CALM
Co-evolution of Algorithms and Language Model
Heuristic evolution where the LLM itself is also fine-tuned with reinforcement learning on how good its heuristics are.
The loop
- Proposes
Heuristic code from a small LLM inside an evolutionary search
- Judged by
Running the heuristic on problem instances to get a quality score that becomes the RL reward
- Steers
Verbal guidance through prompts plus numerical guidance through GRPO fine-tuning of the LLM weights
Headline result
A Qwen2.5-7B-Instruct model (INT4, on a single 24GB GPU) with GRPO fine-tuning reached an average 0.71% gap on online bin packing, against 0.89% for MCTS-AHD and 2.40% for Best Fit, and beat the best listed competitor on CVRP (3.95% vs 4.70%) and OP (12.58% vs 16.34%) at N=200 in the paper's tables.
What this does not prove
The advantage is not uniform: on TSP at N=50 MCTS-AHD (9.69%) beats CALM (10.04%). Numbers come from the paper's own tables and baselines, which mostly ran on GPT-4o-mini.
How it generalizes the harness
- The algorithm is the solver
- Search over a population
- The output outlives the model
- Feedback retrains the generator
- AI at design time
Beyond a harness, the feedback also updates the generator's weights by RL while an evolutionary search runs, and the result is a heuristic that works without the model.
Classification
| What it proposes | Heuristic |
|---|---|
| Generative model | Qwen2.5-7B-Instruct, INT4, fine-tuned with GRPO (about 1.15% of weights) |
| Algorithmic authority | Benchmark evaluation of heuristic quality |
| Feedback | Reward signal |
| What gets updated | Prompt context, population of candidates and model weights |
| When it runs | Offline, at design time |
| Validity | Empirical (measured) |
| Evidence | Experiments reported |
| Lineage | Derivative |