## More on hyper heuristics can

3.2.1. Merge heuristics

The concept of this family of heuristics is to merge two groups, uiui and ujuj, into one, ulul. This operation results in decreasing the number of grouping in the selected solution. The cost value of the new subgroup ulul is greater than or equal to the combined cost values of uiui and ujuj; i.e. f(ul)?f(ui)+f(uj)f(ul)?f(ui)+f(uj). We implemented three versions of the merge heuristic in this study, which differ from each other in the way they PD173955 choose the groups to be merged in a given solution.•M1 merges two randomly selected groups,•M2 merges two groups that contain the least number of items, and•M3 merges two groups with the lowest partial cost values.

Hence, merge heuristics can be considered as diversifying components.

3.2.2. Divide heuristics

In a similar fashion, three divide heuristics were implemented in eyespot study, each of which divides a selected group uiui into two groups, ui1ui1 and ui2ui2. Applying a divide heuristic results in increasing the number of grouping in the selected solution. Also, some of the conflicting items in uiui may end up in different groups, which leads to the elimination of some conflicts. Consequently, the combined cost values of ui1ui1 and ui2ui2 is less than or equal to the cost value of uiui; i.e. f(ui1)+f(ui2)?f(ui)f(ui1)+f(ui2)?f(ui). •D1 divides a randomly selected group,•D2 divides the group which contains the largest number of items and,•D3 divides the group with the highest partial cost value in the selected solution.