Decision-making problems can be represented as mathematical optimization models, finding wide applications in fields such as economics, engineering and manufacturing, transportation, and health care. Optimization models are mathematical abstractions of the problem of making the best decision while satisfying a set of requirements or constraints. One of the primary barriers to deploying these models in practice is the challenge of helping practitioners understand and interpret such models, particularly when they are infeasible, meaning no decision satisfies all the constraints. Existing methods for diagnosing infeasible optimization models often rely on expert systems, necessitating significant background knowledge in optimization. In this paper, we introduce OptiChat, a first-of-its-kind natural language-based system equipped with a chatbot GUI for engaging in interactive conversations about infeasible optimization models. OptiChat can provide natural language descriptions of the optimization model itself, identify potential sources of infeasibility, and offer suggestions to make the model feasible. The implementation of OptiChat is built on GPT-4, which interfaces with an optimization solver to identify the minimal subset of constraints that render the entire optimization problem infeasible, also known as the Irreducible Infeasible Subset (IIS). We utilize few-shot learning, expert chain-of-thought, key-retrieve, and sentiment prompts to enhance OptiChat's reliability. Our experiments demonstrate that OptiChat assists both expert and non-expert users in improving their understanding of the optimization models, enabling them to quickly identify the sources of infeasibility.

翻译：决策问题可抽象为数学优化模型，广泛应用于经济、工程制造、交通运输及医疗健康等领域。优化模型是满足一系列需求或约束条件的同时做出最优决策问题的数学抽象。在实际部署这类模型时，主要障碍之一是帮助从业者理解和解读模型，特别是当模型不可行时——即不存在满足所有约束条件的决策。现有诊断不可行优化模型的方法通常依赖专家系统，需要用户具备深厚的优化领域背景知识。本文首次提出基于自然语言的系统OptiChat，配备聊天机器人图形用户界面，支持对不可行优化模型进行交互式对话。OptiChat能够以自然语言描述优化模型本身，识别潜在不可行性来源，并提供使模型可行的建议。该系统的实现基于GPT-4，通过连接优化求解器识别导致整个优化问题不可行的最小约束子集（即不可约不可行子集，IIS）。我们采用少样本学习、专家思维链、关键信息检索和情感提示等技术提升OptiChat的可靠性。实验表明，OptiChat能帮助专家和非专家用户加深对优化模型的理解，并快速定位不可行性来源。