I don't believe it's impossible. In fact, there are two clear ways to do it: either
1. have a database of known algorithms, and map-reduce out the ones that produce the most signal for your data-set (this isn't Hard, but it requires a globally-networked language-neutral ABI-neutral algorithm repository and a free-use cloud compute cluster to run the heterogeneous algorithm-tests on), or
2. expect the computer to invent a novel, efficient (or at least polynomial) algorithm in response to your data-set on the fly. This is a Hard problem--since solving it basically means that computers can now take the jobs of Mathematicians in proving novel theorems. I don't think that's "impossible" either--obviously, Mathematicians are performing some describable algorithm in their heads to come up with novel proofs--but it's likely a Big Data problem in the same way most AI problems have turned out to be; not something you can ask your workstation to do.
1. have a database of known algorithms, and map-reduce out the ones that produce the most signal for your data-set (this isn't Hard, but it requires a globally-networked language-neutral ABI-neutral algorithm repository and a free-use cloud compute cluster to run the heterogeneous algorithm-tests on), or
2. expect the computer to invent a novel, efficient (or at least polynomial) algorithm in response to your data-set on the fly. This is a Hard problem--since solving it basically means that computers can now take the jobs of Mathematicians in proving novel theorems. I don't think that's "impossible" either--obviously, Mathematicians are performing some describable algorithm in their heads to come up with novel proofs--but it's likely a Big Data problem in the same way most AI problems have turned out to be; not something you can ask your workstation to do.