A Novel Solution to the ATT48 Benchmark Problem

TL;DR

This paper presents a zone-based approach to solving the ATT48 Traveling Salesman Problem by partitioning vertices into zones and finding optimal Hamiltonian Paths, leading to an efficient approximation of the minimum Hamiltonian Cycle.

Contribution

It introduces a novel zone partitioning method combined with boundary vertex analysis to efficiently approximate solutions for the TSP, improving upon traditional methods.

Findings

Achieved an approximate optimal Hamiltonian Cycle with minimal crossings.

The zone-based method reduces computational complexity for the ATT48 problem.

Adding inter-zone edges allows handling more complex TSP instances.

Abstract

A solution to the benchmark ATT48 Traveling Salesman Problem (from the TSPLIB95 library) results from isolating the set of vertices into ten open-ended zones with nine lengthwise boundaries. In each zone, a minimum-length Hamiltonian Path (HP) is found for each combination of boundary vertices, leading to an approximation for the minimum-length Hamiltonian Cycle (HC). Determination of the optimal HPs for subsequent zones has the effect of automatically filtering out non-optimal HPs from earlier zones. Although the optimal HC for ATT48 involves only two crossing edges between all zones (with one exception), adding inter-zone edges can accommodate more complex problems.