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

2025-12-16

AI Summary

Non-expert users struggle to translate ambiguous natural language preferences into well-defined combinatorial optimization problems (e.g., travel or meal planning). Method: We propose the first LLM-driven, preference-guided problem instantiation framework that jointly performs end-to-end dialogue understanding, preference modeling, and constraint parsing to automatically generate candidate sets, preference scores, and hard/soft constraints—then interfaces with CP-SAT or OR-Tools to produce feasible solutions. The framework supports iterative user refinement and cross-scenario transfer. Results: A user study shows 100% feasibility for travel planning solutions and significantly higher preference alignment versus baselines; successful adaptation to meal planning further validates generalizability. Our core contribution is bridging natural language intent and combinatorial optimization through LLM-guided, iterative problem instantiation.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Constraint Satisfaction and Optimization: Constraint Programming
• Search and Optimization: Combinatorial Optimization

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

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 large language models (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.

Problem

• Transforming vague user preferences into well-defined optimization problems.
• Assisting users in defining items, preferences, and constraints via conversation.
• Generating feasible solutions using existing optimization solvers.

Innovation

• LLMs assist users in defining optimization problems
• Natural language conversations transform vague preferences
• Instantiated problems solved by existing optimization solvers