Mapping the royal road and other hierarchical functions

In this paper we present a technique for visualising hierarchical and symmetric, multimodal fitness functions that have been investigated in the evolutionary computation literature. The focus of this technique is on landscapes in moderate-dimensional, binary spaces (i.e., fitness functions defined over {0, 1}(n), for n less than or equal to 16). 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 case-study explorations of three fitness functions: royal road, hierarchical-if-and-only-if (H-IFF), and hierarchically decomposable functions (HDF). The visualisation approach provides an insight into the properties of these functions, particularly with respect to the size and shape of the basins of attraction around each of the local optima.

The road to rulership : Henry Tudor, King of England

At the close of the Wars of the Roses, a new dynasty was founded by a man lacking a prince’s education; moreover, his weak claim to the throne of England gave rise to a set of serious problems. These two crucial, interrelated elements are central in Francis Bacon’s biographical account of Henry VII. The literal road leading Richmond from exile to victory in Bosworth Field, in 1485, is eventually transformed into a metaphoric path that prefigures the long, deep process of learning undertaken during his 24-year reign. This fundamental process carried out by the king will be approached mainly through the passages focused on the Lambert Simnell/Perkin Warbeck affairs, the most difficult probelms the monarch had to face in a time and in a kingdom of many uncertainties. The Simnell/Warbeck menaces embodied Henry Tudor’s greatest dilemmas, continually emphasised in Bacon’s work – the essence of legitimacy and the essence of royalty.