Re-evaluating LLM-based Heuristic Search: A Case Study on the 3D Packing Problem

The art of heuristic design has traditionally been a human pursuit. While Large Language Models (LLMs) can generate code for search heuristics, their application has largely been confined to adjusting simple functions within human-crafted frameworks, leaving their capacity for broader innovation an open question. To investigate this, we tasked an LLM with building a complete solver for the constrained 3D Packing Problem. Direct code generation quickly proved fragile, prompting us to introduce two supports: constraint scaffolding--prewritten constraint-checking code--and iterative self-correction--additional refinement cycles to repair bugs and produce a viable initial population. Notably, even within a vast search space in a greedy process, the LLM concentrated its efforts almost exclusively on refining the scoring function. This suggests that the emphasis on scoring functions in prior work may reflect not a principled strategy, but rather a natural limitation of LLM capabilities. The resulting heuristic was comparable to a human-designed greedy algorithm, and when its scoring function was integrated into a human-crafted metaheuristic, its performance rivaled established solvers, though its effectiveness waned as constraints tightened. Our findings highlight two major barriers to automated heuristic design with current LLMs: the engineering required to mitigate their fragility in complex reasoning tasks, and the influence of pretrained biases, which can prematurely narrow the search for novel solutions.