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 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. (c) 2006 Elsevier B.V. All rights reserved.