\u89e3\u51b3\u9762\u5bf9\u4e0d\u5b8c\u6574\u4fe1\u606f\u53bb\u83b7\u5f97\u6700\u4f73\u7b56\u7565\u8fd9\u4e00\u95ee\u9898\u65f6\uff0c\u7ebf\u6027\u89c4\u5212\u65e9\u5c31\u6210\u4e86\u91cd\u8981\u65b9\u6cd5\uff0c\u5728\u5fae\u89c2\u7ecf\u6d4e\u5b66\u9886\u57df\u5982\u6b64\uff0c\u5728\u5546\u4e1a\u7ba1\u7406\u9886\u57df\u540c\u6837\u5982\u6b64\uff0c\u5728\u8fd9\u4e24\u4e2a\u9886\u57df\u4e2d\uff0c\u8fd9\u79cd\u7b97\u6cd5\u5df2\u5927\u91cf\u7528\u4e8e\u964d\u4f4e\u751f\u4ea7\u6d41\u7a0b\u6210\u672c\uff0c\u4e8e\u4eba\u5de5\u667a\u80fd\u9886\u57df\uff0c\u5176\u548c\u6df1\u5ea6\u5b66\u4e60\u706b\u70ed\u524d\u7684\u4e3b\u6d41\u5373\u8d1d\u53f6\u65af\u7f51\u7edc\u6280\u672f\u7d27\u5bc6\u76f8\u5173\uff0c\u800c\u8d1d\u53f6\u65af\u7f51\u7edc\u6280\u672f\u4e5f\u662f\u76ee\u524d\u4e92\u8054\u7f51\u901a\u7528\u57fa\u7840\u6280\u672f\u4e4b\u4e00\u3002<\/p>\n
<\/p>\n
2017\u5e741\u670811\u65e5\uff0c\u804c\u4e1a\u6251\u514b\u73a9\u5bb6\u8d3e\u68ee\u00b7\u83b1\u65af\uff08Jason Les\uff09\u4e8e\u548cLibratus\u5c55\u5f00\u5fb7\u5dde\u6251\u514b\u7684\u5bf9\u51b3\u5f53\u4e2d\u6e38\u620f\u30021\u670830\u65e5\u5fb7\u4fe1\u7ade\u6280\uff0c\u5361\u5185\u57fa\u6885\u9686\u5927\u5b66\u6240\u7814\u53d1\u7684\u4eba\u5de5\u667a\u80fd\u5728\u540c4\u540d\u9876\u5c16\u5fb7\u5dde\u6251\u514b\u9009\u624b\u4e4b\u95f4\u7684\u8d5b\u4e8b\u91cc\u7ec8\u800c\u5f97\u80dc\u7ed3\u675f\u4e86\u5bf9\u5c40\u3002<\/p>\n
\u5728\u91c7\u8bbf\u5f00\u59cb\u4e4b\u524d\uff0c\u6469\u5c14\u8bb2\u9053\uff0c\u5fb7\u5dde\u6251\u514b\u6e38\u620f\u91cc\u5934\u6709\u7740\u5927\u91cf\u7684\u9690\u85cf\u4fe1\u606f\uff0c\u4ece\u672c\u8d28\u4e0a\u6765\u8bf4\u5b83\u5c31\u662f\u4e00\u79cd\u8c08\u5224\u3002\u800c\u501f\u52a9\u4eba\u5de5\u667a\u80fd\u8fdb\u884c\u8c08\u5224\u5b9e\u9645\u4e0a\u4e43\u662f\u5361\u5185\u57fa\u6885\u9686\u5927\u5b66\u7814\u7a76\u56e2\u961f\u7684\u521d\u8877\u3002\u4ed6\u8bf4\u9053\uff0c\u5728\u6251\u514b\u6e38\u620f\u4e2d\u53d6\u5f97\u80dc\u5229\u4f1a\u8ba9\u4eba\u89c9\u5f97\u4eba\u5de5\u667a\u80fd\u7279\u522b\u4e86\u4e0d\u8d77\uff0c\u7136\u800c\u4ed6\u540c\u6837\u6ee1\u6000\u671f\u5f85\uff0c\u671f\u5f85\u4eba\u5de5\u667a\u80fd\u80fd\u591f\u5728\u534f\u5546\u8c08\u5224\u4ee5\u53ca\u89e3\u51b3\u95ee\u9898\u8fd9\u4e9b\u65b9\u9762\u51fa\u73b0\u66f4\u591a\u7684\u5e94\u7528\u3002<\/p>\n
\u4ee5\u4e0b\u4e3a\u90e8\u5206\u91c7\u8bbf\u5b9e\u5f55\uff0c\u65b0\u6d6a\u79d1\u6280\u6574\u7406\uff1a<\/p>\n
\u65b0\u6d6a\u79d1\u6280\u79f0\uff0c\u51b7\u6251\u5927\u5e08\u4f3c\u4e4e\u4e0eAlphaGo\u5b58\u5728\u5dee\u5f02\uff0c\u5b83\u5e76\u672a\u4ece\u4eba\u7c7b\u73a9\u724c\u7684\u7ed3\u679c\u91cc\u8fdb\u884c\u5b66\u4e60\u3002\u90a3\u4e48\uff0c\u5fb7\u5dde\u6251\u514b\u4eba\u5de5\u667a\u80fd\u8ddf\u56f4\u68cb\u4eba\u5de5\u667a\u80fd\u7a76\u7adf\u6709\u7740\u54ea\u4e9b\u4e0d\u540c\u4e4b\u5904\u5462\uff1f<\/p>\n
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\u65b0\u6d6a\u79d1\u6280\uff1a\u51b7\u6251\u5927\u5e08\u6709\u6ca1\u6709\u4f7f\u7528\u5230\u795e\u7ecf\u7f51\u7edc\u548c\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\uff1f<\/p>\n
AM\uff0c\u51b7\u6251\u5927\u5e08\u672a\u8fd0\u7528\u795e\u7ecf\u7f51\u7edc\u3001\u6df1\u5ea6\u5b66\u4e60\u65b9\u9762\u7684\u6280\u672f\uff0c\u800c\u662f\u91c7\u7528\u4e86\u6700\u4e3a\u4f20\u7edf\u7684\u7ebf\u6027\u89c4\u5212\uff0c\u5373Liner Programming\u3002<\/p>\n
\u6211\u80fd\u591f\u8bb2\u5f97\u7565\u5fae\u7ec6\u81f4\u4e00\u70b9\u513f\u3002\u8ba1\u7b97\u673a\u8981\u7b97\u51fa\u6700\u4e3a\u5408\u9002\u6570\u91cf\u7684\u8bc8\uff0c\u539f\u56e0\u5728\u4e8e\u4e0d\u7ba1\u8bc8\u7684\u6570\u91cf\u8fc7\u591a\uff0c\u8fd8\u662f\u8fc7\u5c11\uff0c\u90fd\u6709\u53ef\u80fd\u88ab\u5176\u4ed6\u724c\u624b\u52a0\u4ee5\u5229\u7528\u3002\u6570\u5b66\u5bb6\u7ea6\u7ff0\u00b7\u7eb3\u4ec0\u66fe\u7ecf\u7b97\u51fa\u4e00\u4e2a\u7b49\u5f0f\u7528\u4ee5\u89e3\u51b3\u7c7b\u4f3c\u7684\u95ee\u9898\uff0c\u7136\u800c\u8981\u60f3\u5207\u5b9e\u7b97\u51fa\u6700\u4e3a\u5408\u9002\u6570\u91cf\u7684\u8bc8\uff0c\u8fd9\u4e2a\u7b49\u5f0f\u6216\u8bb8\u4f1a\u5b58\u5728\u65e0\u6570\u7684\u53d8\u91cf\uff0c\u800c\u6211\u4eec\u5728\u51b7\u6251\u5927\u5e08\u8eab\u4e0a\u8fd0\u7528\u7684\u8ba1\u7b97\u673a\u6280\u672f\u80fd\u591f\u5f97\u51fa\u6700\u63a5\u8fd1\u6b63\u786e\u7b54\u6848\u7684\u89e3\u51b3\u529e\u6cd5\u3002<\/p>\n
\u65b0\u6d6a\u79d1\u6280\uff1a\u4e4b\u524d\u66fe\u5199\u4e0b\u81ea\u8eab\u73a9\u5fb7\u5dde\u6251\u514b\u7684\u611f\u53d7\uff0c\u5176\u8868\u793a\u82e5\u60f3\u73a9\u597d\uff0c\u5c31\u5f97\u5c06\u4eba\u6027\u653e\u7f6e\u4e00\u65c1\u3002\u51b7\u6251\u5927\u5e08\u4e8e\u6bd4\u8d5b\u4e4b\u9645\uff0c\u662f\u51ed\u501f\u7b97\u724c\uff0c\u8fd8\u662f\u8fd0\u7528\u7edf\u8ba1\u65b9\u5f0f\u53bb\u7814\u7a76\u5bf9\u624b\u4ece\u800c\u5c55\u5f00\u5fc3\u7406\u6218\u5462\uff1f<\/p>\n
\u65e9\u76d8\u65f6\u6bb5\uff1a\u901a\u8fc7\u7b97\u724c\u8fd9\u79cd\u529e\u6cd5\u53bb\u8d62\u724c\u624d\u662f\u6b63\u786e\u7684\u65b9\u5f0f\u3002\u7136\u800c\u5462\uff0c\u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\u6240\u6d89\u53ca\u5230\u7684\u8ba1\u7b97\u6570\u91cf\u975e\u5e38\u5927\uff0c\u51b7\u6251\u5927\u5e08\u8981\u8fbe\u6210\u5176\u7b56\u7565\uff0c\u5f97\u5b8c\u62101000\u4e07\u5c0f\u65f6\u7684\u8ba1\u7b97\u624d\u884c\u3002<\/p>\n
\u7136\u800c\uff0c\u8fd0\u7528\u7edf\u8ba1\u6570\u636e\u53bb\u5bf9\u5bf9\u624b\u7684\u73a9\u6cd5\u5c55\u5f00\u7814\u7a76\uff0c\u5e76\u975e\u662f\u4e00\u79cd\u826f\u597d\u7684\u529e\u6cd5\uff0c\u8fd9\u662f\u7531\u4e8e\uff0c\u4e00\u65e6\u6211\u77e5\u6653\u4f60\u6b63\u5728\u5bf9\u6211\u7684\u73a9\u6cd5\u8fdb\u884c\u7edf\u8ba1\uff0c\u90a3\u4e48\u6211\u5c31\u4f1a\u7279\u610f\u91c7\u7528\u53d8\u6362\u62bc\u6ce8\u7684\u65b9\u6cd5\uff0c\u5b9e\u9645\u4e0a\u800c\u8a00\uff0c\u662f\u80fd\u591f\u7ed5\u5f00\u4f60\u7684\u3002<\/p>\n
\u4e8e\u662f\u5c31\u5982\u540c\u6211\u4e4b\u524d\u6240\u8bb2\u7684\u90a3\u822c\uff0c\u51b7\u6251\u5927\u5e08\u4e0d\u5b58\u5728\u8fd0\u7528\u5fc3\u7406\u6218\u672f\u53bb\u8d62\u724c\u7684\u60f3\u6cd5\uff0c\u4ec5\u4ec5\u662f\u8fd0\u7528\u6570\u5b66\u65b9\u5f0f\u7f62\u4e86\u3002<\/p>\n
\u4e8b\u5b9e\u4e0a\uff0c\u8fc7\u53bb\u7684\u5341\u5e74\uff0c\u4e43\u662f\u5927\u6570\u636e\u4ee5\u53ca\u673a\u5668\u5b66\u4e60\u5f97\u4ee5\u53d1\u5c55\u7684\u5341\u5e74\u3002\u7136\u800c\uff0c\u51b7\u6251\u5927\u5e08\u6240\u8fd0\u7528\u7684\u7ebf\u6027\u89c4\u5212\uff0c\u4e0e\u4e0a\u8ff0\u4e24\u8005\u5b58\u5728\u7740\u6781\u5927\u7684\u5dee\u5f02\uff0c\u5b83\u5c5e\u4e8e\u8fbe\u6210\u6700\u4f18\u89e3\uff08Big Optimization\uff09\u7684\u4e00\u9879\u6280\u672f\uff0c\u5e76\u4e14\u76f8\u4fe1\u672a\u6765\u7684\u6280\u672f\u524d\u6cbf\u540c\u6837\u662f\u80fd\u591f\u5b9e\u73b0\u6700\u4f18\u89e3\u7684\u6280\u672f\u3002<\/p>\n
<\/p>\n
\u57284\u67086\u65e5\uff0c\u75316\u4f4d\u534e\u4eba\u724c\u624b\u6240\u7ec4\u6210\u7684\u4e2d\u56fd\u9f99\u4e4b\u961f\uff0c\u5c06\u4f1a\u5728\u6d77\u5357\u5bf9Libratus\u53d1\u8d77\u6311\u6218\u3002\u4e0d\u8fc7\u961f\u957f\u675c\u60a6\uff0c\u4e5f\u5c31\u662f\u4f4d\u4e8e\u5de6\u56db\u4f4d\u7f6e\u7684\u90a3\u4e2a\u4eba\u79f0\uff0c\u9f99\u4e4b\u961f\u7684\u80dc\u7b97\u5927\u6982\u4ec5\u670910%\u3002<\/p>\n
\u65b0\u6d6a\u79d1\u6280\uff0c\u9f99\u4e4b\u961f\u6bd4\u8d5b\u7684\u8d5b\u5236\uff0c\u8ddf\u5e73\u5e38\u591a\u89c1\u7684\u591a\u4eba\u5fb7\u5dde\u6251\u514b\u724c\u5c40\u4e0d\u4e00\u6837\uff0c\u4e3a\u4f55\u4f1a\u6311\u9009\u4e00\u5bf9\u4e00\u5f62\u5f0f\u7684\u6bd4\u8d5b\u5462\uff0c\u8fd9\u662f\u548c\u7b97\u6cd5\u9650\u5236\u6709\u5173\u7cfb\u5417\uff1f<\/p>\n
\u4e0a\u5348\u65f6\u6bb5\uff1a\u5728\u5fb7\u5dde\u6251\u514b\u91cc\u9762\uff0c\u6700\u4e3a\u8003\u9a8c\u724c\u624b\u6280\u672f\u7684\u7adf\u7136\u662f\u53cc\u4eba\u4e4b\u95f4\u7684\u5bf9\u6218\uff0c\u8981\u662f\u5b58\u5728\u66f4\u591a\u724c\u624b\u7684\u60c5\u5883\u4e4b\u4e0b\uff0c\u5176\u4ed6\u724c\u624b\u76f8\u4e92\u4e4b\u95f4\u7684\u6280\u672f\u5dee\u522b\u53cd\u5012\u4f1a\u88ab\u7528\u6765\u52a0\u4ee5\u5229\u7528\u3002<\/p>\n
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\u597d\u7684\uff0c\u4ee5\u4e0b\u662f\u6539\u5199\u540e\u7684\u53e5\u5b50\uff1a\u5728\u4e0a\u5348\u65f6\u6bb5\uff0c\u6211\u6700\u4e3a\u949f\u7231\u7684\u5546\u4e1a\u7528\u9014\uff0c\u65e0\u7591\u5f53\u5c5e\u5546\u4e1a\u8c08\u5224\uff0c\u501f\u52a9\u4eba\u5de5\u667a\u80fd\uff0c\u80fd\u591f\u8fbe\u6210\u5728\u6700\u4e3a\u6070\u5f53\u7684\u65f6\u523b\uff0c\u51ed\u501f\u6700\u4e3a\u5408\u9002\u7684\u4ef7\u4f4d\uff0c\u5bfb\u89c5\u5230\u6700\u4e3a\u5951\u5408\u7684\u4f9b\u5e94\u5546\u3002<\/p>\n
\u8c08\u5224\u662f\u4e2a\u4f8b\u5b50\uff0c\u5728\u975e\u5b8c\u6574\u4fe1\u606f\u535a\u5f08\u7406\u8bba\u91cc\u8fd8\u633a\u4e0d\u9519\uff0c\u4e3a\u5565\u5462\uff0c\u56e0\u4e3a\u8c08\u5224\u4e4b\u9645\uff0c\u6211\u4eec\u4e0d\u89c1\u5f97\u4f1a\u5410\u9732\u771f\u5b9e\u60f3\u6cd5\u3002\u7814\u7a76\u4eba\u5458\u8ba4\u5b9a\uff0c\u8ba1\u7b97\u673a\u5177\u5907\u4e0e\u4eba\u7c7b\u6216\u8005\u522b\u7684\u8ba1\u7b97\u673a\u4ea4\u8c08\u4ee5\u53ca\u8c08\u5224\u7684\u80fd\u529b\u76f8\u5f53\u5173\u952e\u3002\u800c\u8ba1\u7b97\u673a\u7684\u8fd9\u79cd\u80fd\u529b\uff0c\u5c31\u662f\u6211\u4eec\u63a5\u4e0b\u6765\u7684\u7814\u7a76\u65b9\u5411\u3002<\/p>\n
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