  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 $\lambda$ 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 $\lambda$-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.
