Where should control sit? Reliability-cost trade-offs in delegating water distribution network optimisation to LLM...

Computational optimisation is now routinely used to support the design and operation of water distribution networks (WDNs). However, formulating optimisation problems, configuring solution workflows and interpreting results still depend heavily on manual effort, making even standard studies time-consuming to reproduce and difficult to scale. Large language models (LLMs) offer new opportunities to automate these tasks, but their effective use depends on a central design question: which steps should be delegated to an autonomous LLM agent, and which should remain deterministic workflow steps. This study quantifies the reliability and resource cost of delegating individual stages of a WDN optimisation pipeline to an LLM agent. We reformulate an end-to-end optimisation pipeline as a sequence of decision nodes, each of which can operate either as a deterministic workflow step or as a ReAct (Reasoning + Acting) agent, so that the locus of control is varied while the underlying optimisation task remains unchanged. Two representative tasks, i.e., single-objective pump energy minimisation and multi-objective energy-resilience optimisation problems, are evaluated on the benchmark C-Town network across five LLMs spanning an order of magnitude in model scale, with control transferred one node at a time over 250 runs. The results obtained show that control allocation affects reliability and computational cost far more than optimisation quality. Solution quality was largely insensitive to the control model, with variations of about 1% in pump energy and 13% in hypervolume, and neither the deterministic workflow nor the ReAct-agent configuration consistently outperformed the other. In contrast, delegating individual nodes to the ReAct-agent substantially increased resource use: at the formulation node, token consumption rose by roughly sixfold and the number of model calls by an order of magnitude. Workflow failures were structural rather than random and were concentrated at the delegated nodes. Full autonomy was reliable only for the largest LLMs, whereas workflow-dominant configurations remained viable down to a 14B-parameters LLM. These findings indicate that, for well-specified engineering optimisation tasks, LLMs autonomy should be extended selectively rather than by default. More broadly, by establishing where autonomy can be trusted and where it cannot, this work lays a foundation for the reliable, reproducible and auditable LLM-driven decision support on which trustworthy automation of water systems will depend.