The problem with such a tree optimization is that you will only find a locally best solution.
If compressor1 generates the smallest result in step 1 all other compressors will only try to minimize this result. But maybe the compressor did something which the other conpressors are not optimized for. So you'll find a lically best solution for a starting point with conpressor1.
But maybe it would have been better to start with compressor3 because it's result is smaller after step 2 than starting with compressor1.
If compressor1 generates the smallest result in step 1 all other compressors will only try to minimize this result. But maybe the compressor did something which the other conpressors are not optimized for. So you'll find a lically best solution for a starting point with conpressor1. But maybe it would have been better to start with compressor3 because it's result is smaller after step 2 than starting with compressor1.