Please use searchoptions sopt array. You can here make the order what you want

sopt : ["cn", "eq", ....]

See doks here

In the advanced search box, the operations dropdown list options are {"equal", "not equal", "less", "less or equal", "greater", "greater or equal", "begins with", "does not begin with", "ends with", "does not end with", "contains", "does not contain", "is null", "is not null", "is in", "is not in"}.

The default selection is the first item, "equal", but I would like the default selection to be "contains", no matter which column name is selected.

Is there a way to do this? 

If the default cannot be changed from the first item, is it possible to change the order so "contains" is first?

Thanks