Python实现智能优化算法

介绍

智能优化算法是处理不可微和非凸优化问题的一种启发式算法，虽然不能得到精确的最优解，但是在概率意义下可以得到一个不错的近似解。

在Python中，实现智能优化算法主要依赖于mealpy包。

粒子群算法

例1

import mealpy
from mealpy.swarm_based import PSO
from mealpy.utils.space import FloatVar

# 定义一个要优化的目标函数，这里使用简单的 Rosenbrock 函数
def objective_function(x):
    return 100.0 * (x[0] - x[1] ** 2.0) ** 2.0 + (1 - x[1]) ** 2.0


# 定义问题的边界
problem = {
    "obj_func": objective_function,
    "bounds": FloatVar(lb=(-10.,) * 2, ub=(10.,) * 2, name="delta"),
    "minmax": "min",
}
# 创建 PSO 优化器实例
optimizer = PSO.OriginalPSO(epoch=100, pop_size=50)

# 运行优化过程
g_best = optimizer.solve(problem)

# 输出结果
print(f"最优位置: {g_best.solution}")
print(f"最优适应度: {g_best.target}")

例2

import numpy as np
from mealpy import FloatVar, PSO
def objective_function(solution):
    return np.sum(solution**2)

problem_dict = {
 "bounds": FloatVar(lb=(-10.,) * 30, ub=(10.,) * 30, name="delta"),
 "obj_func": objective_function,
 "minmax": "min",
}

model = PSO.OriginalPSO(epoch=1000, pop_size=50, c1=2.05, c2=2.5, w=0.4)
g_best = model.solve(problem_dict)
print(f"Solution: {g_best.solution}, Fitness: {g_best.target.fitness}")
print(f"Solution: {model.g_best.solution}, Fitness: {model.g_best.target.fitness}")

例3: 计算置信区间

import mealpy
from mealpy.swarm_based import PSO
from mealpy.utils.space import FloatVar

x = np.random.normal(loc=2.5, scale=1.3, size=100000)  

def objective_function(q):
    return q[1]-q[0]+(0.9-np.mean((q[0]<x) & (x<q[1])))*500


# 定义问题的边界
problem = {
    "obj_func": objective_function,
    "bounds": FloatVar(lb=(-100.,) * 2, ub=(100.,) * 2, name="delta"),
    "minmax": "min",
}
# 创建 PSO 优化器实例
optimizer = PSO.OriginalPSO(epoch=200, pop_size=50)

# 运行优化过程
g_best = optimizer.solve(problem )


# 输出结果
print(f"最优位置: {g_best.solution}")
print(f"最优适应度: {g_best.target}")