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

Guidong Lu, Yiping Liu, Xiangxiang Zeng

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.

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

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.
Paper Structure (60 sections, 6 equations, 3 figures, 4 tables)

This paper contains 60 sections, 6 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Reformulation: From Static Optimization to Dynamic Control
  3. The Lower Level: Perturbative Search as a Dynamic System
  4. The Static Upper Level: Time-Invariant Algorithm Optimization
  5. The Dynamic Upper Level: Non-stationary Process Control
  6. The DyACE Framework
  7. Framework Overview
  8. Look-Ahead Rollout Search
  9. Landscape Feature Extraction
  10. Landscape Kinematics.
  11. Operator Telemetry.
  12. Iso-State Rollout Evaluation
  13. Decoupled Meta-Reasoning and Three Reasoning Modes
  14. Two-Stage Diagnosis-Prescription Architecture
  15. Phase I: The Diagnosis Agent.
  16. ...and 45 more sections

Figures (3)

  • Figure 1: Overview of the DyACE framework. It illustrates the closed-loop interaction between look-ahead perception, meta-reasoning, and adaptive evolution.
  • Figure 2: Evolutionary iterative process on JSSP instance TA71. (a) The optimality gap of the best algorithm's Monte Carlo evalution at each generation of the algorithm population. (b) The optimality gap of the best solution throughout the entire search process.
  • Figure 3: Case study of algorithmic evolution on JSSP instance ta51. The markers indicate key transitions in heuristic logic synthesized to address specific search stages.