"I created a variable to assign formats to each value based on the value ID."
Not sure but I am not able to understand where ID is being used in variable definition.
Also as we know Aggr function creates virtual table of values against defined dimension, as in your case -
aggr(min(ComponentFormat),COMPONENT_NAME_RELATED_INFO) = 1
you are creating virtual table of minimum values of Component Format for each COMPONENT_NAME_RELATED_INFO
Not sure how it will work if you have multiple "COMPONENT_NAME_RELATED_INFO" , it may work if you have single COMPONENT_NAME_RELATED_INFO.
You may need Min outside Aggr so that left side of equation results to single value.
It's awfully difficult to figure out which one of the many things that could go wrong is causing this issue. Care to upload an example document that shows this behavior?
Complex expressions not working when more than one value is active usually points to one part of the expression returning multiple results instead of the expected single one. A trick that may prove useful: can you break down your expression into its major parts, and display the result of these expression pieces along with the remainder of the object you want to fix? That way you can observe the behavior of - for instance - the aggr() function in the context of the (unknown) dimensions you are using.