---
license: apache-2.0
base_model: Qwen/Qwen2.5-Math-7B
tags:
  - operations-research
  - optimization
  - linear-programming
  - integer-programming
  - lora
  - dpo
  - peft
language:
  - en
library_name: peft
pipeline_tag: text-generation
---

# OptimAI

A 7B model fine-tuned to formulate and solve operations research problems (LP, IP, network flow, queueing, stochastic optimization).

Built on Qwen2.5-Math-7B with a two-stage training pipeline: supervised fine-tuning (SFT) followed by Direct Preference Optimization (DPO). Distributed as a LoRA adapter (~646 MB).

## Intended use

- Formulating optimization problems from natural-language descriptions
- Solving small LPs, IPs, shortest-path, max-flow, knapsack, and similar OR problems end-to-end
- Studying optimality conditions (KKT, dual formulations, sensitivity analysis)
- Educational support for OR / optimization students

Not a replacement for a real solver. Use this to set up the problem; verify with Gurobi, CPLEX, OR-Tools, or SciPy.

## Evaluation

Evaluated on a held-out set of 60 OR problems across three categories: closed_form (n=20, auto-graded), open_conceptual (n=20, qualitative), long_form (n=20, qualitative).

Closed-form numeric accuracy (final-answer grader, last 5 lines of completion only):

| Model | Closed-form score |
|---|---|
| SFT-only | 48.3% |
| SFT + DPO (this model) | 55.4% |

DPO gives a +7.1 percentage point absolute improvement (~15% relative). Across 20 closed-form items, DPO improved 7, regressed 5, tied 8.

### Example: A01 (LP formulation)

Prompt: "A factory produces A and B. A needs 2h labor, 3 units material, profit $5. B needs 1h labor, 2 units material, profit $4. Available: 100h labor, 200 units material. Maximize profit."

Expected: x_A=40, x_B=20, profit=280

SFT (incorrect): "the optimal solution is x_A = 20 and x_B = 60, which gives a total profit of $340"

DPO (correct): "the maximum profit occurs at the point (x_A, x_B) = (40, 20), yielding a total profit of $280"

## How to use

    from peft import PeftModel
    from transformers import AutoModelForCausalLM, AutoTokenizer
    import torch

    base = AutoModelForCausalLM.from_pretrained(
        "Qwen/Qwen2.5-Math-7B",
        torch_dtype=torch.bfloat16,
        device_map="auto",
        trust_remote_code=True,
    )
    model = PeftModel.from_pretrained(base, "billwang37/WWang-Lab-OptimAI")
    tokenizer = AutoTokenizer.from_pretrained("billwang37/WWang-Lab-OptimAI", trust_remote_code=True)

    prompt = "Maximize 3x + 5y subject to x + 2y <= 14, 3x - y >= 0, x - y <= 2, x,y >= 0."
    inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
    out = model.generate(**inputs, max_new_tokens=1024, do_sample=False)
    print(tokenizer.decode(out[0], skip_special_tokens=True))

## Training details

- Base model: Qwen/Qwen2.5-Math-7B
- SFT data: ~6k OR problems with worked solutions
- DPO data: ~1.2k preference pairs (chosen vs rejected)
- Method: LoRA adapter via PEFT + TRL
- Hardware: Single A100 (40 GB) on OU OSCER cluster
- SFT runtime: ~4 hours (3 epochs)
- DPO runtime: ~30 minutes

## Limitations

- 60-problem eval set is small; numbers are a directional signal, not a definitive benchmark
- Grader checks numbers, not reasoning
- Can produce confidently wrong answers, especially on integer programming and combinatorial graph problems
- LoRA adapter format; you must load Qwen2.5-Math-7B base separately
- English-only

## License

Apache-2.0, inherited from the base model.