Improving analytic approximations of TSP tour lengths with adjustment factors

Abstract

Optimizing Traveling Salesman Problem (TSP) tours requires substantial computational effort, leading researchers to develop approximations relating tour length to the number of visited points, n. Existing models, such as the √nA predictor, effectively approximate tour lengths for large-capacity vehicles but sacrifice accuracy for small n values relevant for most practical applications. Consequently, this study addresses this gap by proposing models with uniform node distributions, which incorporate realistic factors, such as central vs. random starting points and various service zone shapes. These factors are then integrated into a single equation, enhancing applicability. Furthermore, the exponent of n is statistically estimated to be significantly different from 0.5, challenging previous studies. Our proposed model estimates TSP tour lengths more accurately, particularly for small n values, and maintains accuracy for large n values, with errors below 3.11% for up to 600 points. This model offers a more precise and versatile alternative to current models.