  We explore a two-step optimization problem in random environments, the
so-called restaurant-coffee shop problem, where a walker aims at visiting the
nearest and better restaurant in an area and then move to the nearest and
better coffee-shop. This is an extension of the Tourist Problem, a one-step
optimization dynamics that can be viewed as a deterministic walk in a random
medium. A certain amount of heterogeneity in the values of the resources to be
visited causes the emergence of power-laws distributions for the steps
performed by the walker, similarly to a L\'{e}vy flight. The fluctuations of
the step lengths tend to decrease as a consequence of multiple-step planning,
thus reducing the foraging uncertainty. We find that the first and second steps
of each planned movement play very different roles in heterogeneous
environments. The two-step process improves only slightly the foraging
efficiency compared to the one-step optimization, at a much higher
computational cost. We discuss the implications of these findings for animal
and human mobility, in particular in relation to the computational effort that
informed agents should deploy to solve search problems.
