An improved self-organizing map approach to traveling salesman problem

In this paper, an improved self-organizing map approach to solving the traveling salesman problem is proposed by fixing the number of nodes in the output layer of neural network, modifying the neighborhood function, and modifying the weight update rules. An overview of previous work on solving the traveling salesman problem is given. An extension of the proposed algorithm can also be used to solve multiple traveling salesman problems and robot path planning. The simulation results demonstrate that the proposed algorithm is capable of providing a better solution within a reasonable time and much faster than conventional self-organizing map algorithms.

1 Introduction

The traveling salesman problem (TSP) can be simply stated as follows: given a finite number of cities and the travel cost between each pair of them, the salesman, starting from his home city, has to visit each city exactly once, and finally return to his home city. The objective of the salesman is to find the traveling order of cities that has the shortest distance. The TSP is a well-known problem and is used as a typical example for optimization and scheduling problem. It was first documented in 1759 by Euler, whose interest was to solve the knights' tour problem. An optimal solution would have a knight to visit each of the 64 squares of a chessboard exactly once in his tour. The term “traveling salesman” was first used in a German book in 1932. The TSP was introduced by the RAND Corporation in 1948 and then became a popular optimization problem. Another reason for the TSP became popular was due to the new subject of linear programming and attempt to solve combinatorial problems at that time [1].