利用PSO算法求函数f(a,g)=3*cos(xy)+α+g2的最小值。其中,n ∈ [-4,4] , y∈ [-4,4]。实验要求∶1.构建适应度函数(代码)。 2.带惯性权重的PSO优化实现(代码)。3.函数三维图(代码)。
时间: 2024-02-06 07:12:18 浏览: 21
好的,这是一个三维优化问题,我们可以使用带惯性权重的PSO算法来求解。
首先,我们需要定义适应度函数,即要最小化的目标函数。根据题意,我们可以定义如下的适应度函数:
```python
def fitness_function(x):
a, y, g = x
return 3 * math.cos(a * y) + a + g ** 2
```
其中,`x`是一个包含`a`、`y`和`g`的元组。
接下来,我们可以使用如下的代码来实现带惯性权重的PSO算法:
```python
import random
import math
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
class Particle:
def __init__(self, bounds):
self.particle_position = [random.uniform(bounds[i][0], bounds[i][1]) for i in range(len(bounds))]
self.particle_velocity = [random.uniform(-1, 1) for _ in range(len(bounds))]
self.local_best_particle_position = self.particle_position
self.fitness_local_best_particle_position = float('inf')
def update_velocity(self, global_best_particle_position, omega, phip, phig):
for i in range(len(self.particle_position)):
r1 = random.uniform(0, 1)
r2 = random.uniform(0, 1)
cognitive_velocity = phip * r1 * (self.local_best_particle_position[i] - self.particle_position[i])
social_velocity = phig * r2 * (global_best_particle_position[i] - self.particle_position[i])
self.particle_velocity[i] = omega * self.particle_velocity[i] + cognitive_velocity + social_velocity
def update_position(self, bounds):
for i in range(len(self.particle_position)):
self.particle_position[i] += self.particle_velocity[i]
if self.particle_position[i] < bounds[i][0]:
self.particle_position[i] = bounds[i][0]
elif self.particle_position[i] > bounds[i][1]:
self.particle_position[i] = bounds[i][1]
def evaluate_fitness(self, fitness_function):
self.fitness_particle_position = fitness_function(self.particle_position)
if self.fitness_particle_position < self.fitness_local_best_particle_position:
self.local_best_particle_position = self.particle_position
self.fitness_local_best_particle_position = self.fitness_particle_position
def particle_swarm_optimization(fitness_function, bounds, num_particles, max_iterations, omega, phip, phig):
global_best_particle_position = None
global_best_fitness = float('inf')
swarm = [Particle(bounds) for _ in range(num_particles)]
for i in range(max_iterations):
for j in range(num_particles):
swarm[j].evaluate_fitness(fitness_function)
if swarm[j].fitness_particle_position < global_best_fitness:
global_best_particle_position = swarm[j].particle_position
global_best_fitness = swarm[j].fitness_particle_position
for j in range(num_particles):
swarm[j].update_velocity(global_best_particle_position, omega, phip, phig)
swarm[j].update_position(bounds)
return global_best_particle_position, global_best_fitness
def plot_3d_function(fitness_function, bounds):
x = np.linspace(bounds[0][0], bounds[0][1], 50)
y = np.linspace(bounds[1][0], bounds[1][1], 50)
X, Y = np.meshgrid(x, y)
Z = np.zeros((50, 50))
for i in range(50):
for j in range(50):
Z[i][j] = fitness_function([X[i][j], Y[i][j], 0])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap='coolwarm')
plt.show()
bounds = [(-4, 4), (-4, 4), (-4, 4)]
num_particles = 20
max_iterations = 100
omega = 0.5
phip = 0.5
phig = 0.5
best_position, best_fitness = particle_swarm_optimization(fitness_function, bounds, num_particles, max_iterations, omega, phip, phig)
print('Best position:', best_position)
print('Best fitness:', best_fitness)
plot_3d_function(fitness_function, bounds)
```
运行以上代码,就可以得到目标函数的最小值及其对应的参数`a`、`y`和`g`,并且在三维坐标系中绘制出函数的图像。