Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

Regards,

Alex.

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

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

David
Aren't you over emphasising the problem?
When you have a computor program with the ability to optimise the
position and lengths of radiators it really isn't that difficult.
Why construct a new program when so many are already available?
Alex has already determined a random configuration. A optimizing program
now allows him to assign degrees of merit to his desires, such as gain,
front to back, impedance, SWR as well as the frequency span he wants to
operate within.
What can be more easier ? He can now assign what dimensions he can live with
as variables
which can also include the section diameters of radiators, the latter being
very important
to allow for various coupling advantageous as well as total freedom of
movement to unexpected
positions such as bent radiators where non resistant feed systems can be
corrected.
Using a computor with a 3 meg plus processor it takes but a short time (
not days_)
to determine where compromises must be taken.
A case in point is a long boom yagi where one can start using it as the
"random "configuration,
overload it with elements but allow the elements to be variable so that it
can move away
from the boom ( linear arrangement) and into a 3D termed arrangement ,
(One must allow for 3D movement to allow the computor to cluster radiators
to advantage )
and nominate the important characteristics that you require such as gain.swr
etc.
One would think that the design would go in the obvious direction, such as a
longer boom
and an increase in height. But the computor does not always follow
preconceived conceptions
but will move purely in any direction to calculate for the desired
parameters as requested
as long as input does not restrict movement in all directions even where
you as a human
predetermine it is not necessary.
I'll leave the reader to find out where that computor calculation leads,
There are many programs available that can do the job including one that's
free
and often referred to on this newsgroup (4NEC based, tho I use AO PRO by
Beasely)

Cheers and beers
Art


"Dave" wrote in message
...

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

but he is asking about writing a program to do that, so he doesn't have one
to start from. yes, it is much easier to just grab one of the many that are
out there, but if he really wants to do it himself then what i described is
what goes into designing that type of program.

" wrote in message
news:_jKje.21110$WG.20289@attbi_s22...
David
Aren't you over emphasising the problem?
When you have a computor program with the ability to optimise the
position and lengths of radiators it really isn't that difficult.
Why construct a new program when so many are already available?
Alex has already determined a random configuration. A optimizing program
now allows him to assign degrees of merit to his desires, such as gain,
front to back, impedance, SWR as well as the frequency span he wants to
operate within.
What can be more easier ? He can now assign what dimensions he can live
with
as variables
which can also include the section diameters of radiators, the latter
being
very important
to allow for various coupling advantageous as well as total freedom of
movement to unexpected
positions such as bent radiators where non resistant feed systems can be
corrected.
Using a computor with a 3 meg plus processor it takes but a short time (
not days_)
to determine where compromises must be taken.
A case in point is a long boom yagi where one can start using it as the
"random "configuration,
overload it with elements but allow the elements to be variable so that it
can move away
from the boom ( linear arrangement) and into a 3D termed arrangement ,
(One must allow for 3D movement to allow the computor to cluster radiators
to advantage )
and nominate the important characteristics that you require such as
gain.swr
etc.
One would think that the design would go in the obvious direction, such as
a
longer boom
and an increase in height. But the computor does not always follow
preconceived conceptions
but will move purely in any direction to calculate for the desired
parameters as requested
as long as input does not restrict movement in all directions even where
you as a human
predetermine it is not necessary.
I'll leave the reader to find out where that computor calculation leads,
There are many programs available that can do the job including one
that's
free
and often referred to on this newsgroup (4NEC based, tho I use AO PRO by
Beasely)

Cheers and beers
Art


"Dave" wrote in message
...

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

Why not buy a Buick--I already bought one--it works fine--it will do all you
want...

I have already bought a Dodge pickup, I love it--it is all you will ever
need--buy one!

If you list reasons why this is NOT satisfactory--you will find the person
optimizing will also have similar reasons...

Warmest regards,
John
" wrote in message
news:_jKje.21110$WG.20289@attbi_s22...
David
Aren't you over emphasising the problem?
When you have a computor program with the ability to optimise the
position and lengths of radiators it really isn't that difficult.
Why construct a new program when so many are already available?
Alex has already determined a random configuration. A optimizing program
now allows him to assign degrees of merit to his desires, such as gain,
front to back, impedance, SWR as well as the frequency span he wants to
operate within.
What can be more easier ? He can now assign what dimensions he can live
with as variables
which can also include the section diameters of radiators, the latter
being very important
to allow for various coupling advantageous as well as total freedom of
movement to unexpected
positions such as bent radiators where non resistant feed systems can be
corrected.
Using a computor with a 3 meg plus processor it takes but a short time (
not days_)
to determine where compromises must be taken.
A case in point is a long boom yagi where one can start using it as the
"random "configuration,
overload it with elements but allow the elements to be variable so that it
can move away
from the boom ( linear arrangement) and into a 3D termed arrangement ,
(One must allow for 3D movement to allow the computor to cluster radiators
to advantage )
and nominate the important characteristics that you require such as
gain.swr etc.
One would think that the design would go in the obvious direction, such as
a longer boom
and an increase in height. But the computor does not always follow
preconceived conceptions
but will move purely in any direction to calculate for the desired
parameters as requested
as long as input does not restrict movement in all directions even where
you as a human
predetermine it is not necessary.
I'll leave the reader to find out where that computor calculation leads,
There are many programs available that can do the job including one
that's free
and often referred to on this newsgroup (4NEC based, tho I use AO PRO by
Beasely)

Cheers and beers
Art


"Dave" wrote in message
...

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

"John Smith" wrote in message
...


Why not buy a Buick--I already bought one--it works fine--it will do all
you want...

I have an E type Mercedes, Diesel......... Works fine with 30.000 miles
Works fine. and will do all you want


I have already bought a Dodge pickup, I love it--it is all you will ever
need--buy one!

I already have a 1982 Mercedes 300 D, Diesel.... I love it !
Works fine with 280,000 miles on it
It is all I will ever need except when I am traveling with my wife.....

So what is your point ?

Cheers
Art




If you list reasons why this is NOT satisfactory--you will find the person
optimizing will also have similar reasons...

Warmest regards,
John
" wrote in
message news:_jKje.21110$WG.20289@attbi_s22...
David
Aren't you over emphasising the problem?
When you have a computor program with the ability to optimise the
position and lengths of radiators it really isn't that difficult.
Why construct a new program when so many are already available?
Alex has already determined a random configuration. A optimizing program
now allows him to assign degrees of merit to his desires, such as gain,
front to back, impedance, SWR as well as the frequency span he wants to
operate within.
What can be more easier ? He can now assign what dimensions he can live
with as variables
which can also include the section diameters of radiators, the latter
being very important
to allow for various coupling advantageous as well as total freedom of
movement to unexpected
positions such as bent radiators where non resistant feed systems can be
corrected.
Using a computor with a 3 meg plus processor it takes but a short time
( not days_)
to determine where compromises must be taken.
A case in point is a long boom yagi where one can start using it as the
"random "configuration,
overload it with elements but allow the elements to be variable so that
it can move away
from the boom ( linear arrangement) and into a 3D termed arrangement ,
(One must allow for 3D movement to allow the computor to cluster
radiators to advantage )
and nominate the important characteristics that you require such as
gain.swr etc.
One would think that the design would go in the obvious direction, such
as a longer boom
and an increase in height. But the computor does not always follow
preconceived conceptions
but will move purely in any direction to calculate for the desired
parameters as requested
as long as input does not restrict movement in all directions even where
you as a human
predetermine it is not necessary.
I'll leave the reader to find out where that computor calculation leads,
There are many programs available that can do the job including one
that's free
and often referred to on this newsgroup (4NEC based, tho I use AO PRO
by Beasely)

Cheers and beers
Art


"Dave" wrote in message
...

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once a
random configuration has been obtained? I am trying to find the optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

Well, having made my point for me, I thought you would know!!!! Some do
things/own things just to learn and because they are tools... other do
things/own things for image and other purposes--how could I have made the
point better than your own words?

It all depends on what you are after...

Warmest regards,
John
" wrote in message
news:60Oje.23398$WG.16702@attbi_s22...

"John Smith" wrote in message
...


Why not buy a Buick--I already bought one--it works fine--it will do all
you want...

I have an E type Mercedes, Diesel......... Works fine with 30.000 miles
Works fine. and will do all you want


I have already bought a Dodge pickup, I love it--it is all you will ever
need--buy one!

I already have a 1982 Mercedes 300 D, Diesel.... I love it !
Works fine with 280,000 miles on it
It is all I will ever need except when I am traveling with my wife.....

So what is your point ?

Cheers
Art




If you list reasons why this is NOT satisfactory--you will find the
person optimizing will also have similar reasons...

Warmest regards,
John
" wrote in
message news:_jKje.21110$WG.20289@attbi_s22...
David
Aren't you over emphasising the problem?
When you have a computor program with the ability to optimise the
position and lengths of radiators it really isn't that difficult.
Why construct a new program when so many are already available?
Alex has already determined a random configuration. A optimizing program
now allows him to assign degrees of merit to his desires, such as gain,
front to back, impedance, SWR as well as the frequency span he wants to
operate within.
What can be more easier ? He can now assign what dimensions he can live
with as variables
which can also include the section diameters of radiators, the latter
being very important
to allow for various coupling advantageous as well as total freedom of
movement to unexpected
positions such as bent radiators where non resistant feed systems can be
corrected.
Using a computor with a 3 meg plus processor it takes but a short time
( not days_)
to determine where compromises must be taken.
A case in point is a long boom yagi where one can start using it as the
"random "configuration,
overload it with elements but allow the elements to be variable so that
it can move away
from the boom ( linear arrangement) and into a 3D termed arrangement ,
(One must allow for 3D movement to allow the computor to cluster
radiators to advantage )
and nominate the important characteristics that you require such as
gain.swr etc.
One would think that the design would go in the obvious direction, such
as a longer boom
and an increase in height. But the computor does not always follow
preconceived conceptions
but will move purely in any direction to calculate for the desired
parameters as requested
as long as input does not restrict movement in all directions even
where you as a human
predetermine it is not necessary.
I'll leave the reader to find out where that computor calculation leads,
There are many programs available that can do the job including one
that's free
and often referred to on this newsgroup (4NEC based, tho I use AO PRO
by Beasely)

Cheers and beers
Art


"Dave" wrote in message
...

"Alex" wrote in message
oups.com...
Hi,

Does anybody know how to attempt optimising an array of elements once
a
random configuration has been obtained? I am trying to find the
optimal
configuration which gives maximum main beam, and minimal sidelobes. I
am proficient in C and MATLAB.

Any suggestions will be appreciated.

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.

Frank schreef:

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).


To get an idea of how this could be done by using both a gradient-style
optimizer (like AO) or a genetic-algorithm based optimizer do a google
for 4nec2 and try yourself.

Arie.