Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Beyond the Node: Clade-level Selection for Efficient MCTS in Automatic Heuristic Design

Kezhao Lai, Yutao Lai, Hai-Lin Liu

TL;DR

Clade-AHD addresses the over-exploitation tendency of node-centric MCTS under sparse evaluation budgets in LLM-driven Automatic Heuristic Design by introducing a clade-level Bayesian framework. It models the potential of entire evolutionary clades with Beta distributions, updates beliefs bottom-up with depth-attenuated credit, and uses budget-aware Clade Thompson Sampling combined with dynamic clade freezing to balance exploration and exploitation. Across NP-hard CO problems, including constructive heuristics and ACO, Clade-AHD achieves state-of-the-art heuristic quality with substantially fewer evaluations, demonstrating robust zero-shot generalization and improved sample efficiency. This approach broadens the practical impact of LLM-driven heuristic design for logistics, manufacturing, and related optimization domains by enabling reliable, low-cost exploration of large heuristic spaces.

Abstract

While Monte Carlo Tree Search (MCTS) shows promise in Large Language Model (LLM) based Automatic Heuristic Design (AHD), it suffers from a critical over-exploitation tendency under the limited computational budgets required for heuristic evaluation. To address this limitation, we propose Clade-AHD, an efficient framework that replaces node-level point estimates with clade-level Bayesian beliefs. By aggregating descendant evaluations into Beta distributions and performing Thompson Sampling over these beliefs, Clade-AHD explicitly models uncertainty to guide exploration, enabling more reliable decision-making under sparse and noisy evaluations. Extensive experiments on complex combinatorial optimization problems demonstrate that Clade-AHD consistently outperforms state-of-the-art methods while significantly reducing computational cost. The source code is publicly available at: https://github.com/Mriya0306/Clade-AHD.

Beyond the Node: Clade-level Selection for Efficient MCTS in Automatic Heuristic Design

TL;DR

Clade-AHD addresses the over-exploitation tendency of node-centric MCTS under sparse evaluation budgets in LLM-driven Automatic Heuristic Design by introducing a clade-level Bayesian framework. It models the potential of entire evolutionary clades with Beta distributions, updates beliefs bottom-up with depth-attenuated credit, and uses budget-aware Clade Thompson Sampling combined with dynamic clade freezing to balance exploration and exploitation. Across NP-hard CO problems, including constructive heuristics and ACO, Clade-AHD achieves state-of-the-art heuristic quality with substantially fewer evaluations, demonstrating robust zero-shot generalization and improved sample efficiency. This approach broadens the practical impact of LLM-driven heuristic design for logistics, manufacturing, and related optimization domains by enabling reliable, low-cost exploration of large heuristic spaces.

Abstract

While Monte Carlo Tree Search (MCTS) shows promise in Large Language Model (LLM) based Automatic Heuristic Design (AHD), it suffers from a critical over-exploitation tendency under the limited computational budgets required for heuristic evaluation. To address this limitation, we propose Clade-AHD, an efficient framework that replaces node-level point estimates with clade-level Bayesian beliefs. By aggregating descendant evaluations into Beta distributions and performing Thompson Sampling over these beliefs, Clade-AHD explicitly models uncertainty to guide exploration, enabling more reliable decision-making under sparse and noisy evaluations. Extensive experiments on complex combinatorial optimization problems demonstrate that Clade-AHD consistently outperforms state-of-the-art methods while significantly reducing computational cost. The source code is publicly available at: https://github.com/Mriya0306/Clade-AHD.
Paper Structure (44 sections, 14 equations, 4 figures, 7 tables, 1 algorithm)

This paper contains 44 sections, 14 equations, 4 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. LLM-driven Heuristic Design
  4. Limitations
  5. Limitation of Standard MCTS in AHD Scenario
  6. Limitations of Node-Centric Bayesian MCTS
  7. Methods
  8. Bayesian Abstraction of Search Space
  9. Definition 1: Clade
  10. Definition 2: Beta Distribution
  11. Clade Belief Updates
  12. Clade-level Thompson Sampling
  13. Dynamic Clade Freezing
  14. Discussion
  15. Similarities between MCTS-AHD and Clade-AHD:
  16. ...and 29 more sections

Figures (4)

  • Figure 1: The schematic overview of the Clade-AHD framework. (a) Bayesian Selection: The policy navigates the tree via Clade-level Thompson Sampling, selecting nodes based on belief distributions. (b) LLM Evaluation: The LLM generates and evaluates new heuristics based on the leaf context. (c) Clade Update: Evidence propagates bottom-up to refine ancestral beliefs (sharper curves), while the Dynamic Clade Freezing mechanism (snowflake icons) prunes suboptimal branches.
  • Figure 2: Mechanism Comparison between Node-Level MCTS (MCTS-AHD) and Clade-Level MCTS (Clade-AHD).(Panel A) The baseline MCTS-AHD relies on scalar point estimates (e.g., mean value), leading to Scalar Myopia where high-potential but high-variance branches are discarded due to initial noise. (Panel B) Our Clade-AHD models potential as belief distributions. By aggregating evidence from the entire clade and applying Thompson Sampling, it effectively identifies promising regions and reduces uncertainty (visualized as sharper posterior curves), while the Dynamic Freezing mechanism prunes suboptimal branches.
  • Figure 3: Evolution curves of LLM-based AHD methods on designing Step-by-step Construction heuristics for TSP. The solid lines represent the mean performance over three independent runs, while the shaded regions indicate the standard deviation. Clade-AHD demonstrates superior asymptotic performance and robust search capabilities compared to population-based baselines and MCTS-AHD.
  • Figure 4: Sensitivity Analysis of the Decay Factor $\lambda$. The main plot (left) shows the best objective value found over 1,000 evaluations. The blue line ($\lambda = 0$) represents a myopic, node-centric baseline, which suffers from premature convergence. The red line ($\lambda = 0.8$, Ours) demonstrates the most robust convergence trajectory. The zoom panel (right) highlights the final optimization stage (iterations 600-1000), showing that $\lambda=0.8$ consistently achieves the lowest objective value with narrower variance compared to $\lambda=0.5$ and $\lambda = 0$.