Trying to minimize a function over the integers

Question

I am trying to evaluate the following expression.

Minimize[
  {Abs[Log[10, 1 - 0.9] - (11 Log[10, 1 - 0.68^x] + 9 Log[10, 1 - 0.74^y])], 
   x >= 0, y >= 0, x <= 20, y <= 20}, 
  {x, y}, Integers]

I want the values of x and y that minimize the above function, but I get the following error:

The function value Indeterminate is not a number at {x,y} = {19.265, 0.0547502}

When I evaluate without the Integers specification, I get the answer

{1.55673*10^-10, {x -> 15.8488, y -> 4.97415}}

I need x and y to be integers in my formulation. Could someone please guide me in the correct direction?

I do not have a strong math background, so I would really appreciate the explanation in layman's terms.