The "evolution" of GA Math
Report on the "evolution" of GA Math Version 1.2
To everyone (sorry for any mangled formatting):
I have continued to modify GA Math. The latest update is version 1.2.
It is now flicker-free and the user interface is simple and stripped-down. The
program is now more sophisticated, faster, and capable of handling moderately
complex formulas.
As before the program is a "tweaker's paradise". If you do change the program,
it might be good to modify a copy.
Here is a list of formulas for which it has successfully created matching
algorithms:
"v=l*w*h"
"a=3.14159*(r^2)"--area of circle
"a=4*3.14159*(r^2)"--harder (area of sphere)
"v=4/3*3.14159*(r^3)"--harder (volume of a sphere)
"x=2*a*3*b*4*c"
"a=100*x"
"a=(x-y)/z"
"a=(2*x-y)/z" -- hard, but doable
"a=(2*x-(3*y))/z" -- harder, but doable
"a=(2*x-(3*y))/(4*z)" -- harder, but doable (takes a longish time)
A typical report with comments added:
--------------------------------------------------
GA Math Beings Report
--------------------------------------------------
Math Beings working on formula : a=(x-y)/z -- <<< the formula
Number of try-sets per run : 1200 --<<< maximum number of try sets per
run
Number of runs this session : 3 -- --<<< number of runs this attempt
Number of tries per try-set : 8 --<<< each population has this number of
tries before assessment
This is try-set number : 520 --<<< this many try-sets have occurred
in this run
Target value : 0.0010 --<<< must get within this percentage
to be successful
Current closeness (percent) : 0.000000 --<<< the percentage at moment of
success
Most successful being's original register values:
{[5.46] , [7.53] , [3.70] , [8.99] , [0.30] , [8.00] , [0] , [0] ,
[0]}--<<<nine register locations (in this case)
-- x-val y-val z-val Priv1 Priv2 Priv3 <<<< three variables
& three private numbers
--**********************************************************************************************
-- <<< Note the private numbers above; there is one for each variable. Each
being has a set of randomly
-- <<< generated private numbers that *do not change* in a being's lifetime, but
do change in transferring
-- <<< to a clone.
--**********************************************************************************************
Most successful being's genes: --<<< In this example, there were only two
relevant genes needed to
-- <<< create an algorithm to solve the formula.
Most successful being's original register values: -- <<< Repeating these two
lines
{[5.46] , [7.53] , [3.70] , [8.99] , [0.30] , [8.00] , [0] , [0] ,
[0]}--<<<nine register locations (in this case)
sub, 1, 2, 2
{[5.46] , [-2.07] , [3.70] , [8.99] , [0.30] , [8.00] , [0] , [0] , [0]}
div, 2, 3, 9
{[0] , [-2.07] , [3.70] , [-5.29] , [0.30] , [-8.99] , [-3.70] , [0] ,
[-0.56]}
Last actual answer from formula: -0.560
------------------------------------------------
The above successful being had to deal with at least 16 randomly generated sets
of x, y, and z values, of which you see in this report only the last one.
More general comments:
There are now 7 register locations in each being where the math operations take
place. The final answer must always be in the last register location.
There are 11 operations as follows:
constant OPS={
{"abs",1},
{"rec",1},
{"chg",1},
{"add",2},
{"sub",2},
{"mul",2},
{"div",2},
{"int",1},
{"rem",2},
{"frc",1},
{"nop",0}
}
Note: the number next to each operation is the number of "from" register
locations it uses.
abs=absolute, rec=reciprocal, chg=change-sign, int=floor, rem=remainder,
frc=decimal fraction, and nop=no operation
=============================================================
To ck,
Well, do you think GA Math does exhibit evolution?
Of course you know that I think it does. One thing I've seen over and over is
that there are two different sorts of evolution: gradual and dramatic.
The gradual type is represented, for example, by the way PI is often found.
Beginning with maybe a "3", using the private numbers (which change when
cloning occurs), the program can edge closer and closer to true PI over time,
and consequently its accuracy improves toward success. This gradual type is
what we often think of as "evolution". However, many math algorithms depend
on a set of discrete actions in the right order or it doesn't work at all, that
is, it is not a matter of being close, but of getting a complex thing right bang
on. Evolution can handle that, but it takes much longer.
The formula "a=(2*x-(3*y))/4z" is an example. GA Math can figure it out, but
it takes a while. You might say it works, but isn't pretty. With
bio-evolution, though, once such a thing is made, it then becomes subject to
gradual evolution.
=============================================================
To Al Getz,
The private numbers occur one-to-one for each variable used. They last the
lifetime of the being, so tracking it shouldn't be an issue. They do evolve
over time as the successful half of the population is cloned.
Many thanks for testing this program and letting me know how it went. Most
of the changes have been in response to your investigations.
=============================================================
A recent example of good luck:
--------------------------------------------------
GA Math Beings Report
--------------------------------------------------
Math Beings working on formula : 3.14159*r*r
Number of try-sets per run : 1200
Number of runs this session : 2
Number of tries per try-set : 8
This is try-set number : 121
Target value : 0.0010
Current closeness (percent) : 0.000058
Most successful being's original register values:
{[11.38] , [3.14] , [0] , [0] , [0] , [0] , [0]}
Most successful being's genes:
mul, 1, 1, 7
{[11.38] , [3.14] , [0] , [0] , [0] , [0] , [129.39]}
mul, 2, 7, 7
{[11.38] , [3.14] , [0] , [0] , [0] , [0] , [406.47]}
Last actual answer from formula: 406.492
--------------------------------------------------
It usually takes longer than that!
Keep in mind that though there are checks to try to eliminate "lucky inputs", it
does happen, so some algorithms will not prove out. For that reason, it is a
good idea to make several runs on a formula to assure getting a decent (though
sometimes quite weird) algorithm.
I want to turn my attention to other programming for awhile, so won't be doing
any more upgrades in the near future, though others can do so if they wish and
send them to RDS. However, I'll be around to answer any questions about the
program.
--Quark
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