BEAM: Bi-level Memory-adaptive Algorithmic Evolution for LLM-Powered Heuristic Design

2026-04-14

AI Summary

This work addresses the limited exploration efficiency of existing large language model–based hyper-heuristics, which stems from insufficient high-level algorithmic modeling. To overcome this, the authors propose a bilevel optimization framework: at the outer level, a genetic algorithm evolves high-level algorithmic structures containing function placeholders; at the inner level, Monte Carlo tree search combined with an adaptive memory module fills these placeholders, augmented by a knowledge-enhanced pipeline to improve code generation quality. The approach substantially advances the automatic design of sophisticated heuristics, outperforming state-of-the-art methods across multiple combinatorial optimization problems—reducing the average optimality gap by 37.84% on CVRP and yielding a novel maximum independent set heuristic that surpasses the current best solver, KaMIS.

Technology Category

• Search and Optimization: Heuristic Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Large Language Model-based Hyper Heuristic (LHH) has recently emerged as an efficient way for automatic heuristic design. However, most existing LHHs just perform well in optimizing a single function within a pre-defined solver. Their single-layer evolution makes them not effective enough to write a competent complete solver. While some variants incorporate hyperparameter tuning or attempt to generate complex code through iterative local modifications, they still lack a high-level algorithmic modeling, leading to limited exploration efficiency. To address this, we reformulate heuristic design as a Bi-level Optimization problem and propose \textbf{BEAM} (Bi-level Memory-adaptive Algorithmic Evolution). BEAM's exterior layer evolves high-level algorithmic structures with function placeholders through genetic algorithm (GA), while the interior layer realizes these placeholders via Monte Carlo Tree Search (MCTS). We further introduce an Adaptive Memory module to facilitate complex code generation. To support the evaluation for complex code generation, we point out the limitations of starting LHHs from scratch or from code templates and introduce a Knowledge Augmentation (KA) Pipeline. Experimental results on several optimization problems demonstrate that BEAM significantly outperforms existing LHHs, notably reducing the optimality gap by 37.84\% on aggregate in CVRP hybrid algorithm design. BEAM also designs a heuristic that outperforms SOTA Maximum Independent Set (MIS) solver KaMIS.

Problem

• Large Language Model
• Hyper-heuristic
• Bi-level Optimization
• Heuristic Design
• Algorithmic Evolution

Innovation

• Bi-level Optimization
• Large Language Model-based Hyper Heuristic
• Genetic Algorithm
• Monte Carlo Tree Search
• Adaptive Memory