# !/usr/bin/env python
# Created by "Thieu" at 14:52, 17/03/2020 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from math import gamma
from copy import deepcopy
from mealpy.optimizer import Optimizer
[docs]class BaseMSA(Optimizer):
"""
My changed version of: Moth Search Algorithm (MSA)
Links:
1. https://www.mathworks.com/matlabcentral/fileexchange/59010-moth-search-ms-algorithm
2. https://doi.org/10.1007/s12293-016-0212-3
Notes
~~~~~
+ The matlab version of original paper is not good (especially convergence chart)
+ I add Normal random number (Gaussian distribution) in each updating equation (Better performance)
Hyper-parameters should fine tuned in approximate range to get faster convergen toward the global optimum:
+ n_best (int): [3, 10], how many of the best moths to keep from one generation to the next, default=5
+ partition (float): [0.3, 0.8], The proportional of first partition, default=0.5
+ max_step_size (float): [0.5, 2.0], Max step size used in Levy-flight technique, default=1.0
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.swarm_based.MSA import BaseMSA
>>>
>>> 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
>>> n_best = 5
>>> partition = 0.5
>>> max_step_size = 1.0
>>> model = BaseMSA(problem_dict1, epoch, pop_size, n_best, partition, max_step_size)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] Wang, G.G., 2018. Moth search algorithm: a bio-inspired metaheuristic algorithm for
global optimization problems. Memetic Computing, 10(2), pp.151-164.
"""
def __init__(self, problem, epoch=10000, pop_size=100, n_best=5, partition=0.5, max_step_size=1.0, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
n_best (int): how many of the best moths to keep from one generation to the next, default=5
partition (float): The proportional of first partition, default=0.5
max_step_size (float): Max step size used in Levy-flight technique, default=1.0
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
self.n_best = n_best
self.partition = partition
self.max_step_size = max_step_size
# np1 in paper
self.n_moth1 = int(np.ceil(self.partition * self.pop_size))
# np2 in paper, we actually don't need this variable
self.n_moth2 = self.pop_size - self.n_moth1
# you can change this ratio so as to get much better performance
self.golden_ratio = (np.sqrt(5) - 1) / 2.0
def _levy_walk(self, iteration):
beta = 1.5 # Eq. 2.23
sigma = (gamma(1 + beta) * np.sin(np.pi * (beta - 1) / 2) / (gamma(beta / 2) * (beta - 1) * 2 ** ((beta - 2) / 2))) ** (1 / (beta - 1))
u = np.random.uniform(self.problem.lb, self.problem.ub) * sigma
v = np.random.uniform(self.problem.lb, self.problem.ub)
step = u / np.abs(v) ** (1.0 / (beta - 1)) # Eq. 2.21
scale = self.max_step_size / (iteration + 1)
delta_x = scale * step
return delta_x
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
pop_best = deepcopy(self.pop[:self.n_best])
pop_new = []
for idx in range(0, self.pop_size):
# Migration operator
if idx < self.n_moth1:
# scale = self.max_step_size / (epoch+1) # Smaller step for local walk
pos_new = self.pop[idx][self.ID_POS] + np.random.normal() * self._levy_walk(epoch)
else:
# Flying in a straight line
temp_case1 = self.pop[idx][self.ID_POS] + np.random.normal() * \
self.golden_ratio * (self.g_best[self.ID_POS] - self.pop[idx][self.ID_POS])
temp_case2 = self.pop[idx][self.ID_POS] + np.random.normal() * \
(1.0 / self.golden_ratio) * (self.g_best[self.ID_POS] - self.pop[idx][self.ID_POS])
pos_new = np.where(np.random.uniform(self.problem.n_dims) < 0.5, temp_case2, temp_case1)
pos_new = self.amend_position(pos_new)
pop_new.append([pos_new, None])
pop_new = self.update_fitness_population(pop_new)
pop_new = self.greedy_selection_population(self.pop, pop_new)
self.pop, _ = self.get_global_best_solution(pop_new)
# Replace the worst with the previous generation's elites.
for i in range(0, self.n_best):
self.pop[-1 - i] = deepcopy(pop_best[i])