An Exponential Lower Bound for the Runtime of the cGA on Jump Functions

In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump functions with high probability is at most polynomial (in the dimension) if the jump size is at most logarithmic (in the dimension), and is at most exponential in the jump size if the jump size is super-logarithmic. The exponential runtime guarantee was achieved with a hypothetical population size that is also exponential in the jump size. Consequently, this setting cannot lead to a better runtime. In this work, we show that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size. This result might be the first non-trivial exponential lower bound for EDAs that holds for arbitrary parameter settings.Comment: To appear in the Proceedings of FOGA 2019. arXiv admin note: text overlap with arXiv:1903.1098

Meta-Modeling by Symbolic Regression and Pareto Simulated Annealing

The subject of this paper is a new approach to Symbolic Regression.Other publications on Symbolic Regression use Genetic Programming.This paper describes an alternative method based on Pareto Simulated Annealing.Our method is based on linear regression for the estimation of constants.Interval arithmetic is applied to ensure the consistency of a model.In order to prevent over-fitting, we merit a model not only on predictions in the data points, but also on the complexity of a model.For the complexity we introduce a new measure.We compare our new method with the Kriging meta-model and against a Symbolic Regression meta-model based on Genetic Programming.We conclude that Pareto Simulated Annealing based Symbolic Regression is very competitive compared to the other meta-model approachesapproximation;meta-modeling;pareto simulated annealing;symbolic regression

Comparison of Weighted Sum Fitness Functions for PSO Optimization of Wideband Medium-gain Antennas

In recent years PSO (Particle Swarm Optimization) has been successfully applied in antenna design. It is well-known that the cost function has to be carefully chosen in accordance with the requirements in order to reach an optimal result. In this paper, two different wideband medium-gain arrays are chosen as benchmark structures to test the performance of four PSO fitness functions that can be considered in such a design. The first one is a planar 3 element, the second one a linear 4 element antenna. A MoM (Method of Moments) solver is used in the design. The results clearly show that the fitness functions achieve a similar global best candidate structure. The fitness function based on realized gain however converges slightly faster than the others

Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Properties of Interstellar Turbulence from Gradients of Linear Radio Polarization Maps

Faraday rotation of linearly polarized radio signals provides a very sensitive probe of fluctuations in the interstellar magnetic field and ionized gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set of statistical tools to analyze images of the spatial gradient of linearly polarized radio emission ($|\nabla \textbf{P}|$) from the ISM for both observational data from a test image of the Southern Galactic Plane Survey (SGPS) and isothermal simulations of MHD turbulence. We compared the observational data with results of synthetic observations obtained with the simulations of 3D turbulence. Visually, in both data sets, a complex network of filamentary structures is seen. Our analysis shows that the filaments in the gradient can be produced by shocks as well as random fluctuations characterizing the non-differentiable field of MHD turbulence. The latter dominates for subsonic turbulence, while the former dominates for supersonic turbulence. In order to quantitatively characterize these differences we use the topology tool known as a genus curve as well as the moments of the image distribution. We find that higher values for the moments correspond to cases of $|\nabla \textbf{P}|$ with larger Mach numbers, but the strength of the dependency is connected to the telescope angular resolution. In regards to the topology, the supersonic filaments observed in $|\nabla \textbf{P}|$ have a positive genus shift, which indicates a "swisscheese" like topology, while the subsonic cases show a negative genus, indicating a "clump" like topology. In the case of the genus, the dependency on the telescope resolution is not as strong. The SGPS test region data has a distribution and morphology that matches subsonic to transsonic type turbulence, which independently confirms what is now expected for the WIM.Comment: Submitted to Ap