Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.Comment: 13th International Conference on Parallel Problem Solving from Nature (PPSN 2014) (2014

Hookworm infection in the Australian sea lion (Neophoca cinerea)

For the Australian sea lion (Neophoca cinerea), an endangered keystone predator that demonstrates high rates of pup mortality and limited population recovery, an understanding of the role of infectious disease in influencing pup health, and how it may contribute towards shaping population demography, is a key knowledge gap. This thesis investigated the taxonomy, epidemiology, clinical impact, and management of hookworm infection in N. cinerea to address the hypothesis that hookworm infection is a significant cause of disease and mortality in this species. Hookworms collected from N. cinerea pups were identified and described as a novel species (Uncinaria sanguinis). Transmammary transmission in the immediate post-parturient period was implicated as the predominant route leading to patent hookworm infection in pups; however, in contrast to the fundamental role that colony substrate appears to play in shaping the epidemiology of hookworm infection in other otariid hosts, this thesis determined that all N. cinerea pups are infected with U. sanguinis irrespective of the type of colony substrate and that the intensity of hookworm infection appears to be influenced by colony-specific seasonal differences in host behaviour. The clinical impact of hookworm infection in pups was quantified and the occurrence of seasonal patterns in health parameters and the magnitude of colony pup mortality were related to the dynamics of hookworm infection. In addition, the effectiveness of ivermectin to eliminate hookworm infection was investigated. This thesis determined that U. sanguinis is an important cause of disease and mortality in N. cinerea; this thesis contributes towards an improved understanding of the role of infectious disease in influencing the health status and population demography of this endangered species, informing conservation management and providing a solid foundation for further investigations of the effect of disease on the health status of free-ranging species

Regional wave propagation using the discontinuous Galerkin method

We present an application of the discontinuous Galerkin (DG) method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER) Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy). We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D <i>EPcrust</i> model, combined with the depth-dependent <i>ak135</i> velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies

A novel population-based multi-objective CMA-ES and the impact of different constraint handling techniques

htmlabstractThe Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is a well-known, state-of-the-art optimization algorithm for single-objective real-valued problems, especially in black-box settings. Although several extensions of CMA-ES to multi-objective (MO) optimization exist, no extension incorporates a key component of the most robust and general CMA-ES variant: the association of a population with each Gaussian distribution that drives optimization. To achieve this, we use a recently introduced framework for extending population-based algorithms from single- to multi-objective optimization. We compare, using six well-known benchmark problems, the performance of the newly constructed MO-CMA-ES with existing variants and with the estimation of distribution algorithm (EDA) known as iMAMaLGaM, that is also an instance of the framework, extending the single-objective EDA iAMaLGaM to MO. Results underline the advantages of being able to use populations. Because many real-world problems have constraints, we also study the use of four constraint-handling techniques. We find that CMA-ES is typically less robust to these techniques than iAMaLGaM. Moreover, whereas we could verify that a penalty method that was previously used in literature leads to fast convergence, we also find that it has a high risk of finding only nearly, but not entirely, feasible solutions. We therefore propose that other constraint-handling techniques should be preferred in general

Tilt effects on moment tensor inversion in the near field of active volcanoes

Dynamic tilts (rotational motion around horizontal axes) change the projection of local gravity onto the horizontal components of seismometers. This causes sensitivity of these components to tilt, especially at low frequencies. We analyse the consequences of this effect onto moment tensor inversion for very long period (vlp) events in the near field of active volcanoes on the basis of synthetic examples using the station distribution of a real deployed seismic network and the topography of Mt. Merapi volcano (Java, Indonesia). The examples show that for periods in the vlp range of 10-30 s tilt can have a strong effect on the moment tensor inversion, although its effect on the horizontal seismograms is significant only for few stations. We show that tilts can be accurately computed using the spectral element method and include them in the Green's functions. The (simulated) tilts might be largely influenced by strain-tilt coupling (stc). However, due to the frequency dependence of the tilt contribution to the horizontal seismograms, only the largest tilt signals affect the source inversion in the vlp frequency range. As these are less sensitive to stc than the weaker signals, the effect of stc can likely be neglected in this application. In the converse argument, this is not necessarily true for longer periods, where the horizontal seismograms are dominated by the tilt signal and rotational sensors would be necessary to account for it. As these are not yet commercially available, this study underlines the necessity for the development of such instrument

A Large Area Fiber Optic Gyroscope on multiplexed fiber network

We describe a fiber optical gyroscope based on the Sagnac effect realized on a multiplexed telecom fiber network. Our loop encloses an area of 20 km2 and coexists with Internet data traffic. This Sagnac interferometer achieves a sensitivity of about (10-8 rad/s)/sqrt(Hz), thus approaching ring laser gyroscopes without using narrow linewidth laser nor sophisticated optics. The proposed gyroscope is sensitive enough for seismic applications, opening new possibilities for this kind of optical fiber sensors

Not all parents are equal for MO-CMA-ES

International audienceThe Steady State variants of the Multi-Objective Covariance Matrix Adaptation Evolution Strategy (SS-MO-CMA-ES) generate one offspring from a uniformly selected parent. Some other parental selection operators for SS-MO-CMA-ES are investigated in this paper. These operators involve the definition of multi-objective rewards, estimating the expectation of the offspring survival and its Hypervolume contribution. Two selection modes, respectively using tournament, and inspired from the Multi-Armed Bandit framework, are used on top of these rewards. Extensive experimental validation comparatively demonstrates the merits of these new selection operators on unimodal MO problems

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure