OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models

• URL: http://arxiv.org/abs/2402.10172v1
• Date: Thu, 15 Feb 2024 18:19:18 GMT
• Title: OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models
• Authors: Ali AhmadiTeshnizi, Wenzhi Gao, Madeleine Udell
• Abstract summary: This paper introduces OptiMUS, a Large Language Model (LL)M-based agent designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. OptiMUS can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve its model and code based on these evaluations. Experiments demonstrate that OptiMUS outperforms existing state-of-the-art methods on easy datasets by more than $20%$ and on hard datasets by more than $30%$.
• Score: 21.519880445683107
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise required to formulate and solve these problems limits the widespread adoption of optimization tools and techniques. This paper introduces OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve (mixed integer) linear programming problems from their natural language descriptions. OptiMUS can develop mathematical models, write and debug solver code, evaluate the generated solutions, and improve its model and code based on these evaluations. OptiMUS utilizes a modular structure to process problems, allowing it to handle problems with long descriptions and complex data without long prompts. Experiments demonstrate that OptiMUS outperforms existing state-of-the-art methods on easy datasets by more than $20\%$ and on hard datasets (including a new dataset, NLP4LP, released with this paper that features long and complex problems) by more than $30\%$.

Related papers

• Autoformulation of Mathematical Optimization Models Using LLMs [50.030647274271516]
  We develop an automated approach to creating optimization models from natural language descriptions for commercial solvers. We identify the three core challenges of autoformulation: (1) defining the vast, problem-dependent hypothesis space, (2) efficiently searching this space under uncertainty, and (3) evaluating formulation correctness.
  arXiv  Detail & Related papers  (2024-11-03T20:41:38Z)
• LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch [16.174567164068037]
  We propose a unified learning-based framework called LLMOPT to boost optimization generalization. LLMOPT constructs the introduced five-element formulation as a universal model for learning to define diverse optimization problem types. We evaluate the optimization generalization ability of LLMOPT and compared methods across six real-world datasets.
  arXiv  Detail & Related papers  (2024-10-17T04:37:37Z)
• Learning Joint Models of Prediction and Optimization [56.04498536842065]
  Predict-Then-Then framework uses machine learning models to predict unknown parameters of an optimization problem from features before solving. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models.
  arXiv  Detail & Related papers  (2024-09-07T19:52:14Z)
• OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale [16.33736498565436]
  We introduce a Large Language Model (LLM)-based system designed to formulate and solve linear programming problems from their natural language descriptions. Our system is capable of developing mathematical models, writing and debugning solver code, evaluating the generated solutions, and improving efficiency and correctness of its model and code. Experiments demonstrate that OptiMUS-0.3 outperforms existing state-of-the-art methods on easy datasets by more than 12% and on hard datasets by more than 8%.
  arXiv  Detail & Related papers  (2024-07-29T01:31:45Z)
• OptiBench Meets ReSocratic: Measure and Improve LLMs for Optimization Modeling [62.19438812624467]
  Large language models (LLMs) have exhibited their problem-solving abilities in mathematical reasoning. We propose OptiBench, a benchmark for End-to-end optimization problem-solving with human-readable inputs and outputs.
  arXiv  Detail & Related papers  (2024-07-13T13:27:57Z)
• Solving General Natural-Language-Description Optimization Problems with Large Language Models [34.50671063271608]
  We propose a novel framework called OptLLM that augments LLMs with external solvers. OptLLM accepts user queries in natural language, convert them into mathematical formulations and programming codes, and calls the solvers to calculate the results. Some features of OptLLM framework have been available for trial since June 2023.
  arXiv  Detail & Related papers  (2024-07-09T07:11:10Z)
• Functional Graphical Models: Structure Enables Offline Data-Driven Optimization [111.28605744661638]
  We show how structure can enable sample-efficient data-driven optimization. We also present a data-driven optimization algorithm that infers the FGM structure itself.
  arXiv  Detail & Related papers  (2024-01-08T22:33:14Z)
• OptiMUS: Optimization Modeling Using MIP Solvers and large language models [21.519880445683107]
  We introduce OptiMUS, a Large Language Model (LLM)-based agent designed to formulate and solve MILP problems from their natural language descriptions. To benchmark our agent, we present NLP4LP, a novel dataset of linear programming (LP) and mixed integer linear programming (MILP) problems. Our experiments demonstrate that OptiMUS solves nearly twice as many problems as a basic LLM prompting strategy.
  arXiv  Detail & Related papers  (2023-10-09T19:47:03Z)
• Large Language Models as Optimizers [106.52386531624532]
  We propose Optimization by PROmpting (OPRO), a simple and effective approach to leverage large language models (LLMs) as prompts. In each optimization step, the LLM generates new solutions from the prompt that contains previously generated solutions with their values. We demonstrate that the best prompts optimized by OPRO outperform human-designed prompts by up to 8% on GSM8K, and by up to 50% on Big-Bench Hard tasks.
  arXiv  Detail & Related papers  (2023-09-07T00:07:15Z)
• Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation [101.22379613810881]
  We consider data-driven optimization problems where one must maximize a function given only queries at a fixed set of points. This problem setting emerges in many domains where function evaluation is a complex and expensive process. We propose a tractable approximation that allows us to scale our method to high-capacity neural network models.
  arXiv  Detail & Related papers  (2021-02-16T06:04:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.