Plural or singular of 'case study'
Solution 1:
"This and the previous case study show the benefits of optimization approaches" means there are two case studies that have shown the benefits, "this" case study, and some other one. It isn't clear from the sentence whether there are any other case studies.
It is correct to use the singular because in that sentence "the previous case study" is one case study. From the structure, we understand that the sentence means, "This case study and the previous case study..."