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

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

2006-03-09

arxiv.org/abs/cond-mat/0603237v3

Physica A 371, 627(2006)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 3 figures, preprint

Scientific paper

10.1016/j.physa.2006.04.052

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.

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