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

TL;DR

This paper introduces a novel annealing method for the traveling salesman problem that leverages the exponential decay pattern of nth-nearest-neighbor distributions, improving solution quality over standard simulated annealing.

Contribution

The paper proposes a new annealing scheme based on the deviation from exponential decay in neighbor distributions, offering a more effective optimization process for TSP.

Findings

The nth-nearest-neighbor distribution follows an exponential decay in optimal tours.

The proposed annealing method outperforms canonical simulated annealing in experiments.

Simulation results on TSPLIB95 instances demonstrate improved solutions.

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 $\lambda$ 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.