Enterprise AI Research Analysis
Behavior and Representation in Large Language Models for Combinatorial Optimization
Authors: Francesca Da Ros, Luca Di Gaspero, Kevin Roitero (University of Udine, Italy)
This study investigates how Large Language Models (LLMs) internally represent combinatorial optimization problems and whether such representations can support downstream decision tasks. Adopting a twofold methodology combining direct querying and probing analyses, we evaluate LLM capacity to explicitly extract instance features and implicitly encode information for per-instance algorithm selection. The research spans four benchmark problems and three instance representations, revealing how LLMs capture meaningful structural information comparable to traditional feature extraction.
Key Findings & Enterprise Impact
Our analysis uncovers critical insights into LLM capabilities for combinatorial optimization, offering pathways to enhanced automation and decision-making.
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Optimization Problems Analyzed
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Instance Representations
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Total Instances Processed
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Alg. Selection Equivalence
Deep Analysis & Enterprise Applications
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RQ1: Direct Querying
RQ2: Feature Probing
RQ3: Algorithm Selection
Methodology Flow
Explicit Feature Extraction (RQ1)
~90%
Accuracy for Simple Features via Direct Querying
Direct querying experiments reveal that LLMs can effectively infer simple instance features from natural language and code-like representations. For features explicitly stated or requiring minimal computation, accuracy often approaches 90% or higher. However, performance significantly deteriorates for features demanding complex numerical or procedural reasoning, indicating a current limitation in LLM's explicit computational capabilities.
Implicit Feature Encoding (RQ2)
Up to 80%
MAE Reduction for Complex Features via Probing
Probing analyses demonstrate that LLMs implicitly encode structural and numerical information about combinatorial optimization instances within their hidden layers. This is particularly evident for high-computation features, where probing models achieve significantly lower Mean Absolute Error (MAE) compared to direct querying. This suggests that complex relational information, while not explicitly extractable, is latently represented and accessible for downstream tasks.
Predictive Power for Algorithm Selection (RQ3)
| Criteria | Traditional ISA-Based Features | LLM-Derived Features |
|---|---|---|
| Feature Origin | Human-engineered, problem-specific descriptors | Automated extraction from LLM hidden layers |
| Expertise Required | High domain expertise for design and extraction | Low/minimal design effort for feature extraction |
| Computational Cost (Extraction) | Relatively low and efficient | Significantly higher for embedding generation |
| Predictive Performance (Accuracy) | Comparable to LLM-derived features | Statistically comparable to ISA-based features |
| Interpretability | High, features are explicit and understandable | Lower, latent embeddings are less interpretable |
LLM-extracted latent representations effectively serve as instance features surrogates for per-instance algorithm selection. When compared with traditional Instance Space Analysis (ISA)-based features, LLM-derived embeddings achieve statistically comparable predictive performance. This demonstrates their potential to automate feature engineering, albeit with a trade-off in computational cost and interpretability.
Unified Experimental Framework
Define CO Problem, Instances & Algorithms
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Generate Instance Representations
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Extract Features (Direct Query)
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Extract Embeddings (Probing)
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Train Predictors (Features/Embeddings)
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Evaluate Performance
Our methodology combined direct querying to assess explicit feature awareness and probing analyses to investigate implicit knowledge within LLM hidden layers. This systematic approach, applied across four COPs and multiple instance representations, provides a comprehensive view of how LLMs learn about problem structure and algorithmic behavior, informing downstream decision tasks like algorithm selection.
Calculate Your Potential AI Impact
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Estimated Annual Savings
$0
Annual Hours Reclaimed
0
Your AI Optimization Roadmap
A typical phased approach to integrating LLM-powered optimization into your enterprise, maximizing impact and minimizing disruption.
Phase 1: Discovery & Assessment
Comprehensive analysis of existing optimization processes, identifying key challenges and potential AI integration points. Define success metrics and scope pilot projects.
Phase 2: Pilot Development & Testing
Develop and test LLM-powered prototypes on specific combinatorial optimization problems. Validate feature extraction, algorithm selection, and performance prediction against benchmarks.
Phase 3: Integration & Scaling
Seamlessly integrate validated AI solutions into your existing enterprise systems. Scale capabilities across additional problem domains and operational workflows, ensuring robust performance.
Phase 4: Monitoring & Continuous Improvement
Establish ongoing monitoring of AI model performance and system-wide impact. Implement feedback loops for continuous learning and adaptation to evolving business needs and data.
Unlock Advanced Optimization for Your Enterprise
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