ADVANCED ALGORITHMS - ADVANCED TECHNIQUES:Local Search

def hill_climbing(initial_solution, neighbors, objective):
    """Hill climbing algorithm"""
    current = initial_solution
    current_value = objective(current)
    
    while True:
        best_neighbor = None
        best_value = current_value
        
        for neighbor in neighbors(current):
            value = objective(neighbor)
            if value > best_value:
                best_neighbor = neighbor
                best_value = value
        
        if best_neighbor is None:
            break  # Local optimum
        
        current = best_neighbor
        current_value = best_value
    
    return current

import random
import math

def simulated_annealing(initial, neighbors, objective, temp, cooling):
    """Simulated annealing"""
    current = initial
    current_value = objective(current)
    best = current
    best_value = current_value
    
    while temp > 0.1:
        neighbor = random.choice(neighbors(current))
        neighbor_value = objective(neighbor)
        
        delta = neighbor_value - current_value
        
        if delta > 0 or random.random() < math.exp(delta / temp):
            current = neighbor
            current_value = neighbor_value
            
            if current_value > best_value:
                best = current
                best_value = current_value
        
        temp *= cooling
    
    return best