# SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations

arXiv: https://arxiv.org/abs/2511.00685 · HTML: https://mlsanity.com/paper/2511.00685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 25 of 25)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [Automated Creation of Digital Cousins for Robust Policy Learning](https://mlsanity.com/paper/2410.07408/) (2024)
- [Efficient Causal Graph Discovery Using Large Language Models](https://mlsanity.com/paper/2402.01207/) (2024)
- [LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages](https://mlsanity.com/paper/2405.13144/) (2024)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [MLZero: A Multi-Agent System for End-to-end Machine Learning Automation](https://mlsanity.com/paper/2505.13941/) (2025)
- [OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents](https://mlsanity.com/paper/2504.16918/) (2025)
- [Comparison of High-Dimensional Bayesian Optimization Algorithms on BBOB](https://mlsanity.com/paper/2303.00890/) (2023)
- [Surrogate-Based Simulation Optimization](https://mlsanity.com/paper/2105.03893/) (2021)
- [Collaborative Bayesian Optimization via Wasserstein Barycenters](https://mlsanity.com/paper/2504.10770/) (2025)
- [Efficient Ranking and Selection in Parallel Computing Environments](https://mlsanity.com/paper/1506.04986/) (2015)
- [RPO: Fine-Tuning Visual Generative Models via Rich Vision-Language Preferences](https://mlsanity.com/paper/2503.11720/) (2025)
- [Pseudo-Bayesian Optimization](https://mlsanity.com/paper/2310.09766/) (2023)
- [Bayesian Geostatistics Using Predictive Stacking](https://mlsanity.com/paper/2304.12414/) (2023)
- [Simulation-Based Digital Twin Development for Blockchain Enabled End-to-End Industrial Hemp Supply Chain Risk Management](https://mlsanity.com/paper/2006.10915/) (2020)
- [Calibrating Over-Parametrized Simulation Models: A Framework via Eligibility Set](https://mlsanity.com/paper/2105.12893/) (2021)
- [Performance Comparison of Surrogate-Assisted Evolutionary Algorithms on Computational Fluid Dynamics Problems](https://mlsanity.com/paper/2402.16455/) (2024)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)

## Built on by (most cited first, 1 of 1)

- [LLM-Assisted Logic Rule Learning: Scaling Human Expertise for Time Series Anomaly Detection](https://mlsanity.com/paper/2601.19255/) (2026)

## Abstract (arXiv)

The field of simulation optimization (SO) encompasses various methods developed to optimize complex, expensive-to-sample stochastic systems. Established methods include, but are not limited to, ranking-and-selection for finite alternatives and surrogate-based methods for continuous domains, with broad applications in engineering and operations management. The recent advent of large language models (LLMs) offers a new paradigm for exploiting system structure and automating the strategic selection and composition of these established SO methods into a tailored optimization procedure. This work introduces SOCRATES (Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations), a novel two-stage procedure that leverages LLMs to automate the design of tailored SO algorithms. The first stage constructs an ensemble of digital replicas of the real system. An LLM is employed to implement causal discovery from a textual description of the system, generating a structural `skeleton' that guides the sample-efficient learning of the replicas. In the second stage, this replica ensemble is used as an inexpensive testbed to evaluate a set of baseline SO algorithms. An LLM then acts as a meta-optimizer, analyzing the performance trajectories of these algorithms to iteratively revise and compose a final, hybrid optimization schedule. This schedule is designed to be adaptive, with the ability to be updated during the final execution on the real system when the optimization performance deviates from expectations. By integrating LLM-driven reasoning with LLM-assisted trajectory-aware meta-optimization, SOCRATES creates an effective and sample-efficient solution for complex SO optimization problems.