Visualisation of Hierarchical Cost Surfaces for Evolutionary Computing

In this paper we present a technique for visualising cost surfaces that are relevant to work in evolutionary computation, particularly genetic algorithms. The focus is on moderate-dimensional, binary cost surfaces (i.e., functions defined over {0, 1}ⁿ for n <= 16 that have a hierarchical, modular structure. The visualisation approach involves an unfolding of the hyperspace into a two-dimensional graph, whose layout represents the topology of the space using a recursive relationship, and whose shading defines the shape of the cost surface defined on the space. Using this technique we present a case-study exploration of the hierarchical-if-and-only-if (H-IFF) function. The visualisation approach provides an insight into the properties of this function, particularly in regards to the size and shape of the basins of attraction around each of the local optima.