The novel has aspects of all three, but its most dominant themes fall in the tragedy and romance area. There are moments of comedy throughout the novel as Pi deals with his parents, his classmates, his religious muses, and even Richard Parker. However, the seriousness of the story itself lends itself better to romance and tragedy. And, depending on which ending you believe, that will lead you towards which of those two best fits.
If you believe the story that involved humans and not animals, then the story is much more tragic. Pi loses his family in the shipwreck, then his mother to a brutal man on the lifeboat. Then, he has to conquer his weaknesses and fears in order to survive against that very evil force. That has all the aspects of a good tragedy there; a huge loss, a struggle, and a protagonist struggling against the odds.
If you believe the story that involved the animals instead of the humans it is more of a romance. Romantic literature is rather fantastical, has elements of the supernatural about it, and focuses on the dignity of human nature. With Richard Parker, Pi is able to maintain his dignity and be the hero of heroes as he fights to keep them both alive. Also, there is a relationship of love between him and Richard Parker; they are reliant on each other, and when Richard Parker leaves suddenly as they approach land, Pi is heartbroken. The relationships, the heroic journey, the amazing adventure--those are elements of a good romance.
I hope that those thoughts help to lead you in the right direction; good luck!