Large Barrier Trees For Studying Search

Description/Abstract

Barrier trees are a method for representing the landscape structure of
high dimensional discrete spaces such as those that occur in the cost
function of combinatorial optimisation problems. The leaves of the
tree represent local optima and a vertex where subtrees join represents
the lowest cost saddle-point between the local optima in the subtrees.
This paper introduces an extension to existing Barrier tree methods
that make them more useful for studying heuristic optimisation
algorithms. It is shown that every configuration in the search
space can be mapped onto a vertex in the Barrier tree. This provides
additional information about the landscape, such as the number of
configurations in a local optimum. It also allows the computation of
additional statistics such as the correlation between configurations
in different parts of the Barrier tree. Furthermore, the mappings
allow the dynamic behaviour of a heuristic search algorithms to be
visualised. This extension is illustrated using an instance of
the MAX-3-SAT problem.