Current methods that use large language models to evolve heuristics for combinatorial optimization converge toward a single best algorithm or a small set of trade-off solutions. When the problem distribution shifts, these methods require expensive re-adaptation and their performance degrades. Here, we propose a quality-diversity evolutionary framework that maintains a structured archive of diverse heuristics, where each is specialized for a particular class of problem instances. A large language model serves as the variation operator within the evolutionary loop. Shapley additive explanations on abstract syntax tree features play a dual role in this framework: they guide the mutation prompts toward productive code modifications, and they extract the behavioral descriptors that organize the archive. An online selector then retrieves the best-matched heuristic for each new unseen instance. We evaluate the approach on vehicle routing, traveling salesman, and job shop scheduling problems under static, perturbed, stochastic, and dynamic conditions. The archive coverage provides inherent robustness to distributional shift, whereas single-heuristic baselines and neural solvers degrade considerably. The resulting heuristic library is interpretable, since each archive cell contains readable code at known feature coordinates.
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