In some simulation code I am working on I need to generate a random set of percentages for various components. The sum of the individual percentages for the components must be 100, but there are constraints on the minimum and maximum percentage for each component.

The current code for generating simulation sets looks somewhat like that shown below.

use strict;
use warnings;

my @constraints = (
          {mid => 20, sd => 15},
          {mid => 30, sd => 25},
          {mid => 50, sd => 10},
     );

my $sum;

for my $cnst (@constraints) {
     my $value = RandFlat ($cnst->{mid}, $cnst->{sd});
     $cnst->{value} = $value;
     $sum += $value;
}

#scale so that percentages add up to 100
# this may push parameters outside bounds!

my $scale = 100.0 / $sum;
for my $cnst (@constraints) {
     my ($mid, $sd, $value) = @{$cnst}{'mid', 'sd', 'value'};
     
     $value = $value * $scale;
     printf "%5.1f +-%5.1f: %5.1f", $mid, $sd, $value;
     print " - bad" if ($value < ($mid - $sd)) || ($value > ($mid + $s
+d));
     print "\n";
}


sub RandFlat {
    #Return a rand () value with a flat distribution about the $mean +
+- $stdDev
    my ($mean, $stdDev) = @_;
    my $range = 2.0 * $stdDev;
    my $value = rand ($range);
    return $value + ($mean-$stdDev);
}
[download]

Prints:

 20.0 +- 15.0:  22.7
 30.0 +- 25.0:  40.1
 50.0 +- 10.0:  37.2 - bad
[download]

However this technique can generate sets that do not conform to the constraints (as shown). Depending on the actual constraints the probability of generating a compliant data set may be rather low! Is there a better technique for solving this problem?

Notes:

• Yes, I appreciate rand is not a good "random" number generator for simulation work
• In a simulation run several million data sets may be required
• There are more components in the real code than are used in the sample code, but there are unlikely to be more than 10
• The mid point values for the components are unlikely to sum to 100 (although they do in the sample)
• A deterministic technique is much preferred over a retrying technique (as is shown in the sample)
• In the forgoing by "random" I actually mean of course "pseudo-random"

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