锦标赛选择（Genetic Algorithm）

锦标赛选择是遗传算法的一种选择算子，其基本思路是在每一代中将种群中的个体随机分成若干个小组进行比较，然后从每个小组中选择适应度最高的个体存活并参与繁殖。这种方法的优点在于能够有效地保留优良基因，缓解早熟收敛问题。

算法流程

1. 将种群中的个体随机分成若干个小组。
2. 对于每个小组，选择适应度最高的个体参与下一代的繁殖。
3. 将选择出来的个体复制并交叉变异产生下一代个体，更新整个种群。

代码实现

def tournament_selection(population, fitness, tournament_size):
    """
    tournament selection operator for genetic algorithm
    :param population: current population
    :param fitness: fitness function to evaluate population
    :param tournament_size: size of each tournament
    :return: selected population
    """
    selected_pop = []
    pop_size = len(population)

    for i in range(pop_size):
        candidates = random.sample(list(range(pop_size)), tournament_size)
        selected = min(candidates, key=lambda j: fitness(population[j]))
        selected_pop.append(population[selected])

    return selected_pop

参数说明

• population：种群
• fitness：适应度函数
• tournament_size：每个小组的大小

示例

population = [Individual(i) for i in range(10)]
selected_pop = tournament_selection(population, lambda x: x.fitness(), 3)

参考文献

• Goldberg, D. E. (1989). Genetic algorithms in search, optimization & machine learning. Addison-Wesley.
• Back, T. (1996). Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press.