Hello,
ther are a lot of "regular" array lattice, among them Hexagonal and triangular have been widely used in real application (wrt rectangular grid, triangular grid can help to reduce the number of array elements and to minimise grating lobes if you have to scan the beam).
Anyway if you are looking for array "optimised in geometry keeping fixed the excitation", a typical example is a class of array named "Thinned array". This kind of array antenna is initially composed by several radiators filling a regular grid (and usaully all the elements are fed in phase with the same amplitude), then by means of optimization code, some of them are switched off (a significant percentage), finally the resulting array is a "sparese array" with a reduced number of elements still fed.
So if I have undestood correctly your question, you can find information also in the IEEE searching "Thinned array" word.
PS: you can also look at more general case where also the element position is optimised, search "not uniform (spaced) array" word.
Bye.