Abstract. We derive a continuous probability distribution which generates neighbours of a point in an interval in a similar way to the bitwise mutation of a Gray code binary string. This distribution has some interesting scale-free properties which are analogues of properties of the Gray code neighbourhood structure. A simple (1+1)-ES using the new distribution is proposed and evaluated on a set of benchmark problems, on which it performs remarkably well. The critical parameter is the precision of the distribution, which corresponds to the string length in the discrete case. The algorithm is also tested on a difficult real-world problem from medical imaging, on which it also performs well. Some observations concerning the scale-free properties of the distribution are made, although further analysis is required to understand why this simple algorithm works so well.

Two distance measures for attributed graphs are presented that are based on the maximal similarity common subgraph of two graphs. They are generalizations of two existing distance measures based on the maximal common subgraph. The new measures are superior to the well-known measures based on elementary edit transformations in that no particular edit operations (together with their costs) need to be defined. Moreover, they can deal not only with structural distortions, but also with perturbations of attributes. It is shown that the new distance measures are metrics.

The colour of colon tissue, which depends on the tissue structure, its optical properties, and the quantities of the pigments present in it, can be predicted by a physics-based model of colouration. The model, created by analysing light interaction with the tissue, is aimed at correlating the histology of the colon and its colours. This could be of a great diagnostic value, as the development of tissue abnormalities and malignancies is characterised by the rearrangement of underlying histology. Once developed, the model has to be validated for correctness. The validation has been implemented as an optimisation problem, and evolutionary techniques have been applied to solve it. An adaptive approximate optimisation method has been developed and applied in order to speed up the computationally expensive optimisation process. This works by iteratively improving a surrogate model based on an approximate physical theory of light propagation (Kubelka Munk). Good fittings, obtained under the histologically plausible values of model parameters, are presented. The performances of the new method were compared to that of a simple Evolution Strategy which uses an accurate, but expensive, Monte Carlo method. The new method is general and can be applied with any surrogate model for optimisation.

We address the problem of comparing attributed trees and propose a novel distance measure centered around the notion of a maximal similarity common subtree. The proposed measure is general and defined on trees endowed with either symbolic or continuous-valued attributes, and can be equally applied to ordered and unordered, rooted and unrooted trees. We prove that our measure satisfies the metric constraints and provide a polynomial-time algorithm to compute it. This is a remarkable and attractive property since the computation of traditional edit-distance-based metrics is NP-complete, except for ordered structures. We experimentally validate the usefulness of our metric on shape matching tasks, and compare it with edit-distance measures.