Optimized annealing of traveling salesman problem from the nth-nearest-neighbor distribution

We report a new statistical general property in traveling salesman problem, that the nth-nearest-neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor n  . Defining the energy function as deviation λλ from this exponential decay, which is different to the tour length d   in normal annealing processes, we propose a distinct highly optimized annealing scheme which is performed in λλ-space and d-space by turns. The simulation results of some standard traveling salesman problems in TSPLIB95 are presented. It is shown that our annealing recipe is superior to the canonical simulated annealing.