多目标粒子群算法python优化ZDT1函数

好的，我来给你提供一个多目标粒子群算法（MOPSO）的Python优化ZDT1函数的例子。在这个例子中，我们使用了Pymoo库实现MOPSO算法。

首先，安装Pymoo库：

!pip install pymoo

然后，导入必要的包：

import numpy as np
from pymoo.model.problem import Problem
from pymoo.algorithms.mopso import MOPSO
from pymoo.factory import get_sampling, get_crossover, get_mutation
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter

接下来，定义ZDT1函数作为优化目标：

class ZDT1(Problem):

    def __init__(self):
        super().__init__(n_var=30, n_obj=2, n_constr=0, xl=0, xu=1)

    def _evaluate(self, x, out, *args, **kwargs):
        f1 = x[:, 0]
        g = 1 + 9 / 29 * np.sum(x[:, 1:], axis=1)
        f2 = g * (1 - np.sqrt(f1 / g))
        out["F"] = np.column_stack([f1, f2])

然后，设置算法参数和运行MOPSO算法：

problem = ZDT1()

algorithm = MOPSO(
    pop_size=100,
    sampling=get_sampling("real_random"),
    crossover=get_crossover("real_sbx", prob=0.9, eta=15),
    mutation=get_mutation("real_pm", prob=0.1),
    eliminate_duplicates=True
)

res = minimize(problem,
               algorithm,
               ('n_gen', 100),
               seed=1,
               verbose=True)

# 输出结果
print(res.X)
print(res.F)

最后，可以用散点图可视化结果：

plot = Scatter(title="MOPSO - ZDT1")
plot.add(res.F)
plot.show()

完整代码如下：

import numpy as np
from pymoo.model.problem import Problem
from pymoo.algorithms.mopso import MOPSO
from pymoo.factory import get_sampling, get_crossover, get_mutation
from pymoo.optimize import minimize
from pymoo.visualization.scatter import Scatter

class ZDT1(Problem):

    def __init__(self):
        super().__init__(n_var=30, n_obj=2, n_constr=0, xl=0, xu=1)

    def _evaluate(self, x, out, *args, **kwargs):
        f1 = x[:, 0]
        g = 1 + 9 / 29 * np.sum(x[:, 1:], axis=1)
        f2 = g * (1 - np.sqrt(f1 / g))
        out["F"] = np.column_stack([f1, f2])

problem = ZDT1()

algorithm = MOPSO(
    pop_size=100,
    sampling=get_sampling("real_random"),
    crossover=get_crossover("real_sbx", prob=0.9, eta=15),
    mutation=get_mutation("real_pm", prob=0.1),
    eliminate_duplicates=True
)

res = minimize(problem,
               algorithm,
               ('n_gen', 100),
               seed=1,
               verbose=True)

# 输出结果
print(res.X)
print(res.F)

# 可视化结果
plot = Scatter(title="MOPSO - ZDT1")
plot.add(res.F)
plot.show()

希望这个例子能够帮助你进行多目标粒子群算法的优化。