A Method to Search Traveling Salesman Problem Backbones Based on GA and Frequency Graph
Yong Wang · Journal of Computers · 2019
The traveling salesman problem (TSP) is a well-known NP-hard problem in combinatorial optimization.The search space of the optimal Hamiltonian cycle (OHC) is increasing exponentially according to the scale n.In order to reduce the search space of TSP, we first convert the complete graph K n into the frequency graph (FG) with the approximate optimal n-vertex paths computed with an improved GA.The GA is improved with a four-vertex-three-line inequality to compute the approximate paths of TSP.Then, TSP backbones with 2n edges are derived from the FG.The experimental results show that the TSP backbones include at least 95% edges in the OHC.Based on the backbones, the search space of the OHC or approximations is greatly reduced.