my %HoH;

foreach my $hashref ( @AoH )
{
    $HoH{ ${ $hashref }{id_a} }{id_a} = ${ $hashref }{id_a};
    $HoH{ ${ $hashref }{id_a} }{id_b} = ${ $hashref }{id_b};
    $HoH{ ${ $hashref }{id_a} }{value_x} += ${ $hashref }{value_x};
    $HoH{ ${ $hashref }{id_a} }{value_y} += ${ $hashref }{value_y};
}

@AoH = sort { ${ $a }{id_a} <=> ${ $b }{id_a} } ( values %HoH );

##</code><code>##

my %HoH;

foreach my $hashref ( @AoH )
{
    my $id_ab = ${ $hashref }{id_a} . '_' . ${ $hashref }{id_b};
    $HoH{$id_ab}{id_a} = ${ $hashref }{id_a};
    $HoH{$id_ab}{id_b} = ${ $hashref }{id_b};
    $HoH{$id_ab}{value_x} += ${ $hashref }{value_x};
    $HoH{$id_ab}{value_y} += ${ $hashref }{value_y};
}

@AoH = sort { ${ $a }{id_a} <=> ${ $b }{id_a} } ( values %HoH );