粒子群算法, 多目标
时间: 2023-12-19 13:31:16 浏览: 32
粒子群算法(Particle Swarm Optimization,PSO)是一种基于群体智能的优化算法,其灵感来源于鸟群捕食行为。在PSO算法中,每个解被看作是一个粒子,粒子通过不断地调整自身的位置和速度来搜索最优解。多目标优化问题是指在优化问题中存在多个目标函数,这些目标函数通常是相互矛盾的,无法通过单一的优化方法得到最优解。多目标粒子群优化算法(Multi-objective Particle Swarm Optimization,MOPSO)是一种基于粒子群算法的多目标优化算法,它通过维护一个外部种群来解决多目标优化问题。外部种群中的解称为非支配解,即在所有目标函数上都优于其他解。MOPSO算法通过自适应网格机制来维护外部种群,使得外部种群中的解能够均匀地分布在整个搜索空间中,从而提高算法的收敛性和搜索效率。
以下是使用Python实现的MOPSO算法的示例代码:
```python
import numpy as np
class MOPSO:
def __init__(self, obj_func, n_particles, n_iterations, w=0.4, c1=1.5, c2=1.5):
self.obj_func = obj_func
self.n_particles = n_particles
self.n_iterations = n_iterations
self.w = w
self.c1 = c1
self.c2 = c2
self.particles = np.random.rand(n_particles, 2)
self.velocities = np.zeros((n_particles, 2))
self.pbest_positions = self.particles.copy()
self.pbest_values = np.zeros(n_particles)
self.gbest_position = np.zeros(2)
self.gbest_value = np.inf
self.external_archive = np.zeros((n_particles, 2))
self.external_archive_values = np.zeros(n_particles)
self.external_archive_size = 0
self.grid_size = 10
self.grid = [[] for _ in range(self.grid_size ** 2)]
self.grid_limits = np.array([[0, 1], [0, 1]])
self.grid_cell_size = (self.grid_limits[:, 1] - self.grid_limits[:, 0]) / self.grid_size
def update(self):
for i in range(self.n_particles):
self.velocities[i] = self.w * self.velocities[i] + \
self.c1 * np.random.rand() * (self.pbest_positions[i] - self.particles[i]) + \
self.c2 * np.random.rand() * (self.gbest_position - self.particles[i])
self.particles[i] += self.velocities[i]
self.particles[i] = np.clip(self.particles[i], 0, 1)
obj_value = self.obj_func(self.particles[i])
if obj_value < self.pbest_values[i]:
self.pbest_positions[i] = self.particles[i].copy()
self.pbest_values[i] = obj_value
if obj_value < self.gbest_value:
self.gbest_position = self.particles[i].copy()
self.gbest_value = obj_value
if self.external_archive_size < self.n_particles:
self.external_archive[self.external_archive_size] = self.particles[i].copy()
self.external_archive_values[self.external_archive_size] = obj_value
self.external_archive_size += 1
else:
worst_index = np.argmax(self.external_archive_values)
if obj_value < self.external_archive_values[worst_index]:
self.external_archive[worst_index] = self.particles[i].copy()
self.external_archive_values[worst_index] = obj_value
self.update_grid(i)
def update_grid(self, particle_index):
grid_index = tuple(((self.particles[particle_index] - self.grid
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