I'd say four ships capable of hosting helicopters, a dozen frigates, at least a dozen Cyclone-class patrol boats (we have only about that many) and a real carrier for the EA-18s. Some of this is in the region now.
Let's see here... Each of the ships involved can get up to about 30 knots if they really want to. Assuming they can maintain that for an hour (I'm not sure about that, but it's simpler this way) and converting, each ship could cover 110-120 km of shoreline (also assuming this is more like a 2D line). You have a total of 29 ships listed, giving us about 3000 km of coverage. Unfortunately, due to the nature of this coverage, there are still areas which no ship can reach for an hour or more. You appear to acknowledge the need for more ships with your next post... but we only have 19 frigates on active duty right now, and I'd be willing to bet most of them already have missions.
Problem two is that this assumes all these ships are on station all at once. This is, to put it bluntly, not possible. There needs to be some downtime in port, for the crew's sake if nothing else. Then we add transit time from home ports into the equation... Either we end up with less coverage, or we use more ships. The latter isn't possible without significant investments in a larger military, and the former is more or less what we have now.
And we would not try to patrol the whole coast, we would set up protected shipping lanes, and probably institute a convoy system.
And if we find Pirate bases, launch Special Operations raids against them.
Not a bad idea, but this still runs into the economic concerns of the merchant vessels. In general, it is actually a better decision, from an economic standpoint, to risk paying a ransom than it would be to add extra time to each voyage through the region. Not the greatest idea from a long term view, but unless the problem gets significantly worse, these companies will simply treat it as an additional cost.
Incidentally, this also doesn't account for traffic like the yacht which started this whole discussion - some people, for whatever reason, aren't going to want to or aren't going to be able to join a convoy.
In my opinion, there's little that can be done short of fixing Somalia - and it's unlikely any government is going to be particularly enthusiastic about nation building given the current political climate. While simply striking the pirates with brutal force is tempting, I don't think that will be effective for any length of time - as long as the current conditions prevail in Somalia, piracy is going to be encouraged. I think we would find that, for each group we found and annihilated, another group would be formed. We would run out of the money and willpower for such a campaign long before we ran out of targets.
Short of that, I believe the best solution requires more action on the part of the merchant vessels than the military. While the military can and should patrol to the greatest extent possible, there's simply too much ocean and not enough navy. These merchant vessels can mount a number of nonlethal weapons and defenses to make pirate attacks more difficult (increasing the amount of time required for the pirates to gain control, thus giving the navy more time to arrive) or can carry more lethal weaponry to fend off attacks all by themselves (risky, since it increases the chance that the pirates will respond in kind, but has the advantage that the ship may not need to wait for help). It's not an ideal solution, but as I already said, I don't think we're going to get one while Somalia remains in its current state.
