Use a Schwartzian transform - like this: (update: but see salva's comment below for a better approach)

@sorted = map {$_->[0]}
          map {
             $i=0; sort {$b->[1]<=>$a->[1]} map {[$i++,$_]} splice (@s
+im,0,9)
          } 0..8;

print "\@index_ordered =(\n";
for(0..8) {
    print " " x 4, join(', ', splice (@sorted,0,9) ),"\n";
}
print ");\n";
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Output:

@index_ordered =(
    0, 1, 3, 2, 4, 5, 7, 8, 6
    1, 0, 3, 8, 2, 4, 7, 6, 5
    2, 3, 8, 0, 1, 4, 7, 5, 6
    3, 0, 1, 2, 8, 7, 6, 4, 5
    4, 8, 7, 0, 1, 2, 6, 3, 5
    5, 0, 7, 1, 2, 3, 6, 8, 4
    6, 7, 8, 3, 4, 1, 2, 0, 5
    7, 6, 8, 3, 4, 0, 1, 5, 2
    8, 7, 6, 3, 4, 1, 2, 0, 5
);
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For equal elements in each row of @sim the order of their indices is undetermined. Note that this is destructive to @sim - it will be empty after the sort.

While the above code DWYM, you would have been better off having an array of arrays in the first place.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}