Diagnosing Infeasible Optimization Problems Using Large Language Models

TL;DR

This work addresses the challenge of diagnosing infeasible optimization models, particularly for non-experts, by introducing OptiChat, an LLM-based autonomous agent that describes optimization models, identifies Irreducible Infeasible Subsets (IIS), and proposes feasible repairs via slack-variable relaxation. The system integrates GPT-4 with an optimization solver (e.g., Gurobi) to compute IIS and to produce actionable, natural-language guidance, leveraging prompting techniques such as expert chain-of-thought, few-shot demonstrations, key-retrieve prompts, and sentiment prompts. The authors demonstrate effectiveness across 63 infeasible instances from diverse domains, comparing performance between inexperienced and experienced users in both quantitative and qualitative assessments, and show improved understanding and faster troubleshooting. The approach enhances accessibility and reliability of optimization diagnostics, with practical impact for real-world decision-making in sectors like finance, logistics, and infrastructure.

Abstract

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.

Figures (5)

• Figure 1: Overview of OptiChat. Users can directly interact with OptiChat using natural language without writing a single line of code. OptiChat is an LLM-powered autonomous agent system.
• Figure 2: Example of Irreducible Infeasible Subset (IIS). The feasible region of each constraint is colored. The original constraint set, $S=\{A,B,C\}$ is infeasible since no solution satisfies the three constraints. However, any proper subset is a feasible constraint set, i.e., if any of the constraints are dropped, then the constraint set becomes feasible.
• Figure 3: Illustrative conversation. This example shows how the OptiChat agent conducts model analysis, infeasibility diagnosis, troubleshoot recommendations, and interactive conversations through the GUI.
• Figure 4: Effects of adding slack variables. (a) shows the problem can be made feasible by adjusting the left-hand side matrix $\mathbf{A}$. (b) shows the effect of adding slack variable $\mathbf{\delta b}^+$ to the right-hand side. The region and the point in black represent the feasible regions after adding the slack variables.
• Figure 5: User study results: Likert graph of survey statements.