アニーリング法のPython実装

参考文献

しっかり学ぶ数理最適化　モデルからアルゴリズムまで
梅谷俊治・著
発行 2020/10/23

準備

オンラインコンパイラを使用します。

ソースコード

sample.py

# -*- coding: utf-8 -*-
import numpy as np
import math
import random

def objective(x):
    return 2 * np.sin(x) + 3 * np.cos(2 * x) + 5 * np.sin(2 / 3 * x)

def acceptance_probability(old_cost, new_cost, temperature):
    if new_cost < old_cost:
        return 1.0
    else:
        return math.exp((old_cost - new_cost) / temperature)

def simulated_annealing(objective, initial_state, initial_temperature, cooling_rate, min_temperature, num_iterations):
    current_state = initial_state
    current_cost = objective(current_state)

    best_state = current_state
    best_cost = current_cost

    temperature = initial_temperature

    for i in range(num_iterations):
        new_state = current_state + np.random.uniform(-0.1, 0.1)
        new_cost = objective(new_state)

        if acceptance_probability(current_cost, new_cost, temperature) > random.random():
            current_state = new_state
            current_cost = new_cost

        if new_cost < best_cost:
            best_state = new_state
            best_cost = new_cost

        temperature *= cooling_rate
        if temperature < min_temperature:
            break

    return best_state, best_cost

# パラメータの設定
initial_state = 0.0
initial_temperature = 100
cooling_rate = 0.9999
min_temperature = 0.01
num_iterations = 100000

# 最適化の実行
best_state, best_cost = simulated_annealing(objective, initial_state, initial_temperature, cooling_rate, min_temperature, num_iterations)

print("Best state:", best_state)
print("Best cost:", best_cost)