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

Abstract

We report a new statistical general property in traveling salesman problem, that the $n$th-nearest-neighbor distribution of optimal tours verifies with very high accuracy an exponential decay as a function of the order of neighbor $n$. With defining the energy function as the deviation $λ$ 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 $λ$-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.