Algorithm Modelization: Transforming Optimization Algorithms into Evolvable Intelligence

Large Language Model (LLM)-guided evolutionary search is increasingly used for automated algorithm discovery, yet most current methods track search progress primarily through executable programs and scalar fitness. Even when natural-language reasoning is used through heuristic descriptions or reflection, it typically remains transient mutation context or unstructured memory, rather than organized as persistent population-level state over strategic directions. As a result, evolutionary search can struggle to distinguish syntactically different implementations of the same idea, preserve lower-fitness but strategically promising directions, or detect when an entire family of strategies has saturated. We introduce \model, a modular strategy-space layer that turns language-level strategic reasoning into first-class population-level evolutionary state in LLM-driven program search. \model represents each candidate program with an explicit natural-language strategy, clusters the archive by strategy semantics, retrieves behaviorally complementary inspirations, and periodically navigates the strategy landscape to avoid saturated directions. Without modifying the underlying evolutionary algorithms, \model improves existing evolutionary backbones across algorithm discovery, systems optimization, and agent-scaffold design tasks in most settings. Across four systems benchmarks, \model achieves a 20.6% average relative improvement, with the best single run on Prism scoring 3$\times$ higher. 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.

Large language models are increasingly participating in complex real-world tasks in the form of algorithm-design agents, designing and refining algorithms. Many successful algorithm-design agents adopt pure in-context evolutionary frameworks, but they may quickly plateau in domains that require specialized knowledge. Parametric adaptation offers a way to internalize specialized knowledge, but conventional training requires abundant domain-specific corpora while high-quality algorithms are scarce in complex algorithm-design scenarios. In this paper, we propose sample-efficient parametric self-evolution where agents can explore and learn from self-generated algorithms. First, we characterize in-context evolutionary stagnation and analytically propose the Improvement Chain proposition, showing how learning successive self-generated algorithms can locally increase the likelihood of neighboring algorithms. Motivated by this local-transfer perspective, we further propose Population-Curated Policy Optimization (PCPO) to utilize a global population and a hybrid policy update scheme for retaining and reusing high-quality, diverse self-generated algorithms, shifting the policy towards stronger algorithms. In the task of learning rate schedule design for global placement in electronic design automation, trained only on 4 chip cases, PCPO outperforms the state-of-the-art in-context evolutionary methods (e.g., OpenEvolve and ShinkaEvolve) on average across 16 chip cases. With an 8B-size base model, PCPO achieves competitive performance compared to frontier closed-source models such as GPT-5.5. PCPO also reduces inference-time token cost by internalizing grounded domain knowledge and prompt distillation. Moreover, PCPO achieves significant speedups on four GPU kernel designs, with an average of 8.27$\times$ speedup against the PyTorch Eager baseline.

Large language models have advanced automated algorithm discovery by synthesizing executable code, but existing frameworks trap them in rigid search pipelines with pre-defined control flows. This limitation restricts adaptive reasoning, blocks cross-paradigm transfer, and overlooks richer execution feedback. To bridge this gap, we introduce an end-to-end framework, AlgoEvo, a unified agentic architecture that transforms automated algorithm discovery into an interactive, knowledge-accumulating process. An autonomous agent dynamically inspects, diagnoses, and edits code based on runtime feedback. A design skill hub decouples paradigm-specific knowledge from the core discovery engine, allowing a unified workflow to seamlessly handle single-heuristic, multi-objective, and multi-component design. Meanwhile, a hierarchical experience bank organizes search trajectories into a task-level tree to guide exploration and consolidates cross-task patterns into reusable skills. Across six representative benchmark tasks, AlgoEvo reaches state-of-the-art performance with as little as 7% of the evaluation budget and reduced token consumption, demonstrating strong intra-task accumulation, cross-task transfer, and the ability to reproduce or exceed the strongest existing methods through flexible skill activation.