Optimization Models for the Quadratic Traveling Salesperson Problem

TL;DR

This paper introduces various optimization models for the quadratic traveling salesperson problem, demonstrating that the domain-independent dynamic programming approach outperforms others in large instances.

Contribution

It presents new compact optimization models for QTSP across multiple paradigms, with a focus on the effectiveness of DIDP for large problem sizes.

Findings

DIDP model achieves better optimality gap.

DIDP provides higher solution quality for large instances.

Models are applicable in mixed-integer and domain-independent frameworks.

Abstract

The quadratic traveling salesperson problem (QTSP) is a generalization of the traveling salesperson problem, in which all triples of consecutive customers in a tour determine the travel cost. We propose compact optimization models for QTSP in mixed-integer quadratic programming (MIQP), mixed-integer linear programming (MILP), constraint programming (CP), and domain-independent dynamic programming (DIDP). Our experimental results demonstrate that the DIDP model performs better than other approaches in optimality gap and solution quality when the problem size is large enough.