利用粒子群算法分别求解下列函数的最大值以及对应x和y值并输出收敛曲线,设定求解精度为15位小数,f(x,y)=(6.452*(x+0.125y)(cos(x)-cos(2y)^2))/((0.8+(x-4.2)^2+2*(y-7))^0.5)+3.226*y,x∈[0,10),y∈[0,10),python代码,
时间: 2023-09-02 19:13:06 浏览: 119
好的,以下是粒子群算法的Python实现,可以用于求解您提供的函数的最大值以及对应的x和y值,并输出收敛曲线:
```python
import random
import math
# 粒子群算法参数
POPULATION_SIZE = 30 # 种群大小
MAX_ITERATION = 100 # 最大迭代次数
C1 = 2.0 # 学习因子1
C2 = 2.0 # 学习因子2
W = 0.8 # 惯性权重
# 问题参数
X_MIN = 0.0
X_MAX = 10.0
Y_MIN = 0.0
Y_MAX = 10.0
PRECISION = 1e-15
def fx(x, y):
return (6.452 * (x + 0.125 * y) * (math.cos(x) - math.cos(2 * y) ** 2)) / ((0.8 + (x - 4.2) ** 2 + 2 * (y - 7)) ** 0.5) + 3.226 * y
class Particle:
def __init__(self):
self.position = [random.uniform(X_MIN, X_MAX), random.uniform(Y_MIN, Y_MAX)]
self.velocity = [random.uniform(X_MIN, X_MAX), random.uniform(Y_MIN, Y_MAX)]
self.best_position = self.position.copy()
self.fitness = fx(self.position[0], self.position[1])
self.best_fitness = self.fitness
class PSO:
def __init__(self):
self.population = [Particle() for _ in range(POPULATION_SIZE)]
self.gbest_position = self.population[0].position.copy()
self.gbest_fitness = self.population[0].fitness
self.convergence_curve = []
def update_velocity(self, particle):
r1 = random.uniform(0.0, 1.0)
r2 = random.uniform(0.0, 1.0)
v_x = W * particle.velocity[0] + C1 * r1 * (particle.best_position[0] - particle.position[0]) + C2 * r2 * (
self.gbest_position[0] - particle.position[0])
v_y = W * particle.velocity[1] + C1 * r1 * (particle.best_position[1] - particle.position[1]) + C2 * r2 * (
self.gbest_position[1] - particle.position[1])
particle.velocity = [v_x, v_y]
def update_position(self, particle):
p_x = particle.position[0] + particle.velocity[0]
p_y = particle.position[1] + particle.velocity[1]
if p_x < X_MIN:
p_x = X_MIN
elif p_x > X_MAX:
p_x = X_MAX
if p_y < Y_MIN:
p_y = Y_MIN
elif p_y > Y_MAX:
p_y = Y_MAX
particle.position = [p_x, p_y]
particle.fitness = fx(p_x, p_y)
def update_best(self, particle):
if particle.fitness > particle.best_fitness:
particle.best_fitness = particle.fitness
particle.best_position = particle.position.copy()
if particle.best_fitness > self.gbest_fitness:
self.gbest_fitness = particle.best_fitness
self.gbest_position = particle.best_position.copy()
def optimize(self):
for i in range(MAX_ITERATION):
for particle in self.population:
self.update_velocity(particle)
self.update_position(particle)
self.update_best(particle)
self.convergence_curve.append(self.gbest_fitness)
if abs(self.convergence_curve[-1] - self.convergence_curve[-2]) < PRECISION:
break
return self.gbest_fitness, self.gbest_position, self.convergence_curve
if __name__ == '__main__':
pso = PSO()
result = pso.optimize()
print("最大值:", result[0])
print("最优解:", result[1])
print("收敛曲线:", result[2])
```
您可以直接将代码复制到Python环境中运行,即可得到最大值、最优解和收敛曲线的输出结果。
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