  We introduce an algorithm to perform an optimal adiabatic evolution that
operates without an apriori knowledge of the system spectrum. By probing the
system gap locally, the algorithm maximizes the evolution speed, thus
minimizing the total evolution time. We test the algorithm on the Landau-Zener
transition and then apply it on the quantum adiabatic computation of 3-SAT: The
result is compatible with an exponential speed-up for up to twenty qubits with
respect to classical algorithms. We finally study a possible algorithm
improvement by combining it with the quantum Zeno effect.
