Supplementary Details on Dependency Determination Algorithm

The following Algorithm, which is introduced in Section Ⅵ B, is supplemented here with an explanation on how to determine dependencies within the sequence.

We construct the collection in reverse order of dependencies to determine and return, for each perturbation, whether it has a dependency relationship with the previous operation. Dependency constraints include checking if a deleted node existed previously, if a newly added edge already existed, if a node to be deleted precedes a newly added node, and if a new edge was added before deleting an existing edge. To maintain diversity among genes in individuals, we selectively perform dependency lookup only on key edges and nodes, following specific rules to avoid overly restricting gene variation:

• For Add Node, check dependencies of its starting node and determine if it's deleted or newly added.

• For Rewire, examine the dependencies of the edge and middle node it selects, considering if the edge is newly added and if the starting node is deleted or newly added.

• For Remove Node, check dependencies with deleted nodes to identify if they are newly added.

• For Add Edge, inspect the dependencies of its starting and ending nodes, considering if the nodes are deleted or newly added.