{"id":75777,"date":"2026-02-13T07:05:52","date_gmt":"2026-02-12T23:05:52","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75777.html"},"modified":"2026-02-13T07:05:52","modified_gmt":"2026-02-12T23:05:52","slug":"%e6%a8%a1%e6%8b%9f%e9%80%80%e7%81%absa","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75777.html","title":{"rendered":"\u6a21\u62df\u9000\u706bSA"},"content":{"rendered":"

1.\u57fa\u672c\u539f\u7406<\/p>\n

(1) \u521d\u59cb\u5316：\u8bbe\u5b9a\u521d\u59cb\u89e3（\u5f85\u4f18\u5316\u53d8\u91cf\u7684\u521d\u59cb\u503c）\u3001\u521d\u59cb\u9ad8\u6e29（\u5982 100）\u3001\u6e29\u5ea6\u8870\u51cf\u7387（\u5982 0.99）\u3001\u7ec8\u6b62\u6e29\u5ea6（\u5982 1e-8），\u8ba1\u7b97\u521d\u59cb\u89e3\u7684\u76ee\u6807\u51fd\u6570\u503c（\u201c\u80fd\u91cf\u201d），\u5e76\u8bb0\u5f55\u4e3a\u5f53\u524d\u6700\u4f18\u89e3\u3002<\/p>\n

(2)\u8fed\u4ee3\u964d\u6e29：\u5728\u5f53\u524d\u6e29\u5ea6\u4e0b，\u5bf9\u5f53\u524d\u89e3\u505a\u968f\u673a\u6270\u52a8\u751f\u6210\u65b0\u89e3，\u8ba1\u7b97\u65b0\u89e3\u7684\u80fd\u91cf，\u5f97\u5230\u80fd\u91cf\u5dee\u503c（\u65b0\u89e3 – \u5f53\u524d\u89e3）\u3002<\/p>\n

(3)Metropolis \u51c6\u5219（\u63a5\u53d7\u65b0\u89e3）：\u82e5\u65b0\u89e3\u66f4\u4f18（\u80fd\u91cf\u66f4\u5c0f）：\u76f4\u63a5\u63a5\u53d7\u65b0\u89e3，\u66f4\u65b0\u5f53\u524d\u89e3；
\n\u82e5\u65b0\u89e3\u66f4\u5dee：\u4ee5\u6982\u7387\u00a0e =exp(\u2212\u0394E\/T) \u63a5\u53d7（T \u4e3a\u5f53\u524d\u6e29\u5ea6，\u0394E \u4e3a\u80fd\u91cf\u5dee），\u6e29\u5ea6\u8d8a\u9ad8，\u63a5\u53d7\u5dee\u89e3\u7684\u6982\u7387\u8d8a\u5927\u3002<\/p>\n

(4)\u66f4\u65b0\u6700\u4f18\u89e3：\u82e5\u5f53\u524d\u89e3\u4f18\u4e8e\u5386\u53f2\u6700\u4f18\u89e3，\u66f4\u65b0\u5168\u5c40\u6700\u4f18\u89e3\u3002<\/p>\n

(5)\u964d\u6e29\u4e0e\u7ec8\u6b62：\u6309\u8870\u51cf\u7387\u964d\u4f4e\u6e29\u5ea6，\u91cd\u590d(2)\u3001（3）\u3001（4），\u76f4\u5230\u6ee1\u8db3\u7ec8\u6b62\u6761\u4ef6（\u5982\u6536\u655b\u3001\u5c06\u81f3\u6700\u4f4e\u6e29\u5ea6）\u505c\u6b62\u8fed\u4ee3，\u8f93\u51fa\u6700\u4f18\u89e3\u3002<\/p>\n

2.\u4ee3\u7801\u5b9e\u73b0<\/p>\n

# -*- coding:utf-8 -*<\/p>\n

import torch
\nimport matplotlib.pyplot as plt
\nimport numpy as np<\/p>\n

plt.rcParams['font.sans-serif'] = ['SimHei']
\nplt.rcParams['axes.unicode_minus'] = False<\/p>\n

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
\nprint(f"\u4f7f\u7528\u8bbe\u5907: {device}")
\nif torch.cuda.is_available():
\n print(f"GPU\u540d\u79f0: {torch.cuda.get_device_name(0)}")<\/p>\n

# ————————– 2. \u5b9a\u4e49\u76ee\u6807\u51fd\u6570（GPU\u5f20\u91cf\u7248） ————————–
\ndef target_function(x):
\n return x ** 2 + 10 * torch.sin(x) + 5 * torch.cos(3 * x)<\/p>\n

def simulated_annealing_gpu(func, # \u76ee\u6807\u51fd\u6570
\n init_x, # \u521d\u59cb\u89e3（GPU\u5f20\u91cf）
\n init_temp=100, # \u521d\u59cb\u6e29\u5ea6
\n min_temp=1e-8, # \u7ec8\u6b62\u6e29\u5ea6
\n decay_rate=0.99, # \u6e29\u5ea6\u8870\u51cf\u7387
\n step_size=0.5 # \u65b0\u89e3\u751f\u6210\u7684\u6b65\u957f
\n ):
\n current_x = init_x.to(device)
\n best_x = current_x.clone()
\n current_energy = func(current_x)
\n best_energy = current_energy.clone()<\/p>\n

temp = torch.tensor(init_temp, dtype=torch.float32, device=device)
\n # \u8fed\u4ee3\u964d\u6e29
\n iteration = 0
\n while temp > min_temp:
\n iteration += 1<\/p>\n

new_x = current_x + step_size * torch.randn_like(current_x, device=device)
\n new_energy = func(new_x)
\n energy_diff = new_energy – current_energy<\/p>\n

if energy_diff < 0:
\n accept = True
\n else:
\n accept_prob = torch.exp(-energy_diff \/ temp)
\n accept = torch.rand(1, device=device) < accept_prob<\/p>\n

if accept:
\n current_x = new_x
\n current_energy = new_energy<\/p>\n

if current_energy < best_energy:
\n best_x = current_x.clone()
\n best_energy = current_energy.clone()<\/p>\n

temp *= decay_rate<\/p>\n

if iteration % 100 == 0:
\n print(f"\u8fed\u4ee3\u6b21\u6570: {iteration}, \u5f53\u524d\u6e29\u5ea6: {temp.item():.6f}, \u6700\u4f18\u503c: {best_energy.item():.4f}")<\/p>\n

return best_x, best_energy<\/p>\n

if __name__ == "__main__":
\n init_x = torch.tensor(2.0, device=device) # \u521d\u59cb\u503c\u8bbe\u4e3a2.0<\/p>\n

best_x, best_energy = simulated_annealing_gpu(
\n func=target_function,
\n init_x=init_x,
\n init_temp=100,
\n min_temp=1e-8,
\n decay_rate=0.99,
\n step_size=0.5
\n )<\/p>\n

best_x_cpu = best_x.cpu().item()
\n best_energy_cpu = best_energy.cpu().item()
\n print("\\\\n===== \u4f18\u5316\u7ed3\u679c =====")
\n print(f"\u6700\u4f18\u89e3 x: {best_x_cpu:.4f}")
\n print(f"\u6700\u4f18\u76ee\u6807\u51fd\u6570\u503c: {best_energy_cpu:.4f}")<\/p>\n

# ————————– \u53ef\u89c6\u5316\u9a8c\u8bc1 ————————–
\n x_range = np.linspace(-6, 6, 1000)
\n y_range = target_function(torch.tensor(x_range, device=device)).cpu().numpy()<\/p>\n

plt.figure(figsize=(10, 6))
\n plt.plot(x_range, y_range, label="\u76ee\u6807\u51fd\u6570: $x^2 + 10\\\\sin(x) + 5\\\\cos(3x)$")
\n plt.scatter(best_x_cpu, best_energy_cpu, color="red", s=100, label=f"\u6700\u4f18\u89e3 (x={best_x_cpu:.4f})")
\n plt.xlabel("x")
\n plt.ylabel("f(x)")
\n plt.title("\u6a21\u62df\u9000\u706b（GPU\u7248）\u6c42\u89e3\u51fd\u6570\u6700\u5c0f\u503c")
\n plt.legend()
\n plt.grid(True)
\n plt.show()<\/p>\n

\u8fd0\u884c\u6548\u679c：<\/p>\n

\u4f7f\u7528\u8bbe\u5907: cpu
\n\u8fed\u4ee3\u6b21\u6570: 100, \u5f53\u524d\u6e29\u5ea6: 36.603275, \u6700\u4f18\u503c: 4.1254
\n\u8fed\u4ee3\u6b21\u6570: 200, \u5f53\u524d\u6e29\u5ea6: 13.397995, \u6700\u4f18\u503c: -12.6188
\n\u8fed\u4ee3\u6b21\u6570: 300, \u5f53\u524d\u6e29\u5ea6: 4.904105, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 400, \u5f53\u524d\u6e29\u5ea6: 1.795063, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 500, \u5f53\u524d\u6e29\u5ea6: 0.657052, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 600, \u5f53\u524d\u6e29\u5ea6: 0.240502, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 700, \u5f53\u524d\u6e29\u5ea6: 0.088032, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 800, \u5f53\u524d\u6e29\u5ea6: 0.032222, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 900, \u5f53\u524d\u6e29\u5ea6: 0.011794, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1000, \u5f53\u524d\u6e29\u5ea6: 0.004317, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1100, \u5f53\u524d\u6e29\u5ea6: 0.001580, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1200, \u5f53\u524d\u6e29\u5ea6: 0.000578, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1300, \u5f53\u524d\u6e29\u5ea6: 0.000212, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1400, \u5f53\u524d\u6e29\u5ea6: 0.000077, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1500, \u5f53\u524d\u6e29\u5ea6: 0.000028, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1600, \u5f53\u524d\u6e29\u5ea6: 0.000010, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1700, \u5f53\u524d\u6e29\u5ea6: 0.000004, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1800, \u5f53\u524d\u6e29\u5ea6: 0.000001, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 1900, \u5f53\u524d\u6e29\u5ea6: 0.000001, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 2000, \u5f53\u524d\u6e29\u5ea6: 0.000000, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 2100, \u5f53\u524d\u6e29\u5ea6: 0.000000, \u6700\u4f18\u503c: -12.6395
\n\u8fed\u4ee3\u6b21\u6570: 2200, \u5f53\u524d\u6e29\u5ea6: 0.000000, \u6700\u4f18\u503c: -12.6395<\/p>\n

===== \u4f18\u5316\u7ed3\u679c =====
\n\u6700\u4f18\u89e3 x: -1.0995
\n\u6700\u4f18\u76ee\u6807\u51fd\u6570\u503c: -12.6395<\/p>\n

\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

1.\u57fa\u672c\u539f\u7406(1) \u521d\u59cb\u5316：\u8bbe\u5b9a\u521d\u59cb\u89e3（\u5f85\u4f18\u5316\u53d8\u91cf\u7684\u521d\u59cb\u503c）\u3001\u521d\u59cb\u9ad8\u6e29（\u5982 100）\u3001\u6e29\u5ea6\u8870\u51cf\u7387（\u5982 0.99）\u3001\u7ec8\u6b62\u6e29\u5ea6（\u5982 1e-8），\u8ba1\u7b97\u521d\u59cb\u89e3\u7684\u76ee\u6807\u51fd\u6570\u503c（\u201c\u80fd\u91cf\u201d），\u5e76\u8bb0\u5f55\u4e3a\u5f53\u524d\u6700\u4f18\u89e3\u3002(2)\u8fed\u4ee3\u964d\u6e29：\u5728\u5f53\u524d\u6e29\u5ea6\u4e0b，\u5bf9\u5f53\u524d\u89e3\u505a\u968f\u673a\u6270\u52a8\u751f\u6210\u65b0\u89e3，\u8ba1<\/p>\n","protected":false},"author":2,"featured_media":75776,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[50,1040,427],"topic":[],"class_list":["post-75777","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-50","tag-1040","tag-427"],"yoast_head":"\n\u6a21\u62df\u9000\u706bSA - 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