Travelling alone, I have had no trouble meeting people even aboard MV Grand Princess. A few recommendations if you are in this situation:
>> 1. Request a large table for dinner. You might not relate to everybody, but you probably will relate to somebody. Also, you probably will have dinner companions every night even if a couple of your tablemates decide to eat elsewhere.
>> 2. Take shore excursions from the ship rather than going off on your own, especially in the first few ports of call.
>> 3. Go to the "Singles Mingles" to meet other solo travellers, many of whom are very interesting folks!
>> 4. Go to the activities and events that are of interest to you. That's where you will meet other folks with similar interests, and the chances are that many of the people who participate in a particular activity or type of activity will do so consistently.
If you do this, your odds of making lifelong friends actually might be better on a larger vessel!