The Frequency of the Optimal Hamiltonian Cycle Computed with Frequency Quadrilaterals for Traveling Salesman Problem

Abstract

Traveling salesman problem is generally represented as a complete graph. The complete graph is converted into a frequency graph where the frequency of each edge is computed with a number of frequency quadrilaterals. The frequency consistency is introduced for deriving the lower frequency bound for an edge in the optimal Hamiltonian cycle (OHC). The frequency of the OHC is compared with that of the other Hamiltonian cycles. Considering the frequency of edges, the OHC is better cultivated. Finally, the experimental results are provided for demonstrating the frequency of the OHC edges.