Two complementary techniques for analyzing search spaces are proposed: (i) an algorithm to detect search points with potential to be local optima; and (ii) a slightly adjusted Wang-Landau sampling algorithm to explore larger search spaces. The detection algorithm assumes that local optima are points which are easier to reach and harder to leave by a slow adaptive walker. A slow adaptive walker moves to a nearest fitter point. Thus, points with larger outgoing step sizes relative to incoming step sizes are marked using the local optima score formulae as potential local optima points (PLOPs). Defining local optima in these more general terms allows their detection within the closure of a subset of a search space, and the sampling of a search space unshackled by a particular move set. Tests are done with NK and HIFF problems to confirm that PLOPs detected in the manner proposed retain characteristics of local optima, and that the adjusted Wang-Landau samples are more representative of the search space than samples produced by choosing points uniformly at random. While our approach shows promise, more needs to be done to reduce its computation cost that it may pave a way toward analyzing larger search spaces of practical meaning.