多目标进化算法——NSGA-II（python实现）

以下是一个简化的NSGA-II算法的Python实现示例，仅包含核心函数，不包含完整的GA包装。

import numpy as np
 
def fast_non_dominated_sort(fitnesses):
    front = {}
    S = np.array(fitnesses)
    n = len(S)
    rank = np.zeros(n)
    S_rank = np.argsort(S, axis=0)
    n_sorted = np.arange(n)
 
    # Assign a constant rank to every solution
    front[0] = np.array(n_sorted, dtype=int)
 
    # Assign a rank to solutions
    for i in range(n):
        for j in range(i+1, n):
            if np.any(S[S_rank[i]] < S[S_rank[j]]):
                rank[S_rank[j]] += 1
            elif np.any(S[S_rank[i]] > S[S_rank[j]]):
                rank[S_rank[i]] += 1
        if rank[S_rank[i]] not in front:
            front[rank[S_rank[i]]] = np.array([S_rank[i]], dtype=int)
 
    # Assign a front number to solutions
    for i in range(n):
        front[rank[i]] = np.union1d(front[rank[i]], i)
 
    return front
 
def crowding_distance_assignment(fitnesses, front):
    n = len(fitnesses)
    crowding_distance = np.zeros(n)
 
    for i in front:
        # Assign crowding distance to the Pareto front
        sorted_front = np.sort(fitnesses[front[i]], axis=0)
        crowding_distance[front[i]] = np.linspace(1, 0, len(front[i]))
 
    return crowding_distance
 
def truncation_selection(population, n):
    front = fast_non_dominated_sort(population)
    crowding_distance = crowding_distance_assignment(population, front)
 
    # Rank solutions by their crowding distance
    sorted_crowding_distance = np.argsort(crowding_distance)
    selected = []
 
    for i in range(n):
        selected.append(sorted_crowding_distance[i])
 
    return selected
 
# 示例使用
population = np.random.rand(100, 2)  # 假设有100个个体，每个个体有2个适应度值
selected_indices = truncation_selection(population, 10)  # 选择10个个体
selected_population = population[selected_indices]
 
# 输出选择后的种群
print(selected_population)

这段代码首先定义了一个快速非支配排序函数fast_non_dominated_sort，该函数用于找到Pareto前沿。然后定义了一个染色距离分配函数crowding_distance_assignment，该函数用于计算Pareto前沿中每个个体的染色距离。最后定义了一个截断选择函数truncation_selection，该函数结合了上述两个函数，用于从种群中选择适当数量的个体。

这个实现没有提供完整的NSGA-II算法，因为它依赖于其他部分，如变异和交叉操作。但是，它提供了一个清晰的起点，用于理解和实现NSGA-II的其余部分。