Back to the Beginning of Heuristic Design: Bridging Code and Knowledge with LLMs

ArXi:2605.06123v1 Announce Type: new Large language models (LLMs) have recently advanced automatic heuristic design (AHD) for combinatorial optimization (CO), where candidate heuristics are iteratively proposed, evaluated, and refined. Most existing approaches search over executable programs and distill insights from execution feedback to guide later iterations. Because this process moves from low-level implementations to high-level principles, we refer to it as a bottom-up paradigm. We argue that this view is incomplete and.