common_optimization_algorithm_ai.py

import math
import random

# Initial state: a random number between 0 and 2π
def initial_state():
    return random.uniform(0, 2*math.pi)

# Neighbor: a new state very close to the current one
def neighbor(state):
    new_state = state + random.gauss(0, 0.1)
    return new_state % (2*math.pi)  # Ensure state is within [0, 2π]

# Evaluation: the value of the sine function (our objective)
def evaluation(state):
    return math.sin(state)

# Temperature: Starts high and decreases over time. We're using a linear schedule here.
def temperature(t, max_iter):
    return max_iter / t

def simulated_annealing(max_iter):
    current = initial_state()

    for t in range(1, max_iter + 1):
        T = temperature(t, max_iter)
        next_neighbor = neighbor(current)
        deltaE = evaluation(next_neighbor) - evaluation(current)
        
        if deltaE > 0:
            current = next_neighbor
        elif random.uniform(0, 1) < math.exp(deltaE / T):
            current = next_neighbor

    return current, math.sin(current)

result_state, result_value = simulated_annealing(1000000)
print(f"The maximum value is {result_value} and it occurs at {result_state}.")