旅行商问题论文摘要

问：求论文摘要 专业汉译英 着急啊！！！！

1. 答：TSP (Traveling Salesman Problem, TSP), is a kind of classic NP hard problem. Delivery of pany generated TSP phenomenon, an improved ant colony algorithm, tree traversal algorithm of two classical algorithms start with an
2. 答：The business problem (Traveling Salesman Problem , TSP) journeying, is a kind of the TSP phenomenon that the classical NP troublesome problem produces specifically for the pany delivers goods , start with one kind of ant group algorithm , tree ergodic algorithm improving two kinds classics algorithm, basal principle having summarized this two kinds method, the TSP problem elicitation method algorithm has reached and algorithmic superior or inferior rank has carried out analysis parison on this three kinds in reality to have brought forward new finding the solution of a kind of
3. 答：TSP (Traveling Salesman Problem, TSP), is a kind of classic NP hard problem. Delivery of pany generated TSP phenomenon, an improved ant colony algorithm, tree traversal algorithm of two classical algorithms start with an overview of the basic principles of these two methods, a new inspiration for solving TSP problems type algorithm. Obtained, and in reality the merits of these three algorithms are analyzed pared

问：旅行商问题的介绍

1. 答：旅行商问题（Traveling Salesman Problem，TSP）又译为旅行推销员问题、货郎担问题，简称为TSP问题，是最基本的路线问题，该问题是在寻求单一旅行者由起点出发，通过所有给定的需求点之后，最后再回到原点的最小路径成本。最早的旅行商问题的数学规划是由Dantzig（1959）等人提出。

问：旅行商问题的研究历史

1. 答：旅行商问题字面上的理解是：有一个推销员，要到n个城市推销商品，他要找出一个包含所有n个城市的具有最短路程的环路。
   TSP的历史很久，最早的描述是1759年欧拉研究的骑士周游问题，即对于国际象棋棋盘中的64个方格，走访64个方格一次且仅一次，并且最终返回到起始点。
   TSP由美国RAND公司于1948年引入，该公司的声誉以及线性规划这一新方法的出现使得TSP成为一个知名且流行的问题。