不吹不黑，这个算法，你肯定不会("揭秘独特算法：不吹不黑，你未必掌握的技巧")

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ithorizon 7个月前 (10-21) 阅读数 25 #后端开发

揭秘独特算法：不吹不黑，你未必掌握的技巧

一、引言

在编程和算法的世界里，总有一些独特的算法让人眼前一亮。这些算法或许并不广为人知，但它们在特定场景下却有着出色的表现。今天，就让我们揭开这些独特算法的神秘面纱，了解它们背后的原理和技巧。

二、遗传算法：大自然的智慧

遗传算法是一种模拟自然界生物进化的计算模型。它通过模拟生物的遗传、变异和自然选择等过程，寻找问题的最优解。

2.1 基本原理

遗传算法核心包括以下步骤：

初始化种群：随机生成一组问题的候选解作为初始种群。

适应度评估：计算每个个体的适应度，即解的质量。

选择操作：按照适应度选择优秀的个体进行交叉和变异。

交叉操作：将两个个体的部分基因进行交换，生成新的个体。

变异操作：随机改变个体的一部分基因。

终止条件：约为最大迭代次数或适应度不再节约时停止。

2.2 应用实例：旅行商问题（TSP）

旅行商问题是一个经典的优化问题，要求在给定的城市列表中找到一条最短路径，让每个城市只访问一次。下面是一个简洁的遗传算法解决TSP问题的示例代码：


def create_route(city_list):
    route = random.sample(city_list, len(city_list))
    return route
def initial_population(pop_size, city_list):
    population = []
    for _ in range(0, pop_size):
        population.append(create_route(city_list))
    return population
def calculate_distance(route):
    distance = 0
    for i in range(len(route)):
        from_city = route[i]
        to_city = None
        if i + 1 < len(route):
            to_city = route[i + 1]
        else:
            to_city = route[0]
        distance += from_city.distance(to_city)
    return distance
def rank_routes(population):
    fitness_results = {}
    for i, route in enumerate(population):
        fitness_results[i] = 1 / calculate_distance(route)
    return sorted(fitness_results.items(), key=lambda x: x[1], reverse=True)
def selection(pop_ranked, elite_size):
    selection_results = []
    df = sum([item[1] for item in pop_ranked])
    relative_fitness = [item[1] / df for item in pop_ranked]
    cumulative_sum = numpy.cumsum(relative_fitness)
    for i in range(0, elite_size):
        selection_results.append(pop_ranked[i][0])
    for _ in range(0, len(pop_ranked) - elite_size):
        pick = random.random()
        for i, individual in enumerate(pop_ranked):
            if cumulative_sum[i] > pick:
                selection_results.append(individual[0])
                break
    return selection_results
def mating_pool(population, selection_results):
    pool = []
    for i in range(0, len(selection_results)):
        index = selection_results[i]
        pool.append(population[index])
    return pool
def breed(parent1, parent2):
    child_p1 = []
    child_p2 = []
    
    gene_a = int(random.random() * len(parent1))
    gene_b = int(random.random() * len(parent1))
    
    start_gene = min(gene_a, gene_b)
    end_gene = max(gene_a, gene_b)
    for i in range(start_gene, end_gene):
        child_p1.append(parent1[i])
        
    child_p2 = [item for item in parent2 if item not in child_p1]
    child = child_p1 + child_p2
    return child
def breed_population(matingpool, elite_size):
    children = []
    length = len(matingpool) - elite_size
    pool = random.sample(matingpool, len(matingpool))
    for i in range(0, elite_size):
        children.append(matingpool[i])
        
    for i in range(0, length):
        child = breed(pool[i], pool[len(matingpool)-i-1])
        children.append(child)
    return children
def mutate(individual, mutation_rate):
    for swapped in range(len(individual)):
        if(random.random() < mutation_rate):
            swap_with = int(random.random() * len(individual))
            
            city1 = individual[swapped]
            city2 = individual[swap_with]
            
            individual[swapped] = city2
            individual[swap_with] = city1
    return individual
def mutate_population(population, mutation_rate):
    mutated_pop = []
    
    for ind in range(0, len(population)):
        mutated_ind = mutate(population[ind], mutation_rate)
        mutated_pop.append(mutated_ind)
    return mutated_pop
def next_generation(current_gen, elite_size, mutation_rate):
    pop_ranked = rank_routes(current_gen)
    selection_results = selection(pop_ranked, elite_size)
    matingpool = mating_pool(current_gen, selection_results)
    children = breed_population(matingpool, elite_size)
    next_gen = mutate_population(children, mutation_rate)
    return next_gen
def genetic_algorithm(population, pop_size, elite_size, mutation_rate, generations):
    pop = initial_population(pop_size, population)
    print("Initial distance: " + str(1 / rank_routes(pop)[0][1]))
    
    for i in range(0, generations):
        pop = next_generation(pop, elite_size, mutation_rate)
    
    print("Final distance: " + str(1 / rank_routes(pop)[0][1]))
    best_route_index = rank_routes(pop)[0][0]
    best_route = pop[best_route_index]
    return best_route

三、模拟退火算法：物理学的启示

模拟退火算法是一种以物理学中退火过程为启发源的优化算法。它通过模拟固体材料的退火过程，寻找问题的全局最优解。

3.1 基本原理

模拟退火算法核心包括以下步骤：

初始化：随机选择一个解作为当前解。

迭代：在当前解的邻域内随机选择一个新解。

接受准则：判断新解是否被接受。如果新解更优，则接受；否则，以一定概率接受。

降温：逐渐降低系统温度，以减小接受较差解的概率。

终止条件：约为最大迭代次数或系统温度降至预定值时停止。

3.2 应用实例：连续函数优化

下面是一个简洁的模拟退火算法解决连续函数优化的示例代码：


import math
import random
def simulated_annealing(objective, initial_temp, final_temp, cooling_rate):
    current_temp = initial_temp
    current_solution = random.uniform(-10, 10)
    current_value = objective(current_solution)
    
    while current_temp > final_temp:
        next_solution = random.uniform(-10, 10)
        next_value = objective(next_solution)
        
        if next_value < current_value:
            current_solution = next_solution
            current_value = next_value
        else:
            probability = math.exp((next_value - current_value) / current_temp)
            if random.random() < probability:
                current_solution = next_solution
                current_value = next_value
        
        current_temp *= (1 - cooling_rate)
    
    return current_solution, current_value
def objective(x):
    return x**2 + 4*x + 4
initial_temp = 10000
final_temp = 1
cooling_rate = 0.01
solution, value = simulated_annealing(objective, initial_temp, final_temp, cooling_rate)
print(f"Optimal solution: {solution}, Optimal value: {value}")