAEO
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> model = IAEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Rizk-Allah, R.M. and El-Fergany, A.A., 2021. Artificial ecosystem optimizer
for parameters identification of proton exchange membrane fuel cells model.
International Journal of Hydrogen Energy, 46(75), pp.37612-37627.
"""
def __init__(self, problem, epoch=10000, pop_size=100, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(problem, epoch, pop_size, **kwargs)
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Production - Update the worst agent
# Eq. 2, 3, 1
a = (1.0 - epoch / self.epoch) * np.random.uniform()
x1 = (1 - a) * self.pop[-1][self.ID_POS] + a * np.random.uniform(self.problem.lb, self.problem.ub)
pos_new = self.amend_position(x1)
fit_new = self.get_fitness_position(pos_new)
self.pop[-1] = [pos_new, fit_new]
## Consumption - Update the whole population left
pop_new = []
for idx in range(0, self.pop_size - 1):
rand = np.random.random()
# Eq. 4, 5, 6
v1 = np.random.normal(0, 1)
v2 = np.random.normal(0, 1)
c = 0.5 * v1 / abs(v2) # Consumption factor
if idx == 0:
j = 1
else:
j = np.random.randint(0, idx)
### Herbivore
if rand < 1.0 / 3:
x_t1 = self.pop[idx][self.ID_POS] + c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) # Eq. 6
### Carnivore
elif 1.0 / 3 <= rand and rand <= 2.0 / 3:
x_t1 = self.pop[idx][self.ID_POS] + c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]) # Eq. 7
### Omnivore
else:
r2 = np.random.uniform()
x_t1 = self.pop[idx][self.ID_POS] + c * (r2 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS])
+ (1 - r2) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
pos_new = self.amend_position(x_t1)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new.append(deepcopy(self.pop[-1]))
pop_new = self.greedy_selection_population(self.pop, pop_new)
## find current best used in decomposition
_, best = self.get_global_best_solution(pop_new)
## Decomposition
### Eq. 10, 11, 12, 9
pop_child = []
for idx in range(0, self.pop_size):
r3 = np.random.uniform()
d = 3 * np.random.normal(0, 1)
e = r3 * np.random.randint(1, 3) - 1
h = 2 * r3 - 1
x_new = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * pop_new[idx][self.ID_POS])
if np.random.random() < 0.5:
beta = 1 - (1 - 0) * ((epoch + 1) / self.epoch) # Eq. 21
x_r = pop_new[np.random.randint(0, self.pop_size - 1)][self.ID_POS]
if np.random.random() < 0.5:
x_new = beta * x_r + (1 - beta) * pop_new[idx][self.ID_POS]
else:
x_new = beta * pop_new[idx][self.ID_POS] + (1 - beta) * x_r
else:
best[self.ID_POS] = best[self.ID_POS] + np.random.normal() * best[self.ID_POS]
pos_new = self.amend_position(x_new)
pop_child.append([pos_new, None])
pop_child = self.update_fitness_population(pop_child)
self.pop = self.greedy_selection_population(pop_new, pop_child)
[docs]class EnhancedAEO(Optimizer):
"""
The original version of: Enhanced Artificial Ecosystem-Based Optimization (EAEO)
Links:
1. https://doi.org/10.1109/ACCESS.2020.3027654
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.system_based.AEO import EnhancedAEO
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> model = EnhancedAEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Eid, A., Kamel, S., Korashy, A. and Khurshaid, T., 2020. An enhanced artificial ecosystem-based
optimization for optimal allocation of multiple distributed generations. IEEE Access, 8, pp.178493-178513.
"""
def __init__(self, problem, epoch=10000, pop_size=100, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = 2 * pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Production - Update the worst agent
# Eq. 13
a = 2 * (1 - (epoch + 1) / self.epoch)
x1 = (1 - a) * self.pop[-1][self.ID_POS] + a * np.random.uniform(self.problem.lb, self.problem.ub)
pos_new = self.amend_position(x1)
fit_new = self.get_fitness_position(pos_new)
self.pop[-1] = [pos_new, fit_new]
## Consumption - Update the whole population left
pop_new = []
for idx in range(0, self.pop_size - 1):
rand = np.random.random()
# Eq. 4, 5, 6
v1 = np.random.normal(0, 1)
v2 = np.random.normal(0, 1)
c = 0.5 * v1 / abs(v2) # Consumption factor
r3 = 2 * np.pi * np.random.random()
r4 = np.random.random()
if idx == 0:
j = 1
else:
j = np.random.randint(0, idx)
### Herbivore
if rand <= 1.0 / 3: # Eq. 15
if r4 <= 0.5:
x_t1 = self.pop[idx][self.ID_POS] + np.sin(r3) * c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS])
else:
x_t1 = self.pop[idx][self.ID_POS] + np.cos(r3) * c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS])
### Carnivore
elif 1.0 / 3 <= rand and rand <= 2.0 / 3: # Eq. 16
if r4 <= 0.5:
x_t1 = self.pop[idx][self.ID_POS] + np.sin(r3) * c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS])
else:
x_t1 = self.pop[idx][self.ID_POS] + np.cos(r3) * c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS])
### Omnivore
else: # Eq. 17
r5 = np.random.random()
if r4 <= 0.5:
x_t1 = self.pop[idx][self.ID_POS] + np.sin(r5) * c * (r5 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) +
(1 - r5) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
else:
x_t1 = self.pop[idx][self.ID_POS] + np.cos(r5) * c * (r5 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) +
(1 - r5) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
pos_new = self.amend_position(x_t1)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new.append(deepcopy(self.pop[-1]))
pop_new = self.greedy_selection_population(self.pop, pop_new)
## find current best used in decomposition
_, best = self.get_global_best_solution(pop_new)
## Decomposition
### Eq. 10, 11, 12, 9
pop_child = []
for idx in range(0, self.pop_size):
r3 = np.random.uniform()
d = 3 * np.random.normal(0, 1)
e = r3 * np.random.randint(1, 3) - 1
h = 2 * r3 - 1
# x_new = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * agent_i[self.ID_POS])
if np.random.random() < 0.5:
beta = 1 - (1 - 0) * ((epoch + 1) / self.epoch) # Eq. 21
r_idx = np.random.choice(list(set(range(0, self.pop_size)) - {idx}))
x_r = pop_new[r_idx][self.ID_POS]
# x_r = pop[np.random.randint(0, self.pop_size-1)][self.ID_POS]
if np.random.random() < 0.5:
x_new = beta * x_r + (1 - beta) * pop_new[idx][self.ID_POS]
else:
x_new = (1 - beta) * x_r + beta * pop_new[idx][self.ID_POS]
else:
x_new = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * pop_new[idx][self.ID_POS])
# x_new = best[self.ID_POS] + np.random.normal() * best[self.ID_POS]
pos_new = self.amend_position(x_new)
pop_child.append([pos_new, None])
pop_child = self.update_fitness_population(pop_child)
self.pop = self.greedy_selection_population(pop_new, pop_child)
[docs]class ModifiedAEO(Optimizer):
"""
The original version of: Modified Artificial Ecosystem-Based Optimization (MAEO)
Links:
1. https://doi.org/10.1109/ACCESS.2020.2973351
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.system_based.AEO import ModifiedAEO
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> model = ModifiedAEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Menesy, A.S., Sultan, H.M., Korashy, A., Banakhr, F.A., Ashmawy, M.G. and Kamel, S., 2020. Effective
parameter extraction of different polymer electrolyte membrane fuel cell stack models using a
modified artificial ecosystem optimization algorithm. IEEE Access, 8, pp.31892-31909.
"""
def __init__(self, problem, epoch=10000, pop_size=100, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = 2 * pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Production
# Eq. 22
H = 2 * (1 - (epoch + 1) / self.epoch)
a = (1 - (epoch + 1) / self.epoch) * np.random.random()
x1 = (1 - a) * self.pop[-1][self.ID_POS] + a * np.random.uniform(self.problem.lb, self.problem.ub)
pos_new = self.amend_position(x1)
fit_new = self.get_fitness_position(pos_new)
self.pop[-1] = [pos_new, fit_new]
## Consumption - Update the whole population left
pop_new = []
for idx in range(0, self.pop_size - 1):
rand = np.random.random()
# Eq. 4, 5, 6
v1 = np.random.normal(0, 1)
v2 = np.random.normal(0, 1)
c = 0.5 * v1 / abs(v2) # Consumption factor
if idx == 0:
j = 1
else:
j = np.random.randint(0, idx)
### Herbivore
if rand <= 1.0 / 3: # Eq. 23
pos_new = self.pop[idx][self.ID_POS] + H * c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS])
### Carnivore
elif 1.0 / 3 <= rand and rand <= 2.0 / 3: # Eq. 24
pos_new = self.pop[idx][self.ID_POS] + H * c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS])
### Omnivore
else: # Eq. 25
r5 = np.random.random()
pos_new = self.pop[idx][self.ID_POS] + H * c * (r5 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) +
(1 - r5) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new.append(deepcopy(self.pop[-1]))
pop_new = self.greedy_selection_population(self.pop, pop_new)
## find current best used in decomposition
_, best = self.get_global_best_solution(pop_new)
## Decomposition
### Eq. 10, 11, 12, 9
pop_child = []
for idx in range(0, self.pop_size):
r3 = np.random.uniform()
d = 3 * np.random.normal(0, 1)
e = r3 * np.random.randint(1, 3) - 1
h = 2 * r3 - 1
# x_new = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * agent_i[self.ID_POS])
if np.random.random() < 0.5:
beta = 1 - (1 - 0) * ((epoch + 1) / self.epoch) # Eq. 21
r_idx = np.random.choice(list(set(range(0, self.pop_size)) - {idx}))
x_r = pop_new[r_idx][self.ID_POS]
# x_r = pop[np.random.randint(0, self.pop_size-1)][self.ID_POS]
if np.random.random() < 0.5:
x_new = beta * x_r + (1 - beta) * pop_new[idx][self.ID_POS]
else:
x_new = (1 - beta) * x_r + beta * pop_new[idx][self.ID_POS]
else:
x_new = best[self.ID_POS] + d * (e * best[self.ID_POS] - h * pop_new[idx][self.ID_POS])
# x_new = best[self.ID_POS] + np.random.normal() * best[self.ID_POS]
pos_new = self.amend_position(x_new)
pop_child.append([pos_new, None])
pop_child = self.update_fitness_population(pop_child)
self.pop = self.greedy_selection_population(pop_new, pop_child)
[docs]class AdaptiveAEO(Optimizer):
"""
The original version of: Adaptive Artificial Ecosystem Optimization (AAEO)
Links:
1. https://doi.org/10.1109/ACCESS.2020.2973351
Notes
~~~~~
+ Used linear weight factor reduce from 2 to 0 through time
+ Applied Levy-flight technique and the global best solution
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.system_based.AEO import AdaptiveAEO
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> model = AdaptiveAEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Under Review
"""
def __init__(self, problem, epoch=10000, pop_size=100, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = 2 * pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Production - Update the worst agent
# Eq. 2, 3, 1
wf = 2 * (1 - (epoch + 1) / self.epoch) # Weight factor
a = (1.0 - epoch / self.epoch) * np.random.random()
x1 = (1 - a) * self.pop[-1][self.ID_POS] + a * np.random.uniform(self.problem.lb, self.problem.ub)
pos_new = self.amend_position(x1)
fit_new = self.get_fitness_position(pos_new)
self.pop[-1] = [pos_new, fit_new]
## Consumption - Update the whole population left
pop_new = []
for idx in range(0, self.pop_size - 1):
if np.random.random() < 0.5:
rand = np.random.random()
# Eq. 4, 5, 6
c = 0.5 * np.random.normal(0, 1) / abs(np.random.normal(0, 1)) # Consumption factor
if idx == 0:
j = 1
else:
j = np.random.randint(0, idx)
### Herbivore
if rand < 1.0 / 3:
pos_new = self.pop[idx][self.ID_POS] + wf * c * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) # Eq. 6
### Omnivore
elif 1.0 / 3 <= rand <= 2.0 / 3:
pos_new = self.pop[idx][self.ID_POS] + wf * c * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]) # Eq. 7
### Carnivore
else:
r2 = np.random.uniform()
pos_new = self.pop[idx][self.ID_POS] + wf * c * (r2 * (self.pop[idx][self.ID_POS] - self.pop[0][self.ID_POS]) +
(1 - r2) * (self.pop[idx][self.ID_POS] - self.pop[j][self.ID_POS]))
else:
pos_new = self.pop[idx][self.ID_POS] + self.get_levy_flight_step(1., 0.0001, case=-1) * \
(1.0 / np.sqrt(epoch + 1)) * np.sign(np.random.random() - 0.5) * (self.pop[idx][self.ID_POS] - self.g_best[self.ID_POS])
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new.append(deepcopy(self.pop[-1]))
pop_new = self.greedy_selection_population(self.pop, pop_new)
## find current best used in decomposition
_, best = self.get_global_best_solution(pop_new)
## Decomposition
### Eq. 10, 11, 12, 9 idx, pop, g_best, local_best
pop_child = []
for idx in range(0, self.pop_size):
if np.random.random() < 0.5:
pos_new = best[self.ID_POS] + np.random.normal(0, 1, self.problem.n_dims) * (best[self.ID_POS] - pop_new[idx][self.ID_POS])
else:
pos_new = best[self.ID_POS] + self.get_levy_flight_step(0.75, 0.001, case=-1) * \
1.0 / np.sqrt(epoch + 1) * np.sign(np.random.random() - 0.5) * (best[self.ID_POS] - pop_new[idx][self.ID_POS])
pos_new = self.amend_position(pos_new)
pop_child.append([pos_new, None])
pop_child = self.update_fitness_population(pop_child)
self.pop = self.greedy_selection_population(pop_new, pop_child)