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

Making and breaking power laws in evolutionary algorithm population dynamics

Deepening our understanding of the characteristics and behaviors of population-based search algorithms remains an important ongoing challenge in Evolutionary Computation. To date however, most studies of Evolutionary Algorithms have only been able to take place within tightly restricted experimental conditions. For instance, many analytical methods can only be applied to canonical algorithmic forms or can only evaluate evolution over simple test functions. Analysis of EA behavior under more complex conditions is needed to broaden our understanding of this population-based search process. This paper presents an approach to analyzing EA behavior that can be applied to a diverse range of algorithm designs and environmental conditions. The approach is based on evaluating an individual’s impact on population dynamics using metrics derived from genealogical graphs.\ud From experiments conducted over a broad range of conditions, some important conclusions are drawn in this study. First, it is determined that very few individuals in an EA population have a significant influence on future population dynamics with the impact size fitting a power law distribution. The power law distribution indicates there is a non-negligible probability that single individuals will dominate the entire population, irrespective of population size. Two EA design features are however found to cause strong changes to this aspect of EA behavior: i) the population topology and ii) the introduction of completely new individuals. If the EA population topology has a long path length or if new (i.e. historically uncoupled) individuals are continually inserted into the population, then power law deviations are observed for large impact sizes. It is concluded that such EA designs can not be dominated by a small number of individuals and hence should theoretically be capable of exhibiting higher degrees of parallel search behavior

A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space.

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps

Optimum Tracking with Evolution Strategies

Evolutionary algorithms are frequently applied to dynamic optimization problems in which the objective varies with time. It is desirable to gain an improved understanding of the influence of different genetic operators and of the parameters of a strategy on its tracking performance. An approach that has proven useful in the past is to mathematically analyze the strategy's behavior in simple, idealized environments. The present paper investigates the performance of a multiparent evolution strategy that employs cumulative step length adaptation for an optimization task in which the target moves linearly with uniform speed. Scaling laws that quite accurately describe the behavior of the strategy and that greatly contribute to its understanding are derived. It is shown that in contrast to previously obtained results for a randomly moving target, cumulative step length adaptation fails to achieve optimal step lengths if the target moves in a linear fashion. Implications for the choice of population size parameters are discussed

Conjunction analysis for uncertain objects in close proximity

In an increasingly dense space environment, collision avoidance has become an essential task in satellite operations. In order to avoid these possible collisions, it is needed to determine a possible conjunction and its associated uncertainty. Satellite conjunction analysis is the assessment of collision risk during a close encounter between a satellite and another object in orbit. A counterintuitive phenomenon has emerged in the conjunction analysis literature, namely, probability dilution, in which lower quality data paradoxically appear to reduce the risk of collision. This work presents a review of the current methods used to estimate the probability of collision between two bodies in orbit as well as an exhaustive analysis of the factors to take into account in this process. The concept of uncertainty propagation, probability dilution and the effect of perturbations and noise is developed.En un entorno espacial cada vez más denso, la prevención de colisiones se ha convertido en una tarea esencial en las operaciones de los satélites. Para evitar estas posibles colisiones, es necesario determinar una posible conjunción y su incertidumbre asociada. El análisis de conjunción de satélites es la evaluación del riesgo de colisión durante un encuentro cercano entre un satélite y otro objeto en órbita. En la literatura sobre análisis de conjunciones ha surgido un fenómeno contrario a la intuición, la dilución de la probabilidad, en el que, paradójicamente, los datos de menor calidad parecen reducir el riesgo de colisión. Este trabajo presenta una revisión de los métodos actuales utilizados para estimar la probabilidad de colisión entre dos cuerpos en órbita así como un análisis exhaustivo de los factores a tener en cuenta en este proceso. Se desarrolla el concepto de propagación de la incertidumbre, dilución de la probabilidad y el efecto de las perturbaciones y el ruido.Universidad de Sevilla. Grado en Ingeniería Aeroespacia

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions