The H-IFF function was originally developed as a case study through which the search strategy of building-block recombination in GAs was demonstrably superior to mutation-based search [16]. The insights provided by the hypergraph visualisation make it clear why mutation-based search was so unsuccessful. Observations that the size of the basins of attraction were equally sized prompted the hypothesis that all outcomes of random-adaptive walks were equally likely. The graphs also made it clear how the number of local optima scaled with the size of the problem. From these two properties it follows that the size of the population for mutation-based search must scale with the number of local optima (2n/2). Thus, from visualisation of the cost surface we (a) gain insight into the most desirable parameters for mutation-based search, and (b) discover that module recombination is a more appropriate approach.
Comparing the visual properties of H-IFF to those of RR (Fig.5) reveals an obvious difference. Relating the performances of different algorithms on these two cost surfaces to features in their visual appearance provides insight into novel problems. Upon recognising that the pattern of RR represents a convex bowl it becomes easy to identify this pattern as a feature of other surfaces (e.g., smooth NK functions). The efficacy of the visual display provides insights into appropriate similarity metrics between cost surfaces (i.e., the features that are important for a particular optimisation algorithm). For example, recursive structure in high dimensions produces repeated patterns in a low dimensional unfolded representation.
The visualisation approach taken in this paper offers some benefits over the more traditional statistical and mathematical analysis of cost surfaces. One benefit is that it is more accessible to those lacking a mathematical background. Another is that it provides an exploratory tool: interesting features `pop out' and can then be subjected to a more rigorous analysis as was the case with H-IFF, where we determined that all local optima were equally likely to be found by a random adaptive walk.
A Java-based version of the visualisation tool is available at http://www.itee.uq.edu.au/~btonkes/hsgp.html.
