GraphSkillEvo: Evolutionary Optimization of Graph-Structured Agent Skills

Skills can improve the performance of Large Language Model (LLM) agents by providing task-specific procedural guidance, while skill optimization further improves their effectiveness through iterative refinement. However, existing skill optimization methods typically represent skills as unstructured natural-language instructions, creating two key challenges: **1)** Unstructured skills often lack explicit workflow-level guidance and contain substantial redundancy, making them difficult for LLMs to execute; **2)** the vast search space of unconstrained natural-language skills makes skill optimization ineffective. To address these challenges, we propose representing skills as **graph-structured natural-language artifacts**. In graph-structured skills, each node represents an execution step together with its operational guidance, while directed edges encode context-dependent transitions between steps. Compared to unstructured skills, graph-structured skills can provide clear workflow-level guidance. Moreover, the proposed graph-structured skill can also facilitate skill optimization. Building on this structured representation, we introduce **GraphSkillEvo**, a population-based evolutionary optimization framework with mutation and crossover operators for graph-structured skills. By maintaining multiple candidate skills and combining effective components, GraphSkillEvo enables broader and more comprehensive exploration of the structured skill space than purely LLM-based iterative self-refinement. Extensive experiments across five agent benchmarks demonstrate that GraphSkillEvo outperforms the strong skill optimization baseline SkillOpt, improving average accuracy by 4.01% on GPT-5.4-nano and 1.76% on GPT-5.4. Our code is available at https://anonymous.4open.science/r/GraphSkillEvo.