Teacher-Aware Evolution of Heuristic Programs from Learned Optimization Policies
Authors: Minyu Chen, Song Qin, Ling-I Wu, Jianxin Xue, Guoqiang Li
Organizations: Shenzhen Technology University · Shanghai Polytechnic University · Shanghai Jiao Tong University
Abstract
LLM-based automatic heuristic design has shown promise for generating executable heuristics for combinatorial optimization, but existing methods mainly rely on delayed endpoint performance. We propose a \emph{teacher-aware evolutionary framework} that uses independently trained learned optimization policies as behavioral teachers. Instead of deploying or imitating the teacher, our method queries it on states visited by candidate heuristic programs and uses its action preferences as local feedback for evolution. The resulting search discovers static executable heuristics guided by both task performance and teacher-derived behavioral signals. Experiments on scheduling, routing, and graph optimization benchmarks show that our method improves over performance-driven LLM heuristic evolution baselines while requiring no neural inference at deployment. These results suggest that learned optimization policies can be repurposed as behavioral feedback sources for automatic heuristic discovery.
The integration of Large Language Models (LLMs) into evolutionary frameworks has established a new paradigm for automated heuristic discovery. Despite their promise, these methods typically search in the discrete space of program syntax, relying on stochastic sampling to navigate a highly non-convex optimization landscape. This work proposes a continuous heuristic discovery framework that shifts optimization to a learned latent manifold. We employ an encoder to map discrete programs into continuous embeddings and train a differentiable surrogate model to predict performance, enabling gradient-based search. To regularize the optimization trajectory, an invertible normalizing flow maps these embeddings to a structured Gaussian prior, where we perform gradient ascent. The resulting optimized latent vectors are projected through a learned mapper into soft prompts, which condition a frozen LLM to synthesize novel executable heuristics. We evaluate the proposed method on the Traveling Salesman Problem (TSP), the Capacitated Vehicle Routing Problem (CVRP), the Knapsack Problem (KSP), and Online Bin Packing (OBP). Empirical results demonstrate that continuous latent-space optimization achieves performance competitive with state-of-the-art discrete evolutionary baselines while offering a complementary methodological alternative for automated algorithm design. The implementation code is available at \url{https://github.com/cheikh025/LHS}.
Automatic Heuristic Design (AHD) has emerged as a transformative approach for solving combinatorial optimization problems. While recent Large Language Model (LLM)-based methods have shown promise, they predominantly rely on fixed evolutionary operators and struggle to effectively accumulate and reuse historical search experience. This paper proposes RefineEvo, a novel evolutionary framework that transforms AHD from a static trial-and-error process into a planning-guided, experience-driven system. RefineEvo introduces a Planner to dynamically schedule evolutionary operators and trigger refinement based on the current search state, and a Reflector to distill valuable lessons into a Bidirectional Experience Pool containing both positive insights and negative pitfalls. This synergistic framework enables the system to adapt its search tools to the evolving complexity of the problem and leverage trajectory-aware, situation-conditioned insights to guide generation. Experiments on several classic combinatorial optimization benchmarks demonstrate that RefineEvo consistently outperforms strong baselines. In particular, RefineEvo delivers superior solution quality while improving token efficiency, enabling more efficient and autonomous heuristic design.
Large Language Models (LLMs) have advanced Automatic Heuristic Design (AHD) by enabling heuristic generation through reasoning and code synthesis. In LLM-based AHD, the LLM reasons about algorithm design and generates executable heuristic code. Existing architectures adopt two main paradigms: Natural Evolution applies crossover and mutation to this code to explore diverse strategies, but discards the reasoning traces behind the design decisions, weakening knowledge retention; Metacognitive Evolution retains these reasoning traces and refines them through reflection, but lacks population-level recombination, limiting exploration. These limitations reduce search efficiency, stability, and solution quality on complex problems. To address this gap, we propose MeEvo, an AHD framework that cyclically couples Natural Evolution and Metacognitive Evolution with operator balance that shifts from exploration to exploitation. Natural Evolution explores heuristic code while recording LLM-generated reasoning traces, fitness values, errors and best heuristic into a shared history; Metacognitive Evolution then reflects on this history to generate improved heuristics that feed into the next Natural Evolution cycle. This design enables population-driven exploration and reflection-driven refinement to reinforce each other. Experiments on five optimization problems show that MeEvo achieves stronger performance and lower variance than tested LLM-based AHD architectures, especially on complex constrained tasks.