Large Language Model (LLM)-based automated algorithm design typically evolves algorithms as complete, indivisible programs. While this whole-program perspective simplifies the search space, it fundamentally couples the useful local logic to its host program. Consequently, valuable code snippets vanish when the overall program is discarded, making it highly difficult to assess the contribution of individual algorithmic components.To address this, we propose Primitive-Aware Code Evolution (PACE), which decouples local logic from complete programs by representing it as persistent units called Executable Algorithmic Primitives (EAPs). To enable code-level transfer, PACE maintains a dynamic set of EAPs. Algorithm evolution is driven by primitive-aware operators that structurally guarantee the retention and cross-program transfer of these components. To evaluate them effectively, PACE leverages Thompson sampling based on parent-relative performance improvements, guiding primitive selection from the set without requiring extra evaluation datasets. Experiments on four tasks demonstrate that PACE effectively discovers competitive algorithms while structurally preserving valuable algorithmic components.
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 discards valuable execution feedback. We propose AlgoEvo, a unified agentic framework 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 single workflow to seamlessly handle single-objective, multi-objective, and multi-component design. Meanwhile, a hierarchical experience mechanism 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 matches or surpasses specialized methods with substantially fewer evaluations and reduced token consumption, demonstrating strong intra-task accumulation, cross-task transfer, and the ability to reproduce or exceed existing state-of-the-art performance through flexible skill activation.
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× 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 (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into sets of corrections, enabling correction-level credit assignment that informs subsequent queries. We complement this framework with theoretical insights into the ideal balance between search depth and breadth at different budget levels. We validate our method empirically on three combinatorial optimization problems, demonstrating consistent superiority of our graph-based search over full-algorithm search at equal token budget. Finally, our experiments suggest that rich contexts help only when the LLM's prior knowledge is shallow, and can hinder performance otherwise.