Analysis for Large Language Model for Discrete Optimization Problems: Evaluation and Step-by-step Reasoning
Unlocking Automated Decision-Making: LLMs in Discrete Optimization
This paper evaluates the performance of LLMs, specifically Llama-3 series and ChatGPT, on discrete optimization problems using natural language datasets. The dataset is unique, covering various problem types and parameter magnitudes, including large sets and augmented data.
The study aims to benchmark LLM capabilities for large-scale problems, offer guidance for automated discrete optimization, and provide a reference for future research. It compares strong vs. weak models, Chain-of-Thought (CoT) vs. No-CoT methods, and analyzes performance on original, expanded, and disordered datasets.
Key findings indicate that stronger models generally perform better. Contrary to common belief, CoT is not always effective. Disordered datasets can improve performance on 'easy-to-understand' problems, though sometimes with high variance. The paper recommends consulting its results and line charts for strategic suggestions on enhancing automated discrete optimization.
Quantifiable Impact at a Glance
0
Mean Accuracy Rate (AR)
0
Average Pass Rate (PR)
0
Max % Improvement (Disordered Data)
0
Timeout Rate (TR)
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Introduction & Background
The introduction highlights the prevalence of Operations Research (OR) problems, especially discrete optimization, in industrial and control systems. It emphasizes the need for automated solutions and the potential of Large Language Models (LLMs) to integrate information and select methods. The paper notes existing LLM research on mathematical problems like MathQA and GSM8K but identifies a gap in evaluating LLMs for discrete optimization problems with wide-ranging parameter magnitudes, focusing on decision-making rather than continuous thinking. This work aims to bridge that gap by creating new datasets and benchmarks.
Related Work
Prior research on automated discrete optimization focused on algorithms and Python repositories (PULP, CVXPY, Gurobi). With LLMs, initial efforts tested basic math problems (MathQA, GSM8K). Studies like ORLM fine-tuned LLaMA-3-8B for OR but had rigid responses. Researchers have also explored LLMs as optimizers and for generating hybrid swarm intelligence algorithms. Fine-tuning LLMs for OR problems (e.g., Deepseek-Math-7B-Base, Mistral-7B) has shown promise in improving stability and reducing latency. Some work also combined LLMs with OR optimization for human-machine collaboration, accelerating expert model creation.
Benchmarking & Data Representation
This section details the construction of large-scale datasets for discrete optimization problems, derived from the OR library and VRP, and presented in natural language. The dataset includes Assignment, 1D-Binpacking, Crew-Scheduling, Steiner, UBQP, CVRP, MDVRP, PVRP, Aircraft Landing, Generalized Assignment, Multi-dimensional Knapsack, Capacitated Warehouse Location, and 2D-cutting Packing-constrained Guillotine problems. Data generation involved manual annotation, referencing papers for specific problems, and data expansion by extracting and continuing backgrounds using GPT-40-mini. Data augmentation introduced 'noise' by randomizing sentence order to test LLMs' true understanding versus pattern matching. The section also covers four evaluation metrics: Pass Rate (PR), Accuracy Rate (AR), Mean Absolute Percentage Error (MAPE), and Timeout Rate (TR), and defines baselines using models like GPT-40-mini, DeepSeek-R1, LLAMA3-8B-Instruct, and ORLM with CoT and PoT techniques.
Experiments & Analysis
Experiments show DeepSeek-R1's strong PR on implicit problems, generally outperforming GPT-40-mini, especially on tasks like Aircraft Landing and Generalized Assignment. CoT prompting doesn't always improve PR, benefiting stronger models more consistently. Disordered datasets can increase PR for stronger models by presenting optimization goals earlier, aligning with Bayesian posterior updates. For AR, GPT-40-mini excels with CoT on original implicit data, while DeepSeek-R1 shines with PoT. Disordered datasets also boost AR for stronger models. ORLM faces consistent formatting issues. MAPE results show LLAMA3 and ORLM frequently producing null values due to outliers, while DeepSeek-R1 generally performs better with both CoT/No-CoT, and GPT-40-mini with CoT only. CoT is recommended for robustness. Error analysis reveals common IndexError, ValueError, TypeError, and SyntaxError for different problem types, often related to list operations, data reading, solver misuse, or syntax issues.
Conclusion & Strategies
The study concludes that LLMs exhibit high sensitivity to input text, with disordered datasets causing higher variance in strong models but poor performance in weaker ones. Performance on disordered datasets helps quantify LLMs' understanding difficulty. Problems are categorized by difficulty: Steiner, UBQP, 2D-Cutting, MDVRP, PVRP are most difficult; CVRP, Generalized Assignment, Aircraft Landing are moderately difficult; Crew Scheduling, Multi-dimensional Knapsack, Capacitated Warehouse, Assignment, and 1D-Binpacking are easier. CoT significantly improves problem-solving for difficult problems, but can hinder easier ones. The paper offers three strategies: (1) weak models use no-CoT with original data, strong models use CoT with disordered data; (2) CoT ensures solution quality, disordered data pursues optimality; (3) disordered datasets are recommended for difficult-to-understand problems (ranked via Table 11). Further research will explore non-PoT approaches if these strategies fail.
97.10%
DeepSeek-R1's Peak Pass Rate (PR) with CoT on Steiner problems, showcasing strong performance regardless of solution quality.
Enterprise Process Flow
Input Normalization
→
Iterative Search (Rounds × Simulations)
→
Verification & Scoring
→
Cross-round Guidance Aggregation
→
Selection
→
Expansion
→
Evaluation
→
Backprop-like Update
| Model & Technique | Strength | CoT Benefit | Disordered Data Effect |
|---|---|---|---|
| DeepSeek-R1 (PoT) | Strong | Excels with PoT for AR, strong PR on implicit data. |
|
| GPT-4o-mini (CoT) | Strong | Significant AR advantages with CoT on original implicit datasets. |
|
| LLAMA3-8B-Instruct | Weaker | CoT may not consistently benefit, or even worsen PR/AR. |
|
| ORLM | Weaker (Finetuned Llama3-8B) | Persistent format compliance issues; CoT does not make PR evaluations meaningful. |
|
Impact of Problem Difficulty on LLM Performance
The study categorized discrete optimization problems by their difficulty for LLMs to understand. Problems like Steiner Tree, UBQP, 2D-Cutting Packing-Constrained Guillotine, MDVRP, and PVRP were found to be most challenging.
Moderately difficult problems included CVRP, Generalised Assignment, and Aircraft Landing. The easiest problems for LLMs were crew scheduling, multi-dimensional knapsack, capacitated warehouse location, assignment problems, and 1D-Binpacking.
A significant finding was the consistency between these classifications and the performance difference on disordered datasets. This suggests that the impact of disordered datasets can serve as a proxy for quantifying LLM understanding difficulty for a given problem type. For easier problems, disorder can enhance problem-solving, but for more complex ones, Chain of Thought (CoT) is crucial.
For problems identified as more challenging to understand, the Chain of Thought (CoT) approach significantly improves LLMs' problem-solving abilities. Conversely, for easier problems, Chain of Thought (CoT) can sometimes negatively impact performance.
Calculate Your Potential ROI
Estimate the impact of integrating advanced AI solutions into your discrete optimization processes.
Estimated Annual Savings
$0
Hours Reclaimed Annually
0
Your AI Implementation Timeline
A phased approach to integrating LLMs into your discrete optimization workflows.
Phase 1: Data Preparation & Model Selection
Curate and preprocess natural language discrete optimization datasets. Select appropriate LLM architectures (e.g., Llama-3 series, ChatGPT) and consider finetuning with ORLM or DeepSeek-R1 for domain-specific tasks. Establish evaluation metrics (PR, AR, MAPE, TR) and baseline performance.
Phase 2: Prompt Engineering & Data Augmentation
Develop and test various prompt engineering techniques, including Chain-of-Thought (CoT) and Program-of-Thought (PoT). Implement data augmentation strategies, such as creating expanded and disordered datasets, to improve LLM robustness and test sensitivity to input text variations.
Phase 3: Experimentation & Performance Analysis
Conduct comprehensive experiments across different models, prompting methods, and datasets. Analyze performance using the defined metrics, identifying error types (IndexError, ValueError, TypeError, SyntaxError, etc.) and their root causes. Compare strong vs. weaker models and the impact of disordered datasets.
Phase 4: Strategic Recommendations & Optimization
Formulate strategic recommendations for enterprises looking to automate discrete optimization problems using LLMs, considering model strength, problem difficulty, and dataset characteristics. Explore advanced optimization techniques (e.g., iterative search, verification & scoring) to enhance solution quality and efficiency, leading to continuous model improvement.
Ready to Transform Your Operations?
Connect with our experts to discover how large language models can revolutionize your discrete optimization challenges.
Ready to Get Started?
Book Your Free Consultation.
Let's Discuss Your AI Strategy!
Lets Discuss Your Needs
Select a Date
Sun
Mon
Tue
Wed
Thu
Fri
Sat