DyACE: Dynamic Algorithm Co-evolution for Online Automated Heuristic Design with Large Language Model

2026-03-07

AI Summary

This work addresses the limitations of traditional automated heuristic design, which relies on static algorithms and struggles to adapt to the dynamic demands of perturbation strategies across different search phases in combinatorial optimization. The authors formulate heuristic design as a non-stationary bilevel control problem and propose a receding-horizon control architecture that leverages lookahead-backtrack search to extract trajectory features. These features drive a large language model acting as a meta-controller to co-evolve heuristic logic and solution populations online. A causal alignment mechanism is established between heuristics and the gradient of the optimization landscape. This approach achieves the first demonstration of perception-feedback-driven dynamic generation and adaptation of heuristics by large language models, significantly outperforming existing static methods on three combinatorial optimization benchmarks while exhibiting strong scalability to high-dimensional problems; ablation studies confirm the critical role of perception feedback in enabling dynamic adaptation.

Technology Category

• Search and Optimization: Heuristic Search
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The prevailing paradigm in Automated Heuristic Design (AHD) typically relies on the assumption that a single, fixed algorithm can effectively navigate the shifting dynamics of a combinatorial search. This static approach often proves inadequate for Perturbative Heuristics, where the optimal algorithm for escaping local optima depends heavily on the specific search phase. To address this limitation, we reformulate heuristic design as a Non-stationary Bi-level Control problem and introduce DyACE (Dynamic Algorithm Co-evolution). Distinct from standard open-loop solvers, DyACE use a Receding Horizon Control architecture to continuously co-evolve the heuristic logic alongside the solution population. A core element of this framework is the Look-Ahead Rollout Search, which queries the landscape geometry to extract Search Trajectory Features. This sensory feedback allows the Large Language Model (LLM) to function as a grounded meta-controller, prescribing phase-specific interventions tailored to the real-time search status. We validate DyACE on three representative combinatorial optimization benchmarks. The results demonstrate that our method significantly outperforms state-of-the-art static baselines, exhibiting superior scalability in high-dimensional search spaces. Furthermore, ablation studies confirm that dynamic adaptation fails without grounded perception, often performing worse than static algorithms. This indicates that DyACE's effectiveness stems from the causal alignment between the synthesized logic and the verified gradients of the optimization landscape.

Problem

• Automated Heuristic Design
• Dynamic Adaptation
• Combinatorial Optimization
• Non-stationary Control
• Perturbative Heuristics

Innovation

• Dynamic Algorithm Co-evolution
• Non-stationary Bi-level Control
• Look-Ahead Rollout Search
• Grounded Meta-control
• Large Language Model