  We discuss how searching for finite amplitude disturbances of a given energy
which maximise their subsequent energy growth after a certain later time $T$
can be used to probe phase space around a reference state and ultimately to
find other nearby solutions. The procedure relies on the fact that of all the
initial disturbances on a constant-energy hypersphere, the optimisation
procedure will naturally select the one which lies nearest to the stable
manifold of a nearby solution in phase space if $T$ is large enough. Then, when
in its subsequent evolution, the optimal disturbance transiently approaches the
new solution, a flow state at this point can be used as an initial guess to
converge the solution to machine precision. We illustrate this approach in
plane Couette flow by: a) rediscovering the spanwise-localised `snake'
solutions of Schneider et al. (2010b); b) probing phase space at very low
Reynolds numbers ($< 127.7$) where the constant linear-shear solution is
believed to be the global attractor; and finally c) examining how the edge
between laminar and turbulent flow evolves when stable stratification kills the
turbulent attractor. We also show that the steady snake solution smoothly
delocalises as unstable stratification is gradually turned on until it connects
(via an intermediary global 3D solution) to 2D Rayleigh-Benard roll solutions.
