Self-adaptation in evolution strategies

In this thesis, an analysis of self-adaptative evolution strategies (ES) is provided. Evolution strategies are population-based search heuristics usually applied in continuous search spaces which ultilize the evolutionary principles of recombination, mutation, and selection. Self-Adaptation in evolution strategies usually aims at steering the mutation process. The mutation process depends on several parameters, most notably, on the mutation strength. In a sense, this parameter controls the spread of the population due to random mutation. The mutation strength has to be varied during the optimization process: A mutation strength that was advantageous in the beginning of the run, for instance, when the ES was far away from the optimizer, may become unsuitable when the ES is close to optimizer. Self-Adaptation is one of the means applied. In short, self-adaptation means that the adaptation of the mutation strength is left to the ES itself. The mutation strength becomes a part of an individual’s genome and is also subject to recombination and mutation. Provided that the resulting offspring has a sufficiently “good” fitness, it is selected into the parent population. Two types of evolution strategies are considered in this thesis: The (1,lambda)-ES with one parent and lambda offspring and intermediate ES with a parental population with mu individuals. The latter ES-type applies intermediate recombination in the creation of the offspring. Furthermore, the analysis is restricted to two types of fitness functions: the sphere model and ridge functions. The thesis uses a dynamic systems approach, the evolution equations first introduced by Hans-Georg Beyer, and analyzes the mean value dynamics of the ES

Intercepting a Target with Sensor Swarms

The article of record as published may be located at http://dx.doi.org/10.1109/HICSS.2013.281This paper introduces a new coordination method to intercept a mobile target in urban areas with a team of sensor platforms. The task is to intercept the target before it leaves the area. The approach combines algorithmic concepts from ant colony and particle swarm optimization in order to bias the search and to spread the team in the search area. The algorithms introduced are tested in simulation experiments on grids. The success probabilities measured are relatively high for most parameter combinations, and the target is intercepted in roughly half the simulation time on average. Furthermore, the experiments reveal robust behavior with regard to the parameter setting

Preface

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Self-Adaptation of Evolution Strategies under Noisy Fitness Evaluations

This paper investigates the self-adaptation behavior of (1, #)- evolution strategies (ES) on the noisy sphere model. To this end, the stochastic system dynamics is approximated on the level of the mean value dynamics. Being based on this "microscopic" analysis, the steady state behavior of the ES for the scaled noise scenario and the constant noise strength scenario will be theoretically analyzed and compared with real ES runs. An explanation will be given for the random walk like behavior of the mutation strength in the vicinity of the steady state. It will be shown that this is a peculiarity of the (1, #)-ES and that intermediate recombination strategies do not su#er from such behavior

Computational networks and systems - Homogenization of self-adjoint differential operators in variational form on periodic networks and micro-architectured systems

Micro-architectured systems and periodic network structures play an import role in multi-scale physics and material sciences. Mathematical modeling leads to challenging problems on the analytical and the numerical side. Previous studies focused on averaging techniques that can be used to reveal the corresponding macroscopic model describing the effective behavior. This study aims at a mathematical rigorous proof within the framework of homogenization theory. As a model example, the variational form of a self-adjoint operator on a large periodic network is considered. A notion of two-scale convergence for network functions based on a so-called two-scale transform is applied. It is shown that the sequence of solutions of the variational microscopic model on varying networked domains converges towards the solution of the macroscopic model. A similar result is achieved for the corresponding sequence of tangential gradients. The resulting homogenized variational model can be easily solved with standard PDE-solvers. In addition, the homogenized coefficients provide a characterization of the physical system on a global scale. In this way, a mathematically rigorous concept for the homogenization of self-adjoint operators on periodic manifolds is achieved. Numerical results illustrate the effectiveness of the presented approach

Predicting the Solution Quality in Noisy Optimization

Abstract. Noise is a common problem encountered in real-world optimization. Although it is folklore that evolution strategies perform well in the presence of noise, even their performance is degraded. One effect on which we will focus in this paper is the reaching of a steady state that deviates from the actual optimal solution. The quality gain is a local progress measure, describing the expected one-generation change of the fitness of the population. It can be used to derive evolution criteria and steady state conditions which can be utilized as a starting point to determine the final fitness error, i.e. the expected difference between the actual optimal fitness value and that of the steady state. We will demonstrate the approach by determining the final solution quality for two fitness functions.

Bridging the gap between variational homogenization results and two-scale asymptotic averaging techniques on periodic network structures

In modern material sciences and multi-scale physics homogenization approaches provide a global characterization of physical systems that depend on the topology of the underlying microgeometry. Purely formal approaches such as averaging techniques can be applied for an identification of the averaged system. For models in variational form, two-scale convergence for network functions can be used to derive the homogenized model. The sequence of solutions of the variational microcsopic models and the corresponding sequence of tangential gradients converge toward limit functions that are characterized by the solution of the variational macroscopic model. Here, a further extension of this result is proved. The variational macroscopic model can be equivalently represented by a homogenized model on the superior domain and a certain number of reference cell problems. In this way, the results obtained by averaging strategies are supported by notions of convergence for network functions on varying domains.Publisher's Versio