The Application Of Hopfield Neural Network In The TSP Problem Lan Zhaoqing

TSP is a typical problem in the field of combinatorial optimization, the core of this problem is to find the shortcut including all the cities. Although it is very simple to state, it is not so easy to solve, what is more, it has been proved to be the NP-complete problem. But it does exist extensively, and it is the central generalize and simplified form of many complex issues. Therefore propose an effective solution to the problem of the TSP algorithms have a higher theoretical and practical value.This paper chose the existing algorithms of TSP to start. By studying a large number of references, to understand the main ideas of a variety of algorithms and organize a variety of algorithms, then make the classification.It is found that genetic algorithm,simulated annealing algorithm and ants algorithm showed a certain advantages in solving the TSP, and they are widely used in the solution of practical problems. Then, to this paper, the three algorithms is deeply researched and programmed. The three algorithms were separately used to solve the 48 cities TSP problems.From the results of the simulated,the author found that annealing's process of optimization is longer;ant algorithm is also relatively long, but also easy in a local optimal solution to search stagnation; At the practical application of premature, GA appears the shortcomings of easy to premature convergence and convergence of poor. How fast and accurate to solve the problem has now become a difficult point in the problem of TSP algorithm. The author presents a Hopfield neural network algorithm, the neural net work is the parallel computing, and its calculation is not the dimension of the increase in the index of "explosion" and therefore,the optimization of high-speed computing particularly effective.In the actual process of the algorithm from the author found in a fatal drawback is the network extremely unstable,often not the results.To this end,the author of the existing algorithms made improved. After the final results of the study found that a large extent depends on the accuracy of the initial parameters set.In recognition of this point,the results of an analysis of the parameters are given a reasonable set of methods.This article's energy function was also improved, making the solution more quickly and accurately.Finally, the author brought up a method of fixed starting point of departure for resolving the "duplication of the problem" from the approach. Finally application of the method to solve the Xi'an tourism, first, based on the Xi'an tourism map, according to the specific issue of tourism, the network's energy function is given; thereby building a Hopfield neural networks. Xi'an has been selected the well-known tourist attractions, the attractions for the transformation and normalization of the algorithm programming experiment. Experimental results show that the method on 10 scenic spots and attractions of the 15 mostly concentrated in the number of iterative 250 to350,and the method to deal with the problem of the route of choice is effective.