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import numpy as np
import time
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']
plt.rcParams['axes.unicode_minus'] = False
def func_double_well(matrix_y):
y = 0
l, k, h = 3.0, 0.5, 20.0
for i in matrix_y:
y += h * pow((pow(i, 2) - pow(l, 2)), 2) / pow(l, 4) + k * i
return y
def func_rastrigin(matrix_y):
y = 10 * len(matrix_y)
y += np.sum(matrix_y**2 - 10 * np.cos(2 * np.pi * matrix_y))
return y
def func_griewank(matrix_y):
a, b, y = 0, 1, 0
index = 1
for i in matrix_y:
a = a + i * i
b = b * np.cos(i / np.sqrt(index))
index += 1
y = 1 + 1 / 4000 * a - b
return y
def max_min_id(matrix, flag, func_to_use):
if matrix.shape[1] == 0:
return -1
walker_id = 0
temp = func_to_use(matrix[:, 0])
for j in range(matrix.shape[1] - 1):
if temp < func_to_use(matrix[:, j + 1]) and flag == 0:
walker_id = j + 1
temp = func_to_use(matrix[:, j + 1])
if temp > func_to_use(matrix[:, j + 1]) and flag == 1:
walker_id = j + 1
temp = func_to_use(matrix[:, j + 1])
return walker_id
def mid_exchange(matrix, func_to_use):
mid_walker = np.mean(matrix, axis=1)
worst_id = max_min_id(matrix, 0, func_to_use)
matrix[:, worst_id] = mid_walker
return matrix
def qda_original_record(dim, walker_n, func_to_use, max_total_iter):
acc = 1e-6
ite_times = 0
begin, end = -6, 6
scale = end - begin
a = np.random.uniform(begin, end, (dim, walker_n))
b = np.zeros((dim, walker_n))
ite_flag = True
convergence_data = []
while scale > acc and ite_times < max_total_iter:
while ite_flag and ite_times < max_total_iter:
ite_times += 1
for j in range(walker_n):
for i in range(dim):
b[i, j] = np.random.normal(a[i, j], scale)
while not (begin <= b[i, j] <= end):
b[i, j] = np.random.normal(a[i, j], scale)
if func_to_use(b[:, j]) > func_to_use(a[:, j]):
b[:, j] = a[:, j]
mid_exchange(b, func_to_use)
a[:, :] = b[:, :]
min_val = func_to_use(a[:, max_min_id(a, 1, func_to_use)])
convergence_data.append(min_val)
ite_flag = False
for i in range(dim):
if np.var(a[i, :]) > pow(scale, 2):
ite_flag = True
scale /= 2
ite_flag = True
return convergence_data
def qda_diff_accept_record(dim, walker_n, func_to_use, max_total_iter):
acc = 1e-6
ite_times = 0
begin, end = -6, 6
scale = end - begin
a = np.random.uniform(begin, end, (dim, walker_n))
b = np.zeros((dim, walker_n))
ite_flag = True
convergence_data = []
while scale > acc and ite_times < max_total_iter:
while ite_flag and ite_times < max_total_iter:
ite_times += 1
for j in range(walker_n):
old_fitness = func_to_use(a[:, j])
for i in range(dim):
b[i, j] = np.random.normal(a[i, j], scale)
while not (begin <= b[i, j] <= end):
b[i, j] = np.random.normal(a[i, j], scale)
new_fitness = func_to_use(b[:, j])
if new_fitness > old_fitness:
acceptance_prob = 1.0 / (ite_times)
if np.random.rand() >= acceptance_prob:
b[:, j] = a[:, j]
mid_exchange(b, func_to_use)
a[:, :] = b[:, :]
min_val = func_to_use(a[:, max_min_id(a, 1, func_to_use)])
convergence_data.append(min_val)
ite_flag = False
for i in range(dim):
if np.var(a[i, :]) > pow(scale, 2):
ite_flag = True
scale /= 2
ite_flag = True
return convergence_data
def plot_multi_dim(dim_list, walker_n, func_to_use, func_name, num_runs, max_total_iter):
print(f"--- QDA 算法对比测试 ---")
print(f"目标函数: {func_name}")
print(f"种群数: {walker_n}")
print(f"每组运行次数: {num_runs}")
print(f"最大迭代次数: {max_total_iter}")
for dim in dim_list:
print(f"--- 维度: {dim}D ---")
print("-" * 25)
n = len(dim_list)
rows = (n + 1) // 2
plt.figure(figsize=(15, 6 * rows))
for i, dim in enumerate(dim_list):
start_time = time.time()
standard_runs = [qda_original_record(dim, walker_n, func_to_use, max_total_iter) for _ in range(num_runs)]
optimized_runs = [qda_diff_accept_record(dim, walker_n, func_to_use, max_total_iter) for _ in range(num_runs)]
end_time = time.time()
print(f"维度 {dim}D 测试完成，耗时: {end_time - start_time:.2f} 秒")
max_len = max_total_iter
standard_padded = np.array([run + [run[-1]] * (max_len - len(run)) for run in standard_runs])
optimized_padded = np.array([run + [run[-1]] * (max_len - len(run)) for run in optimized_runs])
if len(standard_padded) == 0 or len(optimized_padded) == 0:
print(f"警告：维度 {dim}D 的收敛数据点过少，无法绘制有意义的曲线。")
continue
avg_orig = np.mean(standard_padded, axis=0)
avg_diff = np.mean(optimized_padded, axis=0)
x_axis = np.arange(len(avg_orig))
ax = plt.subplot(rows, 2, i + 1)
ax.plot(x_axis, avg_orig, label="标准版", color='blue', linewidth=2)
ax.plot(x_axis, avg_diff, '--', label="优化版", color='red', linewidth=2)
ax.set_title(f"维度: {dim}D", fontsize=14)
ax.set_xlabel("迭代次数", fontsize=12)
ax.set_ylabel("平均最优函数值", fontsize=12)
all_values = np.concatenate((avg_orig, avg_diff))
if np.all(all_values > 0):
ax.set_yscale('log')
ax.grid(True, linestyle=':', alpha=0.6)
ax.legend(loc='upper right', fontsize=10)
plt.suptitle(f"QDA 算法收敛曲线对比 ({func_name})", fontsize=20)
plt.tight_layout(rect=[0, 0, 1, 0.96])
plt.show()
if __name__ == "__main__":
test_dimensions = [2, 5, 10, 20, 30]
test_walker_n = 50
test_func = func_rastrigin
test_func_name = "rastrigin"
num_runs = 10
max_total_iter = 100000
plot_multi_dim(test_dimensions, test_walker_n, test_func, test_func_name, num_runs, max_total_iter)
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