Trajectory stability in the traveling salesman problem

TL;DR

This paper investigates the stability of optimal trajectories in dynamic traveling salesman problems where sites change positions over time, analyzing how trajectory rankings evolve and identifying which are more predictable and robust.

Contribution

It introduces a framework for studying trajectory stability in dynamic TSPs using rank diversity and statistical analysis of rank distributions.

Findings

Shortest and longest trajectories are more predictable.

Trajectory stability varies with rank diversity.

Rank distributions exhibit specific statistical properties.

Abstract

Two generalizations of the traveling salesman problem in which sites change their position in time are presented. The way the rank of different trajectory lengths changes in time is studied using the rank diversity. We analyze the statistical properties of rank distributions and rank dynamics and give evidence that the shortest and longest trajectories are more predictable and robust to change, that is, more stable.