121 lines
5.0 KiB
Python
121 lines
5.0 KiB
Python
import random
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import numpy as np
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class NSGA2:
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def __init__(self, pop_size, objective_num):
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self.pop_size = pop_size
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self.objective_num = objective_num
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def fast_non_dominated_sort(self, objective_values):
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"""标准快速非支配排序实现"""
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pop_size = len(objective_values)
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domination_count = [0] * pop_size
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dominated_solutions = [[] for _ in range(pop_size)]
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ranks = [0] * pop_size
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front = [[]] # 第0层
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# 计算支配关系
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for p in range(pop_size):
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for q in range(pop_size):
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if p == q:
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continue
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# p支配q？
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if self._dominates(objective_values[p], objective_values[q]):
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dominated_solutions[p].append(q)
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# q支配p？
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elif self._dominates(objective_values[q], objective_values[p]):
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domination_count[p] += 1
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if domination_count[p] == 0:
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ranks[p] = 0
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front[0].append(p)
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# 处理后续层
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i = 0
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while len(front[i]) > 0:
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next_front = []
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for p in front[i]:
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for q in dominated_solutions[p]:
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domination_count[q] -= 1
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if domination_count[q] == 0:
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ranks[q] = i + 1
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next_front.append(q)
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i += 1
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front.append(next_front)
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return ranks, front[:-1] # 返回rank数组和各层front列表
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def _dominates(self, a, b):
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"""判断a是否支配b：a的所有目标≤b，且至少一个目标<b"""
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all_le = all(a[i] <= b[i] for i in range(self.objective_num))
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any_lt = any(a[i] < b[i] for i in range(self.objective_num))
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return all_le and any_lt
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def crowding_distance(self, objective_values, front):
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"""计算拥挤度"""
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pop_size = len(front)
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distance = [0.0] * pop_size
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if pop_size <= 1:
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return distance
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# 按每个目标排序
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for m in range(self.objective_num):
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sorted_indices = sorted(range(pop_size), key=lambda i: objective_values[front[i]][m])
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max_val = objective_values[front[sorted_indices[-1]]][m]
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min_val = objective_values[front[sorted_indices[0]]][m]
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if max_val - min_val == 0:
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continue
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# 边界点设为无穷大
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distance[sorted_indices[0]] = float('inf')
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distance[sorted_indices[-1]] = float('inf')
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# 中间点计算距离
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for i in range(1, pop_size - 1):
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distance[sorted_indices[i]] += (
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objective_values[front[sorted_indices[i + 1]]][m] -
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objective_values[front[sorted_indices[i - 1]]][m]
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) / (max_val - min_val)
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return distance
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def selection(self, population, objective_values):
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"""锦标赛选择（2选1）"""
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pop_size = len(population)
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ranks, _ = self.fast_non_dominated_sort(objective_values)
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distances = self._calculate_all_crowding_distances(objective_values, ranks)
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selected = []
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for _ in range(pop_size):
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i = random.randint(0, pop_size - 1)
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j = random.randint(0, pop_size - 1)
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if ranks[i] < ranks[j] or (ranks[i] == ranks[j] and distances[i] >= distances[j]):
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selected.append(population[i])
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else:
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selected.append(population[j])
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return np.array(selected)
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def _calculate_all_crowding_distances(self, objective_values, ranks):
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"""计算所有个体的拥挤度"""
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max_rank = max(ranks) if ranks else 0
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all_distances = [0.0] * len(objective_values)
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for r in range(max_rank + 1):
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front = [i for i in range(len(objective_values)) if ranks[i] == r]
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if len(front) <= 1:
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for i in front:
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all_distances[i] = float('inf')
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continue
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distances = self.crowding_distance(objective_values, front)
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for i, idx in enumerate(front):
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all_distances[idx] = distances[i]
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return all_distances
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def environmental_selection(self, population, objective_values):
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"""环境选择：从合并种群中选择pop_size个个体"""
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ranks, fronts = self.fast_non_dominated_sort(objective_values)
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selected = []
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for front in fronts:
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if len(selected) + len(front) <= self.pop_size:
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selected.extend(front)
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else:
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# 计算当前front的拥挤度，选择剩余数量的个体
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distances = self.crowding_distance(objective_values, front)
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sorted_front = [x for _, x in sorted(zip(distances, front), reverse=True)]
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selected.extend(sorted_front[:self.pop_size - len(selected)])
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break
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return population[selected], [objective_values[i] for i in selected] |