将论文中的摘要翻译成英文，不要翻译工具翻的。

TSP问题(Traveling Salesman Problem)是已知有n个城市，现有一推销员必须遍访这n个城市，且每个城市只能访问一次，最后又必须返回出发城市。要安排其访问次序，使其旅行路线的总长度最短。TSP是经典的NP-hard组合优化问题之一，也是一个测试算法优劣性的标准问题，且现实中有很多应用问题都可归结或转化为TSP问题。故对此问题的求解具有理论与实用两方面的意义。传统的求解方法在面对较大规模的问题时，很不容易得到最优解。
人们一直在尝试用新的方法来改进求解该问题的复杂程度。目前求解TSP问题的主要方法有启发式搜索法、模拟退火算法、遗传算法、Hopfield神经网络算法、二叉树描述算法。所以，有效解决TSP问题在计算理论上和实际应用上都有很高的价值，本文采用Hopfield神经网络和遗传算法来求解TSP问题，深入讨论了Hopfield神经网络和遗传算法解决TSP问题的求解过程，并通过MATLAB对算法进行了实现，最后对实验结果进行分析，并将两种方法进行比较与分析，最终通过仿真得出结论。
关键字：TSP，Hopfield神经网络，遗传算法，HopfieldTSP，GeneticTSP

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推荐答案 2015-05-30

It is known that there are n cities related to TSP problems. Now a promotor needs to visit all n cities. He is required to visit only one time for every city and back to the starting city at last. Please arrange the visiting order so as to make the tatal route shortest. TSP is the typical 组合优化
question of NP-hard as well as a standard question of mearsuring 算法优劣性.

TSP问题(Traveling Salesman Problem)是已知有n个城市，现有一推销员必须遍访这n个城市，且每个城市只能访问一次，最后又必须返回出发城市。要安排其访问次序，使其旅行路线的总长度最短。TSP是经典的NP-hard组合优化问题之一，也是一个测试算法优劣性的标准问题.

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第1个回答 2015-05-30

您好，我看到您的问题很久没有人来回答，但是问题过期无人回答会被扣分的并且你的悬赏分也会被没收！所以我给你提几条建议：

一，你可以选择在正确的分类下去提问，这样知道你问题答案的人才会多一些，回答的人也会多些。

二，您可以到与您问题相关专业网站论坛里去看看，那里聚集了许多专业人才，一定可以为你解决问题的。

三，你可以向你的网上好友问友打听，他们会更加真诚热心为你寻找答案的，甚至可以到相关网站直接搜索.

四，网上很多专业论坛以及知识平台，上面也有很多资料，我遇到专业性的问题总是上论坛求解决办法的。

五，将你的问题问的细一些，清楚一些！让人更加容易看懂明白是什么意思!

谢谢采纳我的建议! !

第2个回答 2015-06-02

这个是要收费翻译的，孩子。专业的英语翻译

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