说明：  自组织映射（SOM）已成功处理的欧式旅行的鹅岭推销员问题（TSP）。通过将其邻域保持财产和 凸包属性数值模拟TSP，我们引入了一个新的SOM如神经网络，称为前panding的SOM（ESOM）的。在每一个学习的迭代，ESOM提请接近的兴奋神经元 输入的城市，并在此期间，推压它们向凸包ofcities合作。 ESOM可能收购邻里保护财产和凸包的属性 的TSP，因此它可以产生接近最优的解决方案。从理论上分析了其可行性 和经验。一个的系列ofexperiments进行合成和基准的TSP， 其大小范围从50到2400个城市。实验结果表明的优越性 通过几个典型的SOM SOM开发由Budinich，凸的ESOM 弹力网，和的克尼斯算法。虽然其解的精度是尚未与 其他一些复杂的的启发式，ESOM是之一最精确的神经网络 的TSP在文献中。
(The self-organizing map (SOM) has been successfully employed to handle the Euclidean trav-eling salesman problem (TSP). By incorporating its neighborhood preserving property and the convex-hull property ofthe TSP, we introduce a new SOM-like neural network, called the ex-panding SOM (ESOM). In each learning iteration, the ESOM draws the excited neurons close to the input city, and in the meantime pushes them towards the convex-hull ofcities cooperatively. The ESOM may acquire the neighborhood preserving property and the convex-hull property of the TSP, and hence it can yield near-optimal solutions. Its feasibility is analyzed theoretically and empirically. A series ofexperiments are conducted on both synthetic and benchmark TSPs, whose sizes range from 50 to 2400 cities. Experimental results demonstrate the superiority of the ESOM over several typical SOMs such as the SOM developed by Budinich, the convex elastic net, and the KNIES algorithms. Though its solution accuracy is no)