Frequency Graphs for Travelling Salesman Problem Based on Ant Colony Optimization

Traveling salesman problem (TSP) is a typical combinatorial optimization problem. A heuristic model called frequency graph is introduced for TSP. It is computed with a set of optimal i-vertex paths (OP) in a weighted graph. The frequencies on the edges are enumerated from the set of OPs. The OPs have more intersections of edges with the optimal Hamiltonian cycle (OHC) than they do with the other Hamiltonian cycles. Thus, the frequencies of the OHC edges are generally bigger than those of most of the other edges. They are taken as the heuristic information instead of edges' weights for TSP. The ant colony optimization is used to find an approximation or OHC based on the frequency graph. The solutions are compared with those using weighted graphs for certain TSP instances. The experimental results show that the frequency graph is better than weighted graph (WG) for most TSPs under the same preconditions.