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

arXiv: https://arxiv.org/abs/2512.14138 · HTML: https://mlsanity.com/paper/2512.14138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 61 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Transformers learn in-context by gradient descent](https://mlsanity.com/paper/2212.07677/) (2022)
- [Prompt Programming for Large Language Models: Beyond the Few-Shot Paradigm](https://mlsanity.com/paper/2102.07350/) (2021)
- [Large Language Models are Zero-Shot Rankers for Recommender Systems](https://mlsanity.com/paper/2305.08845/) (2023)
- [Recommender Systems in the Era of Large Language Models (LLMs)](https://mlsanity.com/paper/2307.02046/) (2023)
- [Recommendation as Instruction Following: A Large Language Model Empowered Recommendation Approach](https://mlsanity.com/paper/2305.07001/) (2023)
- [Preference Transformer: Modeling Human Preferences using Transformers for RL](https://mlsanity.com/paper/2303.00957/) (2023)
- [Leveraging Large Language Models for Sequential Recommendation](https://mlsanity.com/paper/2309.09261/) (2023)
- [GPT Can Solve Mathematical Problems Without a Calculator](https://mlsanity.com/paper/2309.03241/) (2023)
- [Choice Over Control: How Users Write with Large Language Models using Diegetic and Non-Diegetic Prompting](https://mlsanity.com/paper/2303.03199/) (2023)
- [RecipeGPT: Generative Pre-training Based Cooking Recipe Generation and Evaluation System](https://mlsanity.com/paper/2003.02498/) (2020)
- [CoQuest: Exploring Research Question Co-Creation with an LLM-based Agent](https://mlsanity.com/paper/2310.06155/) (2023)
- [Large Language Model Distilling Medication Recommendation Model](https://mlsanity.com/paper/2402.02803/) (2024)
- [Sequential Gallery for Interactive Visual Design Optimization](https://mlsanity.com/paper/2005.04107/) (2020)
- [Exploring Prompt Engineering Practices in the Enterprise](https://mlsanity.com/paper/2403.08950/) (2024)
- [GRIDS: Interactive Layout Design with Integer Programming](https://mlsanity.com/paper/2001.02921/) (2020)
- [Exploiting Preference Elicitation in Interactive and User-centered Algorithmic Recourse: An Initial Exploration](https://mlsanity.com/paper/2404.05270/) (2024)
- [The Multimodal And Modular Ai Chef: Complex Recipe Generation From Imagery](https://mlsanity.com/paper/2304.02016/) (2023)
- [Cooperative Design Optimization through Natural Language Interaction](https://mlsanity.com/paper/2508.16077/) (2025)

## Abstract (arXiv)

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.