欧氏旅行售货员问题是对给定的平面上n 个点确定一条连接这n 个点的长度最短的哈密顿回路。由于欧氏距离满足三角不等式，所以欧氏旅行售货员问题是一个特殊的具有三角不等式性质的旅行售货员问题。它仍是一个NP 完全问题。最短双调TSP 回路是欧氏旅行售货员问题的特殊情况。平面上n 个点的双调TSP 回路是从最左点开始，严格地由左至右直到最右点，然后严格地由右至左直至最左点，且连接每一个点恰好一次的一条闭合回路。-Euclidean traveling salesman problem is a given n points in the plane of a connection to determine the length of these n points the shortest Hamiltonian circuit. Euclidean distance to satisfy the triangle inequality, so the Euclidean traveling salesman problem is a special character with the triangle inequality the traveling salesman problem. It is still a NP complete problem. Double adjustable loop is the shortest Euclidean TSP traveling salesman problem a special case. N points in the plane two-tone TSP from the left point of the loop is started, the most strictly from left to right until the right point, and strictly from right to left until the left point, and connecting each point exactly once in a closed circuit.