Designing effective heuristics for diverse combinatorial optimization problems usually demands extensive expertise and repeated search. Large language models (LLMs) can automate heuristic generation and refinement, yet traditional heuristic search relies on evaluation feedback from the problem at hand, making zero-shot generalization to new problem definitions difficult when only source‑task feedback is available. To address this, we introduce MECo – an LLM‑driven multi‑task evolutionary framework aimed at zero‑shot cross‑problem transfer. MECo maintains task‑conditioned heuristic populations and uses a transfer gap, derived from cross‑task population performance, to regulate their interactions. These interactions enable the transfer and recombination of heuristics. A complementary selection criterion then extracts a compact set of heuristics by rewarding each member’s additional coverage of source‑task combinations. The resulting set can be applied to target problems without further search or adaptation. Experiments on 32 variants across vehicle routing (VRP) and flexible job‑shop scheduling (FJSP) show that MECo achieves the lowest mean costs compared with eight automated heuristic design baselines under equal budgets. On out‑of‑domain problems it also surpasses the strongest baseline in each family. Moreover, integrating MECo with various AHD methods improves both in‑domain and out‑of‑domain performance, confirming its broad effectiveness.
Review: MECo’s task‑conditioned populations and transfer‑gap‑guided interactions provide a powerful mechanism for heuristic transfer and recombination, delivering notable gains in zero‑shot cross‑problem generalization and offering a practical pathway for deploying LLMs in combinatorial optimization.