1. The article is often used with initials that are pronounced letter by letter (initialisms).
2. The article is often NOT used with initials that are pronounced as a word (acronyms).
I used 'often' because I'm not sure about possible exceptions.
In my field of study (Operations Research), initials are frequently used to represent optimization problems (e.g., the TSP). I discussed this point with my university supervisor who makes comments on my reports (English is not his native language). He responded that:
"What I learned from [...] was that whenever we use (specific) acronyms, we don't use 'the' when they are within a sentence, and we use 'the' when a sentence starts with them. For instance,
(i) The HCP is an NP-Complete problem.
(ii) We developed a new algorithm to solve HCP."
HCP stands for the Hamiltonian Cycle Problem. It is really confusing me because I do not know when to use and when not to use the article. For example, on this site, the author Jane Watson writes:
Use a definite article with an initialism if the spelled out term begins with “the” but is not covered in the initialism.
which implies that I should use the article with "HCP". What do you think?