# !/usr/bin/env python
# Created by "Thieu" at 07:03, 18/03/2020 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from mealpy.optimizer import Optimizer
[docs]class BaseEO(Optimizer):
"""
The original version of: Equilibrium Optimizer (EO)
Links:
1. https://doi.org/10.1016/j.knosys.2019.105190
2. https://www.mathworks.com/matlabcentral/fileexchange/73352-equilibrium-optimizer-eo
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.physics_based.EO import BaseEO
>>>
>>> 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 = BaseEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Faramarzi, A., Heidarinejad, M., Stephens, B. and Mirjalili, S., 2020. Equilibrium optimizer: A novel
optimization algorithm. Knowledge-Based Systems, 191, p.105190.
"""
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
## Fixed parameter proposed by authors
self.V = 1
self.a1 = 2
self.a2 = 1
self.GP = 0.5
[docs] def make_equilibrium_pool(self, list_equilibrium=None):
pos_list = [item[self.ID_POS] for item in list_equilibrium]
pos_mean = np.mean(pos_list, axis=0)
pos_mean = self.amend_position(pos_mean)
fit = self.get_fitness_position(pos_mean)
list_equilibrium.append([pos_mean, fit])
return list_equilibrium
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
# ---------------- Memory saving------------------- make equilibrium pool
_, c_eq_list, _ = self.get_special_solutions(self.pop, best=4)
c_pool = self.make_equilibrium_pool(c_eq_list)
# Eq. 9
t = (1 - epoch / self.epoch) ** (self.a2 * epoch / self.epoch)
pop_new = []
for idx in range(0, self.pop_size):
lamda = np.random.uniform(0, 1, self.problem.n_dims) # lambda in Eq. 11
r = np.random.uniform(0, 1, self.problem.n_dims) # r in Eq. 11
c_eq = c_pool[np.random.randint(0, len(c_pool))][self.ID_POS] # random selection 1 of candidate from the pool
f = self.a1 * np.sign(r - 0.5) * (np.exp(-lamda * t) - 1.0) # Eq. 11
r1 = np.random.uniform()
r2 = np.random.uniform() # r1, r2 in Eq. 15
gcp = 0.5 * r1 * np.ones(self.problem.n_dims) * (r2 >= self.GP) # Eq. 15
g0 = gcp * (c_eq - lamda * self.pop[idx][self.ID_POS]) # Eq. 14
g = g0 * f # Eq. 13
pos_new = c_eq + (self.pop[idx][self.ID_POS] - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 16
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
self.pop = self.update_fitness_population(pop_new)
[docs]class ModifiedEO(BaseEO):
"""
The original version of: Modified Equilibrium Optimizer (MEO)
Links:
1. https://doi.org/10.1016/j.asoc.2020.106542
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.physics_based.EO import ModifiedEO
>>>
>>> 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 = ModifiedEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Gupta, S., Deep, K. and Mirjalili, S., 2020. An efficient equilibrium optimizer with mutation
strategy for numerical optimization. Applied Soft Computing, 96, p.106542.
"""
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)
self.nfe_per_epoch = 2 * pop_size
self.sort_flag = False
self.pop_len = int(self.pop_size / 3)
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
# ---------------- Memory saving------------------- make equilibrium pool
_, c_eq_list, _ = self.get_special_solutions(self.pop, best=4)
c_pool = self.make_equilibrium_pool(c_eq_list)
# Eq. 9
t = (1 - epoch / self.epoch) ** (self.a2 * epoch / self.epoch)
pop_new = []
for idx in range(0, self.pop_size):
lamda = np.random.uniform(0, 1, self.problem.n_dims) # lambda in Eq. 11
r = np.random.uniform(0, 1, self.problem.n_dims) # r in Eq. 11
c_eq = c_pool[np.random.randint(0, len(c_pool))][self.ID_POS] # random selection 1 of candidate from the pool
f = self.a1 * np.sign(r - 0.5) * (np.exp(-lamda * t) - 1.0) # Eq. 11
r1 = np.random.uniform()
r2 = np.random.uniform() # r1, r2 in Eq. 15
gcp = 0.5 * r1 * np.ones(self.problem.n_dims) * (r2 >= self.GP) # Eq. 15
g0 = gcp * (c_eq - lamda * self.pop[idx][self.ID_POS]) # Eq. 14
g = g0 * f # Eq. 13
pos_new = c_eq + (self.pop[idx][self.ID_POS] - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 16
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
## Sort the updated population based on fitness
_, pop_s1, _ = self.get_special_solutions(pop_new, best=self.pop_len)
## Mutation scheme
pop_s2_new = []
for i in range(0, self.pop_len):
pos_new = pop_s1[i][self.ID_POS] * (1 + np.random.normal(0, 1, self.problem.n_dims)) # Eq. 12
pos_new = self.amend_position(pos_new)
pop_s2_new.append([pos_new, None])
pop_s2 = self.update_fitness_population(pop_s2_new)
## Search Mechanism
pos_s1_list = [item[self.ID_POS] for item in pop_s1]
pos_s1_mean = np.mean(pos_s1_list, axis=0)
pop_s3 = []
for i in range(0, self.pop_len):
pos_new = (c_pool[0][self.ID_POS] - pos_s1_mean) - np.random.random() * \
(self.problem.lb + np.random.random() * (self.problem.ub - self.problem.lb))
pos_new = self.amend_position(pos_new)
pop_s3.append([pos_new, None])
pop_s3 = self.update_fitness_population(pop_s3)
## Construct a new population
self.pop = pop_s1 + pop_s2 + pop_s3
n_left = self.pop_size - len(self.pop)
idx_selected = np.random.choice(range(0, len(c_pool)), n_left, replace=False)
for i in range(0, n_left):
self.pop.append(c_pool[idx_selected[i]])
[docs]class AdaptiveEO(BaseEO):
"""
The original version of: Adaptive Equilibrium Optimization (AEO)
Links:
1. https://doi.org/10.1016/j.engappai.2020.103836
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.physics_based.EO import AdaptiveEO
>>>
>>> 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 = AdaptiveEO(problem_dict1, epoch, pop_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Wunnava, A., Naik, M.K., Panda, R., Jena, B. and Abraham, A., 2020. A novel interdependence based
multilevel thresholding technique using adaptive equilibrium optimizer. Engineering Applications of
Artificial Intelligence, 94, p.103836.
"""
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)
self.nfe_per_epoch = pop_size
self.sort_flag = False
self.pop_len = int(self.pop_size / 3)
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
# ---------------- Memory saving------------------- make equilibrium pool
_, c_eq_list, _ = self.get_special_solutions(self.pop, best=4)
c_pool = self.make_equilibrium_pool(c_eq_list)
# Eq. 9
t = (1 - epoch / self.epoch) ** (self.a2 * epoch / self.epoch)
## Memory saving, Eq 20, 21
t = (1 - epoch / self.epoch) ** (self.a2 * epoch / self.epoch)
pop_new = []
for idx in range(0, self.pop_size):
lamda = np.random.uniform(0, 1, self.problem.n_dims)
r = np.random.uniform(0, 1, self.problem.n_dims)
c_eq = c_pool[np.random.randint(0, len(c_pool))][self.ID_POS] # random selection 1 of candidate from the pool
f = self.a1 * np.sign(r - 0.5) * (np.exp(-lamda * t) - 1.0) # Eq. 14
r1 = np.random.uniform()
r2 = np.random.uniform()
gcp = 0.5 * r1 * np.ones(self.problem.n_dims) * (r2 >= self.GP)
g0 = gcp * (c_eq - lamda * self.pop[idx][self.ID_POS])
g = g0 * f
fit_average = np.mean([item[self.ID_TAR][self.ID_FIT] for item in self.pop]) # Eq. 19
pos_new = c_eq + (self.pop[idx][self.ID_POS] - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 9
if self.pop[idx][self.ID_TAR][self.ID_FIT] >= fit_average:
pos_new = np.multiply(pos_new, (0.5 + np.random.uniform(0, 1, self.problem.n_dims)))
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
self.pop = self.update_fitness_population(pop_new)