LLM-Based Hierarchical Coordinated Control with Continuation-Aware Policy Learning

Coordinating multiple interacting units in complex engineering systems is challenging when system interactions are difficult to model, operational information is heterogeneous, and low-level actions must satisfy strict constraints. We propose an LLM-based hierarchical framework in which the LLM coordinates interacting units based on heterogeneous operational context, while task-specific controllers or optimizers generate executable and constraint-aware actions. We further introduce Continuation-Aware GRPO to capture the consequences of coordination decisions over subsequent control intervals. Rather than judging a decision only by its immediate outcome, the method also evaluates how the system evolves afterward under the current policy. We validate the framework on multi-ramp traffic control and virtual power plant (VPP) energy management, using simplified system models for training and more realistic simulators for evaluation. Across both tasks, the proposed method consistently outperforms direct task-specific control and optimization, end-to-end reinforcement learning, rule-based and RL-based hierarchical coordination, and prompting-only LLM coordinators, demonstrating the value of heterogeneous-context reasoning, hierarchical execution, and continuation-aware policy learning.

Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems

Large language models (LLMs) increasingly translate natural-language optimization problems into executable solver code. Yet for constraint-dense operations research (OR) problems, existing data-filtering and training pipelines largely rely on objective-equivalence signals such as differential testing and answer agreement, which a program can pass while adding spurious constraints or silently omitting required ones, whenever those constraints are non-binding on the tested instance. We propose constraint injection, which uses feasible probes to expose spurious over-constraint and one-constraint-violating probes to reveal silent constraint omission. Combined with differential testing, it forms a dual verifier. We instantiate and evaluate it on vehicle routing problems (VRPs), a representative constraint-dense combinatorial optimization testbed with coupled operational constraints. We develop VRPCoder, an 8B end-to-end model that translates natural-language VRP scenarios into Gurobi scripts, together with an expert-verified VRP benchmark suite covering 21 variants. The verifier is reused as a rejection-sampling filter during data synthesis and as a per-rollout reward in group relative policy optimization (GRPO). Across four VRP benchmarks, VRPCoder-GRPO reaches 93\% average Pass@1, outperforms Gemini-3.1-Pro Preview on three benchmarks, exceeds Claude-Sonnet-4.5 by 28 average points, and surpasses prior OR-LLMs by 78 average points.