Feedback-integrated prompt optimiser for problem formulation

Problem formulation is a critical yet expertise-intensive step in optimisation modelling. Automating this process offers a promising solution, but requires effective methods to replicate the reasoning and decision-making processes that are both crucial and typically performed by human experts. Recent advancements in Large Language Models (LLMs) have introduced the potential for human-like reasoning in this context, making optimisation more accessible, scalable, and intelligent. However, the substantial computational demands of LLMs limit their practicality in many real-world settings. Small Language Models (SLMs) present a more resource-efficient alternative but face challenges such as limited reasoning capabilities and high sensitivity to prompt structure, reducing their effectiveness in complex tasks like automated problem formulation. To address these limitations, we propose FIPO (Feedback-Integrated Prompt Optimiser), a novel approach designed to enhance the problem formulation capabilities of SLMs through iterative, feedback-driven prompt optimisation. FIPO integrates the local search algorithm with structured feedback generated by agentic workflows that simulate expert evaluations from problem formulation and programming perspectives. We evaluate FIPO on the LPWP dataset and observe consistent performance gains compared to existing state-of-the-art prompt optimisation methods. Our findings establish feedback-guided prompt evolution as a promising strategy for enabling cost-efficient, scalable, and accurate automated problem formulation with SLMs.