# !/usr/bin/env python
# Created by "Thieu" at 09:56, 07/07/2021 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from copy import deepcopy
from mealpy.optimizer import Optimizer
[docs]class OriginalAOA(Optimizer):
"""
The original version of: Arithmetic Optimization Algorithm (AOA)
Links:
1. https://doi.org/10.1016/j.cma.2020.113609
Hyper-parameters should fine tuned in approximate range to get faster convergen toward the global optimum:
+ alpha (int): [3, 8], fixed parameter, sensitive exploitation parameter, Default: 5,
+ miu (float): [0.3, 1.0], fixed parameter , control parameter to adjust the search process, Default: 0.5,
+ moa_min (float): [0.1, 0.4], range min of Math Optimizer Accelerated, Default: 0.2,
+ moa_max (float): [0.5, 1.0], range max of Math Optimizer Accelerated, Default: 0.9,
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.math_based.AOA import OriginalAOA
>>>
>>> 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
>>> alpha = 5
>>> miu = 0.5
>>> moa_min = 0.2
>>> moa_max = 0.9
>>> model = OriginalAOA(problem_dict1, epoch, pop_size, alpha, miu, moa_min, moa_max)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M. and Gandomi, A.H., 2021. The arithmetic
optimization algorithm. Computer methods in applied mechanics and engineering, 376, p.113609.
"""
def __init__(self, problem, epoch=10000, pop_size=100, alpha=5, miu=0.5, moa_min=0.2, moa_max=0.9, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
alpha (int): fixed parameter, sensitive exploitation parameter, Default: 5,
miu (float): fixed parameter, control parameter to adjust the search process, Default: 0.5,
moa_min (float): range min of Math Optimizer Accelerated, Default: 0.2,
moa_max (float): range max of Math Optimizer Accelerated, Default: 0.9,
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = pop_size
self.sort_flag = False
self.epoch = epoch
self.pop_size = pop_size
self.alpha = alpha
self.miu = miu
self.moa_min = moa_min
self.moa_max = moa_max
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
moa = self.moa_min + epoch * ((self.moa_max - self.moa_min) / self.epoch) # Eq. 2
mop = 1 - (epoch ** (1.0 / self.alpha)) / (self.epoch ** (1.0 / self.alpha)) # Eq. 4
pop_new = []
for idx in range(0, self.pop_size):
pos_new = deepcopy(self.pop[idx][self.ID_POS])
for j in range(0, self.problem.n_dims):
r1, r2, r3 = np.random.rand(3)
if r1 > moa: # Exploration phase
if r2 < 0.5:
pos_new[j] = self.g_best[self.ID_POS][j] / (mop + self.EPSILON) * \
((self.problem.ub[j] - self.problem.lb[j]) * self.miu + self.problem.lb[j])
else:
pos_new[j] = self.g_best[self.ID_POS][j] * mop * ((self.problem.ub[j] - self.problem.lb[j]) * self.miu + self.problem.lb[j])
else: # Exploitation phase
if r3 < 0.5:
pos_new[j] = self.g_best[self.ID_POS][j] - mop * ((self.problem.ub[j] - self.problem.lb[j]) * self.miu + self.problem.lb[j])
else:
pos_new[j] = self.g_best[self.ID_POS][j] + mop * ((self.problem.ub[j] - self.problem.lb[j]) * self.miu + self.problem.lb[j])
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)