Automating operations research (OR) with large language models (LLMs) remains limited by hand-crafted reasoning--execution workflows. Complex OR tasks require adaptive coordination among problem interpretation, mathematical formulation, solver selection, code generation, and iterative debugging. To address this limitation, we propose EvoOR-Agent, a co-evolutionary framework for automated optimization. The framework represents agent workflows as activity-on-edge (AOE)-style networks, making workflow topology, execution dependencies, and alternative reasoning paths explicit. On this representation, the framework maintains an architecture graph and evolves a population of reasoning individuals through graph-mediated path-conditioned recombination, multi-granularity semantic mutation, and elitist population update. A knowledge-base-assisted experience-acquisition module further injects reusable OR practices into initialization and semantic variation. Empirical results on heterogeneous OR benchmarks show that the proposed framework consistently improves over zero-shot LLMs, fixed-pipeline OR agents, and representative evolutionary agent frameworks. Case studies and ablation analyses further indicate that explicit architecture evolution and graph-supported reasoning-trajectory search contribute to both performance improvement and structural interpretability. These results suggest that treating agent architectures and reasoning trajectories as evolvable objects provides an effective route toward adaptive and interpretable automated optimization.