AlphaRoute: Large Language Models as Semantic Optimizers for Multi-Objective Routing

Detailed routing remains a dominant runtime bottleneck in physical design due to increasing complexity of design rules. Modern routers can struggle to resolve persistent violations under dense operating conditions. While recent work leverages reinforcement learning (RL) to dynamically select costs for each routing iteration, we find that this technique struggles with high-density designs where routing solutions are significantly harder. To address this, we present a history-aware offline RL policy which predicts iterative cost weights in these dense regimes to improve convergence across placement densities by utilizing readily available features from the router. Our policy uses conservative Q-learning similarly to prior work; however, our key insight is that addition of a lightweight LSTM architecture and additional features can retain sequence context and improve routing convergence across multiple densities and route guide qualities. Our policy can be integrated into any cost-based router with minimal pipeline changes, as it does not interfere with the core search algorithm. We evaluate our policy on held-out density and adjustment settings, including difficult operating points induced by dense placement and low guide quality. Our policy reduces design rule violations (DRVs) by an average of 92% over the top public baseline while simultaneously reducing runtime by 10%.

Efficient routing optimization is essential to freight transportation, urban logistics, and shared mobility, where high-quality heuristics are often required under limited computational budgets. Recent large language model (LLM)-based automated heuristic design methods can generate effective routing rules, but aggregate evaluation may mask recurrent failures on particular instance structures. To address this limitation, this study develops RouteRepair, which diagnoses parent-specific weaknesses from instance-level performance and applies targeted modifications to the corresponding heuristic components while protecting behavior that already performs well. Routing evidence, solver behavior, and program context are combined to define bounded repair objectives, and each intervention is validated through matched parent-child evaluation of failure recovery and collateral degradation. Experiments on the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) span constructive search, guided local search, and ant colony optimization. RouteRepair-GLS reduces the mean TSP optimality gap from 1.7476% to 0.7587%, while the constructive CVRP heuristic lowers average route cost by 1.91% relative to the savings heuristic; the generated ACO priors also outperform matched hand-designed priors. These results show that failure-aware, evidence-constrained refinement can improve routing heuristics on difficult instances while preserving performance on cases they already solve well.

We study the online routing problem in large language model serving, where requests arrive sequentially and must be dispatched to parallel decode workers under tight batch-size and KV-cache constraints. Unlike widely used routing heuristics that are not tied to explicit service-level objectives (SLOs) and offer limited control over latency-throughput trade-offs, we introduce a multi-objective optimization framework that formulates routing as an online linear programming with interpretable decision rewards. We apply an efficient bid-price control policy based on the online linear programming that admits requests when their SLO-weighted benefit exceeds their shadow prices. To meet millisecond decision requirements, we develop a warm-started, projected first-order updates that track the evolving dual shadow prices online with predictable runtime. We integrate our router into the Vidur simulator and demonstrate substantial improvements over standard baselines across multiple SLO regimes, including end-to-end latency, time-to-first-token, throughput, and tail performance. A big picture from our result: a science-based approach outperforms others based on heuristics.