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This function whose reference is passed to I<text_evol>
must accept a list of text strings;
the first will contain the current values
while the others contain alternative values.
The user should then judge which of the strings produces the best result.
I<choose_best_text> must return I<($preference, $continue)> where
I<$preference> is the index of the preferred string (0, 1, etc).
The other argument I<($continue)> is set false if the user
thinks the optimal result has been arrived at;
this is I<text_evol>'s only convergence criterion.

As an example, see the script called I<ps_evol> for fine-tuning
A4 PostScript drawings which is included with this package.

=back

=head1 CONVERGENCE CRITERIA

$ec (>0.0) is the convergence test, absolute.  The search is
terminated if the distance between the best and worst values
of the objective function within the last 25 trials is less
than or equal to $ec.
The absolute convergence test is suppressed if $ec is undefined.

$ed (>0.0) is the convergence test, relative. The search is
terminated if the difference between the best and worst values
of the objective function within the last 25 trials is less
than or equal to $ed multiplied by the absolute value of the
objective function.
The relative convergence test is suppressed if $ed is undefined.

These interact with two other small numbers $ea and $eb, which are
the minimum allowable step-sizes, absolute and relative respectively.

These number are set within Math::Evol as follows:

 $ea = 0.00000000000001;   # absolute stepsize
 $eb = 0.000000001;        # relative stepsize
 $ec = 0.0000000000000001; # absolute error
 $ed = 0.00000000001;      # relative error

You can change those settings before invoking the evol subroutine, e.g.:

 $Math::Evol::ea = 0.00000000000099;   # absolute stepsize
 $Math::Evol::eb = 0.000000042;        # relative stepsize
 undef $Math::Evol::ec;  # disable absolute-error-criterion
 $Math::Evol::ec = 0.0000000000000031; # absolute error
 $Math::Evol::ed = 0.00000000067;      # relative error

The most robust criterion is the maximum-cpu-time parameter $tm

=head1 LUA

In the C<lua/> subdirectory of the install directory there is
I<Evol.lua>, which is an exact translation of this Perl code into Lua.
The function names and arguments are unchanged,
except that I<text_evol> is not yet implemented.
Brief Synopsis:

 local M = require 'Evol'
 local function minimise(x) -- returns a number to be minimised
    local sum = 1.0
    for k,v in pairs(x) do sum = sum + v * v end
    return sum
 end
 local function constrain(x)
    if x[1] > 1.0 then x[1] = 1.0  -- it's a greyscale value
    elseif x[1] < 0.0 then x[1] = 0.0
    end
    return x
 end
 local function choose_best(arglist)
    local preference = 1; local i_arg
    for i_arg=1,#arglist do
       local x = arglist[i_arg]
       if that_suits_me() then preference = i_arg; break end
    end
    local continue   = true or false
    return preference, continue
 end
 M.ed = 0.00000000067                       -- relative error
 local x  = {3.456, 1.234, -2.345, 4.567}  -- starting values
 local sm = {.8, .4, .6, 1.2}          -- starting step-sizes
 local tm = 5.0                        -- max time in seconds

 -- and now...
 xb,sm,fb,lf = M.evol(xb, sm, minimise, constrain, tm)
 -- or
 xb,sm = M.select_evol(xb, sm, choose_best, constrain)

 -- not yet implemented :
 -- new_text = M.text_evol(text, choose_best_text, nchoices)

=head1 AUTHOR

Peter J Billam, www.pjb.com.au/comp/contact.html

=head1 CREDITS

The strategy of adjusting the step-size to give a success rate of 0.2
comes from the work of I. Rechenberg in his
I<Optimisation of Technical Systems in Accordance with the
Principles of Biological Evolution>
(Problemata Series, Vol. 15, Verlag Fromman-Holzboog, Stuttgart 1973).

The code of I<evol> is based on the Fortran version in
I<Numerical Optimisation of Computer Models>
by Hans-Paul Schwefel, Wiley 1981, pp 104-117, 330-337,
translated into english by M.W. Finnis from
I<Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie>
(Interdiscipliniary Systems Research, Vol. 26), Birkhaeuser Verlag, Basel 1977.
The calling interface has been greatly Perlised,
and the constraining of values has been much simplified.

=head1 SEE ALSO

The deterministic optimistation strategies can offer faster
convergence on smaller problems (say 50 or 60 variables or less)
with fairly smooth functions;
see John A.R. Williams CPAN module Math::Amoeba