Self-adaptive exploration in evolutionary search

We address a primary question of computational as well as biological research on evolution: How can an exploration strategy adapt in such a way as to exploit the information gained about the problem at hand? We first introduce an integrated formalism of evolutionary search which provides a unified view on different specific approaches. On this basis we discuss the implications of indirect modeling (via a ``genotype-phenotype mapping'') on the exploration strategy. Notions such as modularity, pleiotropy and functional phenotypic complex are discussed as implications. Then, rigorously reflecting the notion of self-adaptability, we introduce a new definition that captures self-adaptability of exploration: different genotypes that map to the same phenotype may represent (also topologically) different exploration strategies; self-adaptability requires a variation of exploration strategies along such a ``neutral space''. By this definition, the concept of neutrality becomes a central concern of this paper. Finally, we present examples of these concepts: For a specific grammar-type encoding, we observe a large variability of exploration strategies for a fixed phenotype, and a self-adaptive drift towards short representations with highly structured exploration strategy that matches the ``problem's structure''.Comment: 24 pages, 5 figure

Self-Tuned Deep Super Resolution

Deep learning has been successfully applied to image super resolution (SR). In this paper, we propose a deep joint super resolution (DJSR) model to exploit both external and self similarities for SR. A Stacked Denoising Convolutional Auto Encoder (SDCAE) is first pre-trained on external examples with proper data augmentations. It is then fine-tuned with multi-scale self examples from each input, where the reliability of self examples is explicitly taken into account. We also enhance the model performance by sub-model training and selection. The DJSR model is extensively evaluated and compared with state-of-the-arts, and show noticeable performance improvements both quantitatively and perceptually on a wide range of images

Topology and grid adaption for high-speed flow computations

This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption

pde2path - A Matlab package for continuation and bifurcation in 2D elliptic systems

pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on the FEM of the Matlab pdetoolbox, and is explained by a number of examples, including Bratu's problem, the Schnakenberg model, Rayleigh-Benard convection, and von Karman plate equations. These serve as templates to study new problems, for which the user has to provide, via Matlab function files, a description of the geometry, the boundary conditions, the coefficients of the PDE, and a rough initial guess of a solution. The basic algorithm is a one parameter arclength continuation with optional bifurcation detection and branch-switching. Stability calculations, error control and mesh-handling, and some elementary time-integration for the associated parabolic problem are also supported. The continuation, branch-switching, plotting etc are performed via Matlab command-line function calls guided by the AUTO style. The software can be downloaded from www.staff.uni-oldenburg.de/hannes.uecker/pde2path, where also an online documentation of the software is provided such that in this paper we focus more on the mathematics and the example systems

Evolutionary algorithms for robust methods

A drawback of robust statistical techniques is the increased computational effort often needed compared to non robust methods. Robust estimators possessing the exact fit property, for example, are NP-hard to compute. This means thatunder the widely believed assumption that the computational complexity classes NP and P are not equalthere is no hope to compute exact solutions for large high dimensional data sets. To tackle this problem, search heuristics are used to compute NP-hard estimators in high dimensions. Here, an evolutionary algorithm that is applicable to different robust estimators is presented. Further, variants of this evolutionary algorithm for selected estimatorsmost prominently least trimmed squares and least median of squaresare introduced and shown to outperform existing popular search heuristics in difficult data situations. The results increase the applicability of robust methods and underline the usefulness of evolutionary computation for computational statistics. --Evolutionary algorithms,robust regression,least trimmed squares (LTS),least median of squares (LMS),least quantile of squares (LQS),least quartile difference (LQD)