LAPPI: Interactive Optimization with LLM-Assisted Preference-Based Problem Instantiation

Abstract: Many real-world tasks, such as trip planning or meal planning, can be formulated as combinatorial optimization problems. However, using optimization solvers is difficult for end users because it requires problem instantiation: defining candidate items, assigning preference scores, and specifying constraints. We introduce LAPPI (LLM-Assisted Preference-based Problem Instantiation), an interactive approach that uses LLMs to support users in this instantiation process. Through natural language conversations, the system helps users transform vague preferences into well-defined optimization problems. These instantiated problems are then passed to existing optimization solvers to generate solutions. In a user study on trip planning, our method successfully captured user preferences and generated feasible plans that outperformed both conventional and prompt-engineering approaches. We further demonstrate LAPPI's versatility by adapting it to an additional use case.