#!/usr/bin/env python
# Created by "Thieu" at 16:31, 13/09/2025 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from mealpy.optimizer import Optimizer
from mealpy.utils.opt_info import OptInfo
[docs]class OriginalMSO(Optimizer):
"""
The original version of: Mirage Search Optimization (MSO)
Parameters
----------
epoch : int
Maximum number of iterations, in range [1, 100000]. Default is 10000.
pop_size : int
Number of population size, in range [5, 10000]. Default is 100.
Links
-----
1. https://doi.org/10.1016/j.advengsoft.2025.103883
2. https://www.mathworks.com/matlabcentral/fileexchange/180042-mirage-search-optimization
References
~~~~~~~~~~
1. He, J., Zhao, S., Ding, J., & Wang, Y. (2025).
Mirage search optimization: Application to path planning and engineering design problems.
Advances in Engineering Software, 203, 103883.
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy import FloatVar, MSO
>>>
>>> def objective_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict = {
>>> "bounds": FloatVar(lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
>>> "minmax": "min",
>>> "obj_func": objective_function
>>> }
>>>
>>> model = MSO.OriginalMSO(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}")
"""
OPT_INFO = OptInfo(name="Mirage Search Optimization", year=2025, difficulty="medium", kind="original")
def __init__(self, epoch: int = 10000, pop_size: int = 100, **kwargs: object) -> None:
super().__init__(**kwargs)
self.epoch = self.validator.check_int("epoch", epoch, [1, 100000])
self.pop_size = self.validator.check_int("pop_size", pop_size, [10, 10000])
self.set_parameters(["epoch", "pop_size"])
self.sort_flag = False
self.is_parallelizable = False
[docs] def sind(self, x):
return np.sin(np.deg2rad(x))
[docs] def cosd(self, x):
return np.cos(np.deg2rad(x))
[docs] def tand(self, x):
x = np.asarray(x, dtype=float)
bad = (np.mod(x, 90) == 0) & (np.mod(x, 180) != 0)
x[bad] = x[bad] - self.EPSILON
return np.tan(np.deg2rad(x))
[docs] def atand(self, x):
return np.rad2deg(np.arctan(x))
[docs] def asind(self, x):
x = np.clip(x, -1, 1) # asin bound [-1, 1]
val = np.rad2deg(np.arcsin(x))
return val
[docs] def atanh(self, x):
if np.abs(x) >= 1:
return 1.0
return np.arctanh(x)
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
# Random permutation for agent selection
ac = self.generator.permutation(self.pop_size - 1) + 1
# Selection of individuals for Superior mirage search
cv = int(np.ceil((self.pop_size * (2 / 3)) * ((self.epoch - self.nfe_counter + 1) / self.epoch)))
# Superior mirage search
pop_new = []
for idx in ac[:cv]:
pos_new = np.zeros(self.problem.n_dims)
for k in range(self.problem.n_dims):
h = (self.g_best.solution[k] - self.pop[idx].solution[k]) * self.generator.random()
cmax = 1
hmax = 5 * self.atanh(-(self.nfe_counter / self.epoch) + 1) + cmax
if h > hmax:
h = hmax
if h < cmax:
h = cmax
zf = self.generator.choice([-1, 1])
a = self.generator.random() * 20
b = self.generator.random() * (45 - a / 2)
z = self.generator.integers(1, 3)
A = B = C = D = 90
if z == 1:
C = b + 90
D = 180 - C - a
B = 180 - 2 * D
A = 180 - B + a - 90
elif z == 2 and a < b:
C = 90 - b
D = 90 + a - b
B = 180 - 2 * D
A = 180 - B - a - 90
elif z == 2 and a > b:
C = 90 - b
D = 180 - C - a
B = 180 - 2 * D
A = 180 - B - 90 + a
else:
zf = 0
dx = (self.sind(B) * h * self.sind(C)) / (self.sind(D) * self.sind(A))
dx = dx * zf
pos_new[k] = self.pop[idx].solution[k] + dx
# Bound the variables
pos_new = self.correct_solution(pos_new)
agent = self.generate_agent(pos_new)
pop_new.append(agent)
self.pop = self.get_sorted_and_trimmed_population(self.pop + pop_new, self.pop_size, minmax=self.problem.minmax)
# Inferior mirage search
pop_new = []
for idx in range(self.pop_size):
if self.g_best == self.pop[idx]:
hh = np.ones(self.problem.n_dims) * 0.05 * self.generator.choice([-1, 1])
else:
hh = self.g_best.solution - self.pop[idx].solution
zf = np.sign(hh)
hh = np.abs(hh * self.generator.random(self.problem.n_dims))
gama = self.generator.random(self.problem.n_dims) * 90 * ((self.epoch - self.nfe_counter * 0.99) / self.epoch)
amax = self.atand(1.0 / (2 * self.tand(gama)))
amin = self.atand((self.sind(gama) * self.cosd(gama)) / (1 + (self.sind(gama)) ** 2))
fai = (amax - amin) * self.generator.random() + amin
omg = self.asind(self.generator.random() * self.sind(fai + gama))
x = (hh / self.tand(gama)) - (((hh / self.sind(gama)) - (hh * self.sind(fai)) / (self.cosd(fai + gama))) * self.cosd(omg)) / self.cosd(omg - gama)
pos_new = self.pop[idx].solution + x * zf
pos_new = self.correct_solution(pos_new)
agent = self.generate_agent(pos_new)
pop_new.append(agent)
self.pop = self.get_sorted_and_trimmed_population(self.pop + pop_new, self.pop_size, minmax=self.problem.minmax)