SeaEvo: Strategy as State for LLM-Driven Evolution

Large language model (LLM)-driven evolutionary search is increasingly used for automated algorithm discovery and program optimization. However, most existing methods represent search progress primarily through executable programs and scalar fitness, while language-level strategies remain transient mutation context or unstructured memory. This makes it difficult to organize search progress across related algorithmic directions or reason about which directions are promising, saturated, or underexplored. We introduce \model, which treats strategy as persistent population-level evolutionary state. Each candidate is associated with an explicit strategy description, and these candidate-aligned strategies form a semantic space that supports complementary experience retrieval and population-level search guidance. \model operates as a lightweight layer over existing evolutionary backbones without modifying their selection or evaluation logic. Across mathematical and systems optimization benchmarks, \model improves the mean performance of its matched evolutionary backbone in 23 of 24 comparisons across two mutation models. By retrieving compact strategy descriptions rather than full source programs, \model reduces average LLM token usage by 48.8%. These results suggest that persistent strategy representations provide a practical mechanism for improving the effectiveness and cost-efficiency of LLM-guided evolutionary search, pointing toward compound AI systems whose search capabilities benefit from the structured accumulation and reuse of algorithmic strategies.