#!/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 OriginalEO(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 import FloatVar, EO
>>>
>>> def objective_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict = {
>>> "bounds": FloatVar(n_vars=30, lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
>>> "minmax": "min",
>>> "obj_func": objective_function
>>> }
>>>
>>> model = EO.OriginalEO(epoch=1000, pop_size=50)
>>> g_best = model.solve(problem_dict)
>>> print(f"Solution: {g_best.solution}, Fitness: {g_best.target.fitness}")
>>> print(f"Solution: {model.g_best.solution}, Fitness: {model.g_best.target.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, epoch: int = 10000, pop_size: int = 100, **kwargs: object) -> None:
"""
Args:
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(**kwargs)
self.epoch = self.validator.check_int("epoch", epoch, [1, 100000])
self.pop_size = self.validator.check_int("pop_size", pop_size, [5, 10000])
self.set_parameters(["epoch", "pop_size"])
self.sort_flag = False
## 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 = [agent.solution for agent in list_equilibrium]
pos_mean = np.mean(pos_list, axis=0)
pos_mean = self.correct_solution(pos_mean)
agent = self.generate_agent(pos_mean)
list_equilibrium.append(agent)
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_agents(self.pop, n_best=4, minmax=self.problem.minmax)
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 = self.generator.uniform(0, 1, self.problem.n_dims) # lambda in Eq. 11
r = self.generator.uniform(0, 1, self.problem.n_dims) # r in Eq. 11
c_eq = c_pool[self.generator.integers(0, len(c_pool))].solution # 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 = self.generator.uniform()
r2 = self.generator.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].solution) # Eq. 14
g = g0 * f # Eq. 13
pos_new = c_eq + (self.pop[idx].solution - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 16
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_new.append(agent)
if self.mode not in self.AVAILABLE_MODES:
agent.target = self.get_target(pos_new)
self.pop[idx] = self.get_better_agent(agent, self.pop[idx], self.problem.minmax)
if self.mode in self.AVAILABLE_MODES:
pop_new = self.update_target_for_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new, self.problem.minmax)
[docs]class ModifiedEO(OriginalEO):
"""
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 import FloatVar, EO
>>>
>>> def objective_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict = {
>>> "bounds": FloatVar(n_vars=30, lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
>>> "minmax": "min",
>>> "obj_func": objective_function
>>> }
>>>
>>> model = EO.ModifiedEO(epoch=1000, pop_size=50)
>>> g_best = model.solve(problem_dict)
>>> print(f"Solution: {g_best.solution}, Fitness: {g_best.target.fitness}")
>>> print(f"Solution: {model.g_best.solution}, Fitness: {model.g_best.target.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, epoch: int = 10000, pop_size: int = 100, **kwargs: object) -> None:
"""
Args:
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(epoch, pop_size, **kwargs)
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_agents(self.pop, n_best=4, minmax=self.problem.minmax)
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 = self.generator.uniform(0, 1, self.problem.n_dims) # lambda in Eq. 11
r = self.generator.uniform(0, 1, self.problem.n_dims) # r in Eq. 11
c_eq = c_pool[self.generator.integers(0, len(c_pool))].solution # 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 = self.generator.uniform()
r2 = self.generator.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].solution) # Eq. 14
g = g0 * f # Eq. 13
pos_new = c_eq + (self.pop[idx].solution - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 16
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_new.append(agent)
if self.mode not in self.AVAILABLE_MODES:
agent.target = self.get_target(pos_new)
self.pop[idx] = self.get_better_agent(agent, self.pop[idx], self.problem.minmax)
if self.mode in self.AVAILABLE_MODES:
pop_new = self.update_target_for_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new, self.problem.minmax)
## Sort the updated population based on fitness
_, pop_s1, _ = self.get_special_agents(self.pop, n_best=self.pop_len, minmax=self.problem.minmax)
## Mutation scheme
pop_s2 = pop_s1.copy()
pop_s2_new = []
for idx in range(0, self.pop_len):
pos_new = pop_s2[idx].solution * (1 + self.generator.normal(0, 1, self.problem.n_dims)) # Eq. 12
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_s2_new.append(agent)
if self.mode not in self.AVAILABLE_MODES:
agent.target = self.get_target(pos_new)
pop_s2[idx] = self.get_better_agent(agent, pop_s2[idx], self.problem.minmax)
if self.mode in self.AVAILABLE_MODES:
pop_s2_new = self.update_target_for_population(pop_s2_new)
pop_s2 = self.greedy_selection_population(pop_s2_new, pop_s2, self.problem.minmax)
## Search Mechanism
pos_s1_list = [agent.solution for agent in pop_s1]
pos_s1_mean = np.mean(pos_s1_list, axis=0)
pop_s3 = []
for idx in range(0, self.pop_len):
pos_new = (c_pool[0].solution - pos_s1_mean) - self.generator.random() * \
(self.problem.lb + self.generator.random() * (self.problem.ub - self.problem.lb))
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_s3.append(agent)
if self.mode not in self.AVAILABLE_MODES:
pop_s3[-1].target = self.get_target(pos_new)
pop_s3 = self.update_target_for_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 = self.generator.choice(range(0, len(c_pool)), n_left, replace=False)
for idx in range(0, n_left):
self.pop.append(c_pool[idx_selected[idx]])
[docs]class AdaptiveEO(OriginalEO):
"""
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 import FloatVar, EO
>>>
>>> def objective_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict = {
>>> "bounds": FloatVar(n_vars=30, lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
>>> "minmax": "min",
>>> "obj_func": objective_function
>>> }
>>>
>>> model = EO.AdaptiveEO(epoch=1000, pop_size=50)
>>> g_best = model.solve(problem_dict)
>>> print(f"Solution: {g_best.solution}, Fitness: {g_best.target.fitness}")
>>> print(f"Solution: {model.g_best.solution}, Fitness: {model.g_best.target.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, epoch: int = 10000, pop_size: int = 100, **kwargs: object) -> None:
"""
Args:
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
"""
super().__init__(epoch, pop_size, **kwargs)
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_agents(self.pop, n_best=4, minmax=self.problem.minmax)
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 = self.generator.uniform(0, 1, self.problem.n_dims)
r = self.generator.uniform(0, 1, self.problem.n_dims)
c_eq = c_pool[self.generator.integers(0, len(c_pool))].solution # 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 = self.generator.uniform()
r2 = self.generator.uniform()
gcp = 0.5 * r1 * np.ones(self.problem.n_dims) * (r2 >= self.GP)
g0 = gcp * (c_eq - lamda * self.pop[idx].solution)
g = g0 * f
fit_average = np.mean([item.target.fitness for item in self.pop]) # Eq. 19
pos_new = c_eq + (self.pop[idx].solution - c_eq) * f + (g * self.V / lamda) * (1.0 - f) # Eq. 9
if self.compare_fitness(self.pop[idx].target.fitness, fit_average, self.problem.minmax):
pos_new = np.multiply(pos_new, (0.5 + self.generator.uniform(0, 1, self.problem.n_dims)))
pos_new = self.correct_solution(pos_new)
agent = self.generate_empty_agent(pos_new)
pop_new.append(agent)
if self.mode not in self.AVAILABLE_MODES:
agent.target = self.get_target(pos_new)
self.pop[idx] = self.get_better_agent(agent, self.pop[idx], self.problem.minmax)
if self.mode in self.AVAILABLE_MODES:
pop_new = self.update_target_for_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new, self.problem.minmax)