Geospatial algorithms start rewriting their own code: seeded with Two-stage K-Models, an evolved version beats its seed across 150 simulated grids

Improving a geospatial algorithm no longer has to depend entirely on researchers writing each variant by hand; a multi-agent search can generate, evaluate and retain candidate variants once a seed algorithm and a computable objective are given. Algorithm discovery had been expert-driven: a researcher spots a limitation, proposes a structural fix, implements it and validates it against established baselines, with each step bounded by one group's time and cognitive resources. Seeded with Two-stage K-Models and using the Rand Index against the ground-truth partition as fitness, the evolved algorithm outperforms its seed, knowledge-free baselines and four classical regionalization methods on 150 simulated grids.

Search runs only on synthetic data, and the resulting algorithm is frozen and applied unchanged to real data, so real-world performance counts as out-of-sample evidence. Driving evolution directly with the real-data metrics that will be reported makes the same metric both training target and evaluation target, and the resulting numbers tell us less than they appear to. The frozen algorithm attains the lowest cross-dataset mean RMSE of 1.220 and the highest SSR Reduction of 0.658 on 11 real datasets spanning climate, health, hydrology and politics, with nine first-place wins on SSR Reduction out of 11 datasets.

The channel through which geographic knowledge enters the search is itself load-bearing; structured retrieval is not the same as hints written into a static prompt. A general-purpose evolution engine could only place domain knowledge into the prompt as static text, without retrieving it against the current state of the code. An ablation compares no knowledge, a general prompt hint, a task-specific prompt hint, multi-agent dialogue without retrieval, and the full pipeline with GeoKnowRAG enabled, and the results indicate the knowledge-injection channel is a load-bearing design choice.

The demonstrated scope is one seed algorithm (Two-stage K-Models) and one task family (spatial regime discovery); evolution runs only on synthetic grids, and the frozen algorithm is applied unchanged to 11 real datasets, where the four metrics are model-fit statistics rather than predictions at unobserved locations.

The ordering among evolved variants is reported as descriptive because run-to-run standard deviations are of the same order as the gaps between variants; whether LLM-assisted search speeds up the inner loop, and whether it holds for other seeds and task families, is explicitly left open.