Experiments with explicit for-loops in genetic programming

Evolving programs with explicit loops presents major difficulties, primarily due to the massive increase in the size of the search space. Fitness evaluation becomes computationally expensive and a method for dealing with infinite loops must be implemented. We have investigated ways of dealing with these problems by the evolution of for-loops of increasing semantic complexity. We have chosen two problems - a modified Santa Fe ant problem and a sorting problem - which have natural looping constructs in their solution and a solution without loops is not possible unless the tree depth is very large. We have shown that by controlling the complexity of the loop structures it is possible to evolve smaller and more understandable programs for these problems

Applying genetic programming to learn spatial differences between textures using a translation invariant representation

This paper describes an approach to evolving texture feature extraction programs using tree based genetic programming. The programs are evolved from a learning set of 13 textures selected from the Brodatz database. In the evolutionary phase, texture images are first "binarised" to 256 grey levels. An encoding of the positions of the black pixels is used as the input to the evolved programs. A separate feature extraction program is evolved for each of the 256 grey levels. Fitness is measured by applying the evolved program to all of the images in the learning set, using one dimensional clustering on the outputs and then using the separation between the clusters as the fitness value. On two benchmark problems using the evolved programs for feature extraction and a nearest neighbour classifier, the evolved features gave test accuracies of 74.6% and 66.2% respectively for a 13 Brodatz and a 15 Vistex texture problem. This is better than a number of human derived methods on the same problems

Multi-objective techniques in genetic programming for evolving classifier systems

The application of multi-objective evolutionary computation techniques to the genetic programming of classifiers has the potential to both improve the accuracy and decrease the training time of the classifiers.The performance of two such algorithms are investigated on the even 6-parity problem and the Wisconsin Breast Cancer, Iris and Wine data sets from the UCI repository. The first method explores the addition of an explicit size objective as a parsimony enforcement technique. The second represents a program¿s classification accuracy on each class as a separate objective. Both techniques give a lower error rate with less computational cost than was achieved using a standard GP with the same parameters

Multiobjective parsimony enforcement for superior generalisation performance

Program Bloat - phenomenon of ever-increasing program size during a GP run - is a recognised and widespread problem. Traditional techniques to combat program bloat are program size limitations of parsimony pressure (penalty functions). These techniques suffer from a number of problems, in particular their reliance on parameters whose optimal values it is difficult to a priori determine. In this paper, we introduce POPE-GP, a system that makes use of the NSGA-II multiobjective evolutionary algorithm as an alternative, parameter-free technique for eliminating program bloat. We test it on a classification problem and find that while vastly reducing program size, it does improve generalisation performance

Market segments based on the dominant movement patterns of tourists

This paper presents an innovative method for tourist market segmentation-based on dominant movement patterns of tourists; that is, the travel sequences or patterns used by tourists most frequently. There were three steps to achieve this goal. In the first step, general log-linear models were adopted to identify the dominant movement patterns, while the second step was to discover the characteristics of the groups of tourists who travelled with these patterns. The Expectation–Maximisation algorithm was then used to partition tourist segments in terms of socio-demographic and travel behavioural variables. The third step was to select target markets based upon the earlier analysis. These methods were applied to a sample of tourists, over the period of a week, on Phillip Island, Victoria, Australia. A significant outcome of this research is that it will assist tourism organisations to identify tourism market segments and develop better tour packages and more efficient marketing strategies aligned to the characteristics of the tourists

Multi-objective improvement of software using co-evolution and smart seeding

Optimising non-functional properties of software is an important part of the implementation process. One such property is execution time, and compilers target a reduction in execution time using a variety of optimisation techniques. Compiler optimisation is not always able to produce semantically equivalent alternatives that improve execution times, even if such alternatives are known to exist. Often, this is due to the local nature of such optimisations. In this paper we present a novel framework for optimising existing software using a hybrid of evolutionary optimisation techniques. Given as input the implementation of a program or function, we use Genetic Programming to evolve a new semantically equivalent version, optimised to reduce execution time subject to a given probability distribution of inputs. We employ a co-evolved population of test cases to encourage the preservation of the program’s semantics, and exploit the original program through seeding of the population in order to focus the search. We carry out experiments to identify the important factors in maximising efficiency gains. Although in this work we have optimised execution time, other non-functional criteria could be optimised in a similar manner

Total 4He Photoabsorption Cross Section Revisited: Correlated HH versus Effective Interaction HH

Two conceptually different hyperspherical harmonics expansions are used for the calculation of the total 4He photoabsorption cross section. Besides the well known method of CHH the recently introduced effective interaction approach for the hyperspherical formalism is applied. Semi-realistic NN potentials are employed and final state interaction is fully taken into account via the Lorentz integral transform method. The results show that the effective interaction leads to a very good convergence, while the correlation method exhibits a less rapid convergence in the giant dipole resonance region. The rather strong discrepancy with the experimental photodisintegration cross sections is confirmed by the present calculations.Comment: LaTeX, 7 pages, 3 ps figure

Fractional Laplacian in Bounded Domains

The fractional Laplacian operator, $-(-\triangle)^{\frac{\alpha}{2}}$, appears in a wide class of physical systems, including L\'evy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.Comment: 11 pages, 11 figure

Automatic music classification problems

Attempts to categorise music by extracting audio features from a sample have had mixed results. Some categories such as classical are easy to identify but attempts to distinguish between various types of popular music yield poor results. Part of the difficulty is that humans also disagree with each other when classifying music. We report on experiments that compare human classification of music samples to that based on audio feature extraction and machine learning techniques. We extracted a set of audio features and applied a range of machine learning techniques to aset of 128 pieces of music. Our work demonstrates that a single feature and a simple machine learning approach achieve results that are almost as consistent as humans for the same task. Further experiments revealed an even greater inconsistency amongst humans in selecting categories for music. Using a self organising map on the same set of pieces and features produced some meaningful song clusters, that is, pieces by the same artist or composer, or of the same genre, were grouped together. It also showed some of the same cross-genre relationships shown by the human-based classifications

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi