How to choose a good research problem? I am working to get a PhD, maybe next year this time around. Currently, this is my second year. I have published 3 papers. All of them are not about one problem but consider different problems. My strategy to find a research idea/problem is given below.

1 - Read papers whose titles are either interesting or I have some apriori understanding of those titles.

2 - Understand those papers as best as I can. That is, I try to understand each detail presented in the paper except the simulation results (this is because I think simulation results are hard to reproduce).

3 - I analyze the paper and try to find a very small problem which can be addressed (i.e. I can solve it) by the methodology of the paper.

4 - If I am successful at step 3 I start working on that problem otherwise I repeat the process from step 1.

By applying this strategy I have been able to write 3 papers and I have submitted a fourth (I am not satisfied with those papers because at very best they can be considered average papers). But my concern is that the problems addressed in those papers do not belong to one area. As far as I have seen, for the profiles of some of the renowned researchers in my field their PhD work is focused on one area. One main thing I console myself with is that almost all of those researchers had good supervisors. My supervisor does not even read the draft/reviews of my papers and the suggestions that he provides during the meetings are so broad that the problem becomes intractable. Under these circumstances what are your opinions: Is there any better strategy to do research? 

I will be very thankful to you for providing me suggestions or commenting on my dilemma.
This is a really important question, and it's one that isn't asked enough.

From reading your question, though, it sounds like you are rushing a bit. Renowned physicist and biologist Uri Alon (34k+ citations) has written an excellent paper on 'How To Choose a Good Scientific Problem' and one of his main points is that one, however cliché it sounds, should take ones time to conceive a good project.

I strongly suggest you read his paper. It's not exhaustingly long, and reads like a good talk. He also has a TED talk that challenges the 'A to B' dogma in science, which has helped me a lot.