Large language models (LLMs) are increasingly being employed as variation operators in metaheuristics, generating or modifying candidate solutions, heuristics, or programs inside iterative search loops. This shift reframes variation as a model call conditioned on different types of information. We introduce an operator-level framework with two descriptors: (1) the type of prompt-conditioning information at variation time (\texttt{Numeric}, \texttt{Symbolic}, \texttt{Linguistic}), and (2) artifact persistence, identifying what survives the model call (\texttt{Transient}, \texttt{Amortized}, \texttt{Transfer}). The tutorial shows how to classify, build, and select these operators through a worked build template, a method survey, an evidence table, and a cost-aware decision guide.

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