optimization is not a simple process. the two things you mention are just
a
very small part of it. first you have to figure out what your goals in
optimizing are and then how you measure them. for instance, your 'maximum
main beam'... how do you define 'main beam', do you tell the program where
to start looking or let it find it by some algorithm? then how do you
measure it? do you take the absolute peak field or average over some
range
of angles? how about vertical angles?? remember, this is, or can be, a
3d
problem depending on what you are trying to do. then how do you define
'minimal sidelobes'? by peak field in any angle outside the 'main beam'
or
by total power in all the sidelobes? or do you want them all to be below
some percentage of the 'main lobe'?? or some other criteria??? then there
are other common optimization constraints like feed point impedance,
minimum
bandwidth for forward gain, f/b, or impedance/swr.

after you have figured out what you are going to measure and how you are
going to measure it then you have to figure out a strategy. do you
systematically change one parameter at a time and recompute then figure
slopes and always head toward the maximum? how far do you go before you
try
a different parameter? how do you determine if you have found an absolute
maximum or just a local one?? and how do you get around local ones? when
have you gone too far in changing a parameter and have to reset to try
some
other path. remember, this can be a large multidimensional problem, each
parameter is one dimension of the problem, and each measured result is a
different space to optimize, and you are trying to optimize multiple
surfaces at once. you also must consider how to avoid 'traps'... those
odd
situations where field summations give huge gains but with totally
unuseful
conditions, like putting a parasitic only inches away from the driven
element in some algorithms gives huge gains, but worthless feed point
impedances.

oh, and all this assumes you already have a field pattern calculating
engine
that models your antenna and feed system, gives you an output that you can
examine programatically, and allows you a way to modify and recalculate
the
fields.

this is not something to throw together in a weekend, no matter how
proficient you are in any given language.

I agree with Dave's comments. The only way to optimize an antenna array is
to run successive NEC models. If you are really serious about this I
suggest a copy of "Field Computation by Moment Methods" by Roger F.
Harrington. Don't buy it, just check it out at a university library, and
see what you think. There is also "Finite Element" analysis, which is
implemented in Ansoft's HFSS program (www.ansoft.com).

Regards,

Frank