最优化方法用Python

Question

用python随机生成100组区间，用0.618法和抛物线法计算

Answer 1

m0_69473531 晚上好🌙🌙🌙
本答案参考ChatGPT-3.5

解决方案：

1. 导入必要的库

import numpy as np
import random

1. 生成100组随机区间

intervals = []
for _ in range(100):
    start = random.randint(0, 100)
    end = random.randint(start, 100)
    intervals.append((start, end))

1. 定义0.618法函数

def golden_section_search(intervals, func):
    alpha = 0.618  # 黄金分割比例
    epsilon = 0.0001  # 误差范围

    results = []
    for interval in intervals:
        a, b = interval
        x1 = a + (1 - alpha) * (b - a)
        x2 = a + alpha * (b - a)

        while abs(b - a) > epsilon:
            if func(x1) < func(x2):
                b = x2
                x2 = x1
                x1 = a + (1 - alpha) * (b - a)
            else:
                a = x1
                x1 = x2
                x2 = a + alpha * (b - a)
        results.append((a + b) / 2)
    
    return results

1. 定义抛物线法函数

def quadratic_interpolation(intervals, func):
    results = []
    for interval in intervals:
        a, b = interval
        x1 = a
        x2 = b
        x3 = (x1 + x2) / 2

        while abs((x3 - x1) / x3) >= 0.0001:
            f1 = func(x1)
            f2 = func(x2)
            f3 = func(x3)

            numerator = (x2**2 - x3**2) * f1 + (x3**2 - x1**2) * f2 + (x1**2 - x2**2) * f3
            denominator = (x2 - x3) * f1 + (x3 - x1) * f2 + (x1 - x2) * f3

            x = 1/2 * numerator / denominator
            fx = func(x)

            if x > x3:
                if fx > f3:
                    x2 = x
                else:
                    x1 = x3
                    x3 = x
            else:
                if fx > f3:
                    x1 = x
                else:
                    x2 = x3
                    x3 = x
        results.append(x3)
    
    return results

1. 定义目标函数（示例使用二次函数）

def target_func(x):
    return 2 * x**2 - 3 * x + 1

1. 调用0.618法和抛物线法函数并打印结果

results_0_618 = golden_section_search(intervals, target_func)
results_parabolic = quadratic_interpolation(intervals, target_func)

print("0.618法结果:", results_0_618)
print("抛物线法结果:", results_parabolic)

希望以上解决方案对你有帮助。