A self-organised travelling salesman

Abstract

Using the principles of self-organisation and Darwin's theory of evolution, an algorithm has been developed to solve the geometric travelling salesman problem (TSP). In this approach, we have virtual and real nodes (cities) which can have equal or different masses (weights). The virtual nodes and their neighours are attracted toward the fixed cities by a Newtonian force. The birth and death of the virtual nodes creates a world in which only the fittest survive. This approach has been successfully tested on many problems of different sizes, with a constant error of about 4.6% across the whole range. The computing time follows a power series (square law) versus the number of cities. Comparison of our results with those obtained by a simulated annealing method showed the solutions that obtained by this self-organisation method are of a better quality, especially for large size problems.