Deployed LLM agents rely on agentic context, the model-external textual control content assembled by an operational harness. In this work, the mutable component of that context is a persistent system-level instruction that is updated from operational experience while the model, tools, and harness remain fixed. Over long evolution horizons, flat-text maintenance makes verification increasingly difficult as accumulated instructions grow and interact. We propose Graph-Regularized Agentic Context Evolution (GRACE), which maintains the persistent instruction component as a typed semantic graph and validates proposed updates within the local typed neighborhoods of modified nodes. Accepted graph updates are reconstructed as incremental edits to the textual instruction checkpoint used at deployment. We evaluate GRACE within a fixed telecom agent harness derived from $τ^2$-bench under a controlled distribution-shift protocol. Across five independent replications, GRACE improves strict reliability, measured by pass^3, from the Gemini 2.5 Flash zero-shot value of 0.091 to 0.673$\pm$0.136 at the final checkpoint. This exceeds a Gemini 3.1 Pro zero-shot reference of 0.242 on the same held-out set, while the flat-text HCE baseline finishes at 0.191$\pm$0.051. These results identify two requirements for reliable long-horizon context evolution, a structural substrate that makes verification local and a consolidation mechanism that keeps accumulated instruction content usable.
Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods optimize heuristics for a fixed training instance set and may fail catastrophically when deployed under real-world distributional shifts. We propose Robust Adversary Instance Search (RAISE), a framework that integrates constrained worst-case instance search within a principled neighborhood of the training distribution into the LLM-based evolutionary search loop. RAISE treats robust AHD as a constrained adversarial instance search problem: the outer loop evolves heuristics via LLM operators, while an LLM-free inner loop efficiently identifies hard instances within an epsilon-ball around the training instance set using a basis distribution parameterization with boundary projection. Comprehensive experiments on Online Bin Packing (OBP), Online Job Shop Scheduling (OJSP), and Online Vehicle Routing (OVRP) across five distribution families demonstrate that existing LLM-based AHD methods degrade by up to 19 times under distribution shift, while RAISE consistently maintains strong performance across all tested distributions and problem scales