ZDT2 - NSGA2 by pxc

NSGA2.py

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+import math
+import random
+import matplotlib.pyplot as plt
+import copy
+
+
+# 用的是ZDT2测试函数
+
+# First function to optimize
+def function1(x):
+    return x[0]
+
+
+# Second function to optimize
+def function2(x):
+    gx = funcationG(x)
+    value = 1 - (x[0] / gx) ** 2
+    return gx * value
+
+
+def funcationG(x):
+    sumX = 0
+    for i in range(1, varNum):
+        sumX = sumX + x[i]
+    return 1 + (9 * sumX) / (varNum - 1)
+
+
+# Function to find index of list
+def index_of(a, list):
+    for i in range(0, len(list)):
+        if list[i] == a:
+            return i
+    return -1
+
+
+# Function to sort by values
+def sort_by_values(list1, values):
+    sorted_list = []
+    while (len(sorted_list) != len(list1)):
+        if index_of(min(values), values) in list1:
+            sorted_list.append(index_of(min(values), values))
+        values[index_of(min(values), values)] = math.inf
+    return sorted_list
+
+
+# Function to carry out NSGA-II's fast non dominated sort
+def fast_non_dominated_sort(values1, values2):
+    S = [[] for i in range(0, len(values1))]  # 解所支配的集合
+    front = [[]]  # 排序结果
+    n = [0 for i in range(0, len(values1))]  # 支配者数量
+    rank = [0 for i in range(0, len(values1))]
+
+    for p in range(0, len(values1)):
+        S[p] = []
+        n[p] = 0
+        for q in range(0, len(values1)):
+            if (values1[p] < values1[q] and values2[p] < values2[q]) or (
+                    values1[p] <= values1[q] and values2[p] < values2[q]) or (
+                    values1[p] < values1[q] and values2[p] <= values2[q]):
+                if q not in S[p]:
+                    S[p].append(q)
+            elif (values1[q] < values1[p] and values2[q] < values2[p]) or (
+                    values1[q] <= values1[p] and values2[q] < values2[p]) or (
+                    values1[q] < values1[p] and values2[q] <= values2[p]):
+                n[p] = n[p] + 1
+        if n[p] == 0:
+            rank[p] = 0
+            if p not in front[0]:
+                front[0].append(p)
+
+    i = 0
+    while (front[i] != []):
+        Q = []
+        for p in front[i]:
+            for q in S[p]:
+                n[q] = n[q] - 1
+                if (n[q] == 0):
+                    rank[q] = i + 1
+                    if q not in Q:
+                        Q.append(q)
+        i = i + 1
+        front.append(Q)
+
+    del front[len(front) - 1]
+    return front
+
+
+# Function to calculate crowding distance 拥挤度距离计算
+def crowding_distance(values1, values2, front):
+    distance = [0 for i in range(0, len(front))]
+
+    sorted1 = sort_by_values(front, values1[:])
+    sorted2 = sort_by_values(front, values2[:])
+
+    distance[0] = math.inf
+    distance[len(front) - 1] = math.inf
+
+    for k in range(1, len(front) - 1):
+        distance[k] = distance[k] + (values1[sorted1[k + 1]] - values1[sorted1[k - 1]]) / (max(values1) - min(values1))
+
+    for k in range(1, len(front) - 1):
+        distance[k] = distance[k] + (values2[sorted2[k + 1]] - values2[sorted2[k - 1]]) / (max(values2) - min(values2))
+
+    return distance
+
+
+# 二进制交叉
+def crossover(individuala, individualb, a, b):
+    individual1 = copy.deepcopy(individuala)
+    individual2 = copy.deepcopy(individualb)
+
+    for j in range(min(a, b), max(a, b) + 1):
+        u = random.random()
+        if u < 0.5:
+            r = (2 * u) ** (1 / (NC + 1))
+        else:
+            r = (1 / (2 * (1 - u))) ** (1 / (NC + 1))
+        individual1[j] = 0.5 * ((1 + r) * individual1[j] + (1 - r) * individual2[j])
+        individual2[j] = 0.5 * ((1 - r) * individual1[j] + (1 + r) * individual2[j])
+
+        individual1[j] = 1 if individual1[j] > 1 else individual1[j]  # 此处需要修改为常量
+        individual2[j] = 1 if individual2[j] > 1 else individual2[j]
+
+        individual1[j] = 0 if individual1[j] < 0 else individual1[j]
+        individual2[j] = 0 if individual2[j] < 0 else individual2[j]
+    return individual1, individual2
+
+
+# 多项式变异
+def mutation(individual, a):
+    individualTemp = copy.deepcopy(individual)
+    u = random.random()
+    if u < 0.5:
+        r = (2 * u) ** (1 / (NM + 1)) - 1
+    else:
+        r = (1 - (2 * (1 - u))) ** (1 / (NM + 1))
+
+    individualTemp[a] = individualTemp[a] + r
+
+    individualTemp[a] = 1 if individualTemp[a] > 1 else individualTemp[a]  # 此处需要修改为常量
+    individualTemp[a] = 0 if individualTemp[a] < 0 else individualTemp[a]
+    return individualTemp
+
+
+# 使用此函数之前要确保非支配排序解中都按照拥挤度排序过了
+def competition(non_dominated_sorted, numOfSelect):
+    selectionResult = []
+    non_dominated_sortedTemp = []
+    for i in range(0, len(non_dominated_sorted)):
+        for j in range(0, len(non_dominated_sorted[i])):
+            non_dominated_sortedTemp.append(non_dominated_sorted[i][j])
+
+    while len(selectionResult) < numOfSelect:
+        selections = [random.randint(0, popSize - 1) for i in range(0, popSize // 2)]
+        selectionResult.append(non_dominated_sortedTemp[min(selections)])
+
+    return selectionResult
+
+
+min_x = 0
+max_x = 1  # x1 属于[0,1]
+varNum = 30  # xi 中i的最大个数
+popSize = 100  # 种群个数
+max_gen = 500  # 最大迭代次数
+pc = 0.9  # 交叉
+pm = 0.01  # 变异
+NC = 20
+NM = 20
+
+# 初始化种群
+solution = []
+for i in range(0, popSize):
+    solution.append([random.random() for j in range(0, varNum)])
+
+times = 0
+non_dominated_sorted_solution = []
+function1_values = []
+function2_values = []
+
+while times < max_gen:
+    # 计算种群中，每个个体的两个目标函数值
+    function1_values = [function1(solution[i]) for i in range(0, popSize)]
+    function2_values = [function2(solution[i]) for i in range(0, popSize)]
+
+    # 快速非支配排序
+    non_dominated_sorted_solution = fast_non_dominated_sort(function1_values[:], function2_values[:])
+
+    # 计算拥挤度
+    crowding_distance_values = []
+    for i in range(0, len(non_dominated_sorted_solution)):
+        crowding_distance_values.append(
+            crowding_distance(function1_values[:], function2_values[:], non_dominated_sorted_solution[i][:]))
+
+    # 按照拥挤度排序
+    for i in range(0, len(non_dominated_sorted_solution)):
+        non_dominated_sorted_solution2_1 = [
+            index_of(non_dominated_sorted_solution[i][j], non_dominated_sorted_solution[i]) for j in
+            range(0, len(non_dominated_sorted_solution[i]))]
+        front22 = sort_by_values(non_dominated_sorted_solution2_1[:], crowding_distance_values[i][:])  # 按照拥挤度排序
+        non_dominated_sorted_solution[i] = [non_dominated_sorted_solution[i][front22[j]] for j in
+                                            range(0, len(non_dominated_sorted_solution[i]))]
+        non_dominated_sorted_solution[i].reverse()  # 翻转之后是从大到小排序，拥挤度
+
+    solution2 = copy.deepcopy(solution)
+
+    # 竞标赛选取
+    offSpring = competition(non_dominated_sorted_solution, popSize)
+    # 交叉
+    for i in range(0, len(offSpring) // 2):
+        rc = random.random()
+        if (rc < pc):
+            index1 = random.randint(0, varNum - 1)
+            index2 = random.randint(0, varNum - 1)
+            while index1 == index2:
+                index1 = random.randint(0, varNum - 1)
+            indi1, indi2 = crossover(solution[offSpring[i]], solution[offSpring[len(offSpring) - i - 1]], index1,
+                                     index2)
+            solution2.append(indi1)
+            solution2.append(indi2)
+    # 变异
+    for i in range(0, len(offSpring)):
+        rm = random.random()
+        if rm < pm:
+            indexOfM = random.randint(0, varNum - 1)
+            muIndi = mutation(solution[offSpring[i]], indexOfM)
+            solution2.append(muIndi)
+
+    # 计算函数值
+    lengthOfSolution2 = len(solution2)
+    function1_values2 = [function1(solution2[i]) for i in range(0, lengthOfSolution2)]
+    function2_values2 = [function2(solution2[i]) for i in range(0, lengthOfSolution2)]
+
+    # 非支配快速排序
+    non_dominated_sorted_solution2 = fast_non_dominated_sort(function1_values2[:], function2_values2[:])
+
+    # 计算拥挤度
+    crowding_distance_values2 = []
+    for i in range(0, len(non_dominated_sorted_solution2)):
+        crowding_distance_values2.append(
+            crowding_distance(function1_values2[:], function2_values2[:], non_dominated_sorted_solution2[i][:]))
+
+    # 产生新的种群
+    new_solution = []
+    for i in range(0, len(non_dominated_sorted_solution2)):
+        non_dominated_sorted_solution2_1 = [
+            index_of(non_dominated_sorted_solution2[i][j], non_dominated_sorted_solution2[i]) for j in
+            range(0, len(non_dominated_sorted_solution2[i]))]
+        front22 = sort_by_values(non_dominated_sorted_solution2_1[:], crowding_distance_values2[i][:])  # 按照拥挤度排序
+        front = [non_dominated_sorted_solution2[i][front22[j]] for j in
+                 range(0, len(non_dominated_sorted_solution2[i]))]
+        front.reverse()  # 翻转之后是从大到小排序，拥挤度
+        for value in front:
+            new_solution.append(value)
+            if (len(new_solution) == popSize):
+                break
+        if (len(new_solution) == popSize):
+            break
+    solution = [solution2[i] for i in new_solution]
+    times = times + 1
+    print('This is ', times, '\n')
+
+# Lets plot the final front now
+minF1 = []
+minF2 = []
+for k in non_dominated_sorted_solution[0]:
+    minF1.append(function1_values[k])
+    minF2.append(function2_values[k])
+
+# 打印第一层
+print("The best front for Generation number ", times, " is")
+for valuez in non_dominated_sorted_solution[0]:
+    print(solution[valuez:], end=" ")
+print("\n")
+
+plt.xlabel('F 1', fontsize=15)
+plt.ylabel('F 2', fontsize=15)
+plt.scatter(minF1, minF2)
+plt.show()