I disagree. My main goal is first to locathe the ships, then to destroy them. thus i am trying to hit a ship only once, then forget about it untill all other ships have been hit at least once.

Of course, this might be a mistake, but it's A strategy.

(The best strategy placing in one game may well be to place them in exactly the same positions as for the previous one. As long as you don't go it often.)

.0.0.0.0.0.0.0
0.0.0.0.0.0.0.
.0.0.0.0.0.0.0

Then when all ships are 3 blocks or larger increase the spacing between the diagonal lines to two empty spaces. which would look like this

.00.00.00.00
0.00.00.00.0
00.00.00.00.

I'd add my suggestions:
You might want to search the center squares first.

Suppose the battlefield was 3X3, and that there is only 1 ship and it takes up 2 squares.
There are 12 possible positions for that ship.

If you fire at the center square, you eliminate all but 8 positions.
If you fire at the corner, you eliminate all but 10 positions.
If you fire at an edge, you eliminate all but 9 positions.

Because the ships can't be placed on a edge and wrap around to the other edge, there is a bias for ships to be located on center squares.

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Non-mathematical considerations:
1- People probably do not place their ships randomly. e.g. in lotteries, the distribution of lottery picks is skewed towards certain numbers. In battleship, I suspect it's likely that people do not place their ships randomly.

If I were playing, I might try to hide a ship in the corner.

There may be a tendency not to cluster ships together. This is probably a smart idea anyways. If you hit a ship, you will eventually need to search and find the rest of the ship. If you cluster, the search might accidentally find the other ships in the cluster.
But, there is also a small chance someone might do extreme clustering and put all five of their ships together.

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You might be able to gain an edge by reading the other player. If you could do this, it may be by far the best strategy.

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Should you try to sink a ship right away when you find it? I suspect the answer is usually yes.
Suppose you've found three ships. By sinking them, you know the size of the last ship. And you can adjust your search pattern accordingly, since you know how big the gaps between your lines of searching need to be.

What I do now is this:

.000.000.0
0.000.000.
00.000.000
000.000.00
.000.000.0

This is guaranteed to locate all ships of size 4 or greater, and I believe (but have not proved) that it's a more efficient search strategy than the simple checkerboard. This is because there's a greater than 50% chance that I find the destroyer (the size 2 ship) with this initial, coarse search. If I do, then I don't need to proceed to a checkerboard. If I don't find the destroyer, then I fill in the checkerboard as per your first strategy above.

U: set of unknown (remaining) squares
M: set of previous misses
H: set of previous hits

For every U(i,j) compute the possible number of ways that each of the 5 types of ships could lie on top of it, given your knowledge of previous hits H(i,j) and misses M(i,j). We can call this score N(i,j)

Rank order all N(i,j) and consider only those U(i,j) that are tied for the higest score, N(i,j).

Among these U(i,j); fire on the square that will give you the most valuable information. The way to do this is to recalculate N(i,j) for all squares within X squares of an edge assuming that you will miss. X is the length of you opponent's longest ship still afloat. A known miss or a sunken ship counts as an edge.

Repeat