Gerund with and without "of" preposition
Solution 1:
With "of" before a logical object, an "-ing" form is not a gerund, but is rather a derived noun. A gerund, being a verb, does not allow an article, but the "-ing" noun does, and your first example, which is not grammatical as it stands, is improved by adding an article:
?I've worked on the improving of the article. ("improvement" would sound better)
However, if you try adding an article before the gerund, the example gets much worse (because verbs don't take articles):
*I've worked on the improving the article.