  Routing problems are common in mobile robotics, encompassing tasks such as
inspection, surveillance, and coverage. Depending on the objective and
constraints, these problems often reduce to variants of the Traveling Salesman
Problem (TSP), with solutions traditionally derived by translating high-level
objectives into an optimization formulation and using modern solvers to arrive
at a solution. Here, we explore the potential of Large Language Models (LLMs)
to replace the entire pipeline from tasks described in natural language to the
generation of robot routes. We systematically investigate the performance of
LLMs in robot routing by constructing a dataset with 80 unique robot routing
problems across 8 variants in both single and multi-robot settings. We evaluate
LLMs through three frameworks: single attempt, self-debugging, and
self-debugging with self-verification and various contexts, including
mathematical formulations, pseudo-code, and related research papers. Our
findings reveal that both self-debugging and self-verification enhance success
rates without significantly lowering the optimality gap. We observe
context-sensitive behavior - providing mathematical formulations as context
decreases the optimality gap but significantly decreases success rates and
providing pseudo-code and related research papers as context does not
consistently improve success rates or decrease the optimality gap. We identify
key challenges and propose future directions to enhance LLM performance in
solving robot routing problems. Our source code is available on the project
website: https://sites.google.com/view/words-to-routes/.
