# !/usr/bin/env python
# Created by "Thieu" at 15:53, 07/07/2021 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from math import gamma
from mealpy.optimizer import Optimizer
[docs]class OriginalAO(Optimizer):
"""
The original version of: Aquila Optimization (AO)
Links:
1. https://doi.org/10.1016/j.cie.2021.107250
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.swarm_based.AO import OriginalAO
>>>
>>> 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 = OriginalAO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Abualigah, L., Yousri, D., Abd Elaziz, M., Ewees, A.A., Al-Qaness, M.A. and Gandomi, A.H., 2021.
Aquila optimizer: a novel meta-heuristic optimization algorithm. Computers & Industrial Engineering, 157, p.107250.
"""
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 = pop_size
self.sort_flag = False
self.epoch = epoch
self.pop_size = pop_size
self.alpha = 0.1
self.delta = 0.1
[docs] def get_simple_levy_step(self):
beta = 1.5
sigma = (gamma(1 + beta) * np.sin(np.pi * beta / 2) / (gamma((1 + beta) / 2) * beta * 2 ** ((beta - 1) / 2))) ** (1 / beta)
u = np.random.normal(0, 1, self.problem.n_dims) * sigma
v = np.random.normal(1, self.problem.n_dims)
step = u / abs(v) ** (1 / beta)
return step
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
g1 = 2 * np.random.rand() - 1 # Eq. 16
g2 = 2 * (1 - epoch / self.epoch) # Eq. 17
dim_list = np.array(list(range(1, self.problem.n_dims + 1)))
miu = 0.00565
r0 = 10
r = r0 + miu * dim_list
w = 0.005
phi0 = 3 * np.pi / 2
phi = -w * dim_list + phi0
x = r * np.sin(phi) # Eq.(9)
y = r * np.cos(phi) # Eq.(10)
QF = (epoch + 1) ** ((2 * np.random.rand() - 1) / (1 - self.epoch) ** 2) # Eq.(15) Quality function
pop_new = []
for idx in range(0, self.pop_size):
x_mean = np.mean(np.array([item[self.ID_TAR][self.ID_FIT] for item in self.pop]), axis=0)
if (epoch + 1) <= (2 / 3) * self.epoch: # Eq. 3, 4
if np.random.rand() < 0.5:
pos_new = self.g_best[self.ID_POS] * (1 - (epoch + 1) / self.epoch) + \
np.random.rand() * (x_mean - self.g_best[self.ID_POS])
else:
idx = np.random.choice(list(set(range(0, self.pop_size)) - {idx}))
pos_new = self.g_best[self.ID_POS] * self.get_simple_levy_step() + \
self.pop[idx][self.ID_POS] + np.random.rand() * (y - x) # Eq. 5
else:
if np.random.rand() < 0.5:
pos_new = self.alpha * (self.g_best[self.ID_POS] - x_mean) - np.random.rand() * \
(np.random.rand() * (self.problem.ub - self.problem.lb) + self.problem.lb) * self.delta # Eq. 13
else:
pos_new = QF * self.g_best[self.ID_POS] - (g2 * self.pop[idx][self.ID_POS] *
np.random.rand()) - g2 * self.get_simple_levy_step() + np.random.rand() * g1 # Eq. 14
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new)