On the Solution of the Travelling Salesman Problem for Nonlinear Salesman Dynamics using Symbolic Optimal Control

TL;DR

This paper introduces a symbolic control-based heuristic algorithm to solve the nonlinear, continuous-space Travelling Salesman Problem, providing provably correct coverage solutions and heuristic route optimization for complex dynamic systems.

Contribution

It presents a novel symbolic control framework for solving nonlinear TSP with continuous dynamics, combining formal guarantees with heuristic route optimization.

Findings

Successfully applied to urban parcel delivery and UAV reconnaissance tasks.

Provides a provably correct coverage controller for nonlinear dynamics.

Heuristic route optimization improves overall route cost.

Abstract

This paper proposes an algorithmic method to heuristically solve the famous Travelling Salesman Problem (TSP) when the salesman's path evolves in continuous state space and discrete time but with otherwise arbitrary (nonlinear) dynamics. The presented method is based on the framework of Symbolic Control. In this way, our method returns a provably correct state-feedback controller for the underlying coverage specification, which is the TSP leaving out the requirement for optimality on the route. In addition, we utilize the Lin-Kernighan-Helsgaun TSP solver to heuristically optimize the cost for the overall taken route. Two examples, an urban parcel delivery task and a UAV reconnaissance mission, greatly illustrate the powerfulness of the proposed heuristic.