The object is to find the smallest combination of items that "fills" each bin, while still using as many of the smaller items as possible. So for 1 1 1 2 2 3 4 6 7 7...

1 1 1 2 4 (all 1's always go in first bin, and 2 4 adds up to 7 and uses a 2)
2 3 (adds up to 5 and uses 2 and 3)
6
7
7

I've tested with various sequences of numbers, and this method seems to always work. You still have to brute-force a small number of combinations to find the smallest value, but the most you'll have to do for each bin is maybe a dozen. EDIT: This assumes the bin size is small. Complexity increases relative to the number of combinations possible for the current bin, which can be fairly large if you have a large bin and a lot of small items. I'm still trying to figure out a way to increase efficiency for that. Anyhow:

use strict;
use warnings;

my ($binsize, %n, @n, $total, $smallest, $bin, @bin, @bins);

$binsize = 50;
push @_, ((int rand 10) + 1) for 1..1000;

my $c = 0;
my $time = time();

$n{$_}++, $total += $_ for @_;
while ($n{1} && $n{1} > $binsize) {
    push @bins, [split //, '1'x$binsize];
    $n{1} -= $binsize;
    $total -= $binsize;
}
while ($total > $binsize) {
    @n = (); push @n, [$_, $n{$_}] for sort {$a <=> $b} keys %n;
    $smallest = $binsize + 1;
    find(\@n, 0, 0, 0, '');
    $n{$_}--, $total -= $_ for @bin = split / /, $bin;
    push @bins, [@bin];
}
$bin = '';
$bin .= "$_ "x$n{$_} for sort {$a <=> $b} keys %n;
push @bins, [split / /, $bin];

for (@bins) {
    print "@$_\n";
}

print "$c iterations in " . (time() - $time) . " seconds";

sub find {
    $c++;
    my ($n, $p, $stotal, $small, $set) = @_;
    my ($num, $count) = $n[$p] ? @{$n[$p]} : 0;
    if ($p > $#$n || $stotal + $num > $binsize) {
        if ($smallest > $stotal && (!$small || $stotal + $small > $bin
+size)) {
            $bin = $set;
            $smallest = $stotal;
        }
        return;
    }
    my $remains = $binsize - $stotal;
    my $max = $remains < $num * $count ? int($remains / $num) : $count
+;
    for (reverse 0..$max) {
        find($n, $p+1, $stotal+$num*$_, ($small || $_ == $max ? $small
+ : $num), $set."$num "x$_);
    }
}
[download]

This required 1586177 function calls and 19 seconds for 1000 items between 1 and 10 and a bin size of 50. If you reduce the bin size to 10, then it only takes 15526 iterations and 5 seconds. I'm sure there's a way to significantly improve on this. For instance, if you have a bin size of 50, 20 2's, 10 3's, and a 5, then the minimum number of 2's you'll be using is all of them, since 40 + the largest number is smaller than 50. There's no need to go through the entire range of possibilities.

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