Positive Definite Quadratic Forms with Bounded Condition Number

The (1+1) Evolution Strategy (ES), a simple, mutation-based evolutionary algorithm for continuous optimization problems, is analyzed. In particular, we consider the most common type of mutations, namely Gaussian mutations, and the 1/5-rule for mutation adaptation, and we are interested in how the runtime, which we define as the number of function evaluations, to obtain a predefined reduction of the approximation error depends on the dimension of the search space. The most discussed function in the area of ES is the so-called Sphere-function given by Sphere: R n → R with x ↦ → x ⊤ Ix (where I ∈ R n×n is the identity matrix), which also has already been the subject of a runtime analysis. This analysis is extended to arbitrary positive definite quadratic forms (PDQFs) that induce ellipsoidal fitness landscapes which are “close to being spherically symmetric. ” Namely, all functions x ↦ → x ⊤ Qx are covered, where Q ∈ R n×n is positive definite such that its condition number, which equals the ratio of the largest of the n eigenvalues of Q to the smallest one, is O(1)

gedruckt. On the Complexity of Overcoming Gaps When Using Elitist Selection and Isotropic Mutations

We consider the (1+λ) evolution strategy, an evolutionary algorithm for minimization in R n, using isotropic mutations. Thus, for instance, Gaussian mutations adapted by the 1/5-rule or by σ-self-adaptation are covered. Lower bounds on the (expected) runtime (defined as the number of function evaluations) to overcome a gap in the search space are proved (where the search faces a gap of size ∆ if the distance between the current search point and the set of all better points is at least ∆), showing when the runtime is potentially polynomial and when the runtime is necessarily super-polynomial or even necessarily exponential in n, the dimensionality of the search space.

An Adaptive Shallow Water Model on the Sphere

amatos erzeugt das Rechengitter- untersucht werden sowohl statisch

gedruckt. A Library of Multiobjective Functions with Corresponding Graphs

Testing multiobjective evolutionary algorithms with benchmark functions improves the knowledge about algorithms and allows a standardized comparison. In the following, an alphabetically ordered and updated list of multiobjective test functions is given (based on [7]). The graphs of the Pareto fronts and Pareto sets are displayed

gedruckt. Local Search in Memetic Algorithms: the Impact of the Local Search Frequency

Memetic algorithms are popular randomized search heuristics combining evolutionary algorithms and local search. Their efficiency has been demonstrated in countless applications covering a wide area of practical problems. However, theory of memetic algorithms is still in its infancy and there is a strong need for a rigorous theoretical foundation to better understand these heuristics. Here, we attack one of the fundamental issues in the design of memetic algorithms from a theoretical perspective, namely the choice of the frequency with which local search is applied. Since no guidelines are known for the choice of this parameter, we care about its impact on memetic algorithm performance. We present worst-case problems where the choice of the local search frequency has an enormous impact on the performance of a simple memetic algorithm. A rigorous theoretical analysis shows that on these problems, with overwhelming probability, even a small factor of 2 decides about polynomial versus exponential optimization times.

gedruckt. Controlled Model Assisted Evolution Strategy with Adaptive Preselection

Abstract — The utility of evolutionary algorithms for direct optimization of real processes or complex simulations is often limited by the large number of required fitness evaluations. Model assisted evolutionary algorithms economize on actual fitness evaluations by partially selecting individuals on the basis of a computationally less complex fitness model. We propose a novel model management scheme to regulate the number of preselected individuals to achieve optimal evolutionary progress with a minimal number of fitness evaluations. The number of preselected individuals is adapted to the model quality expressed by its ability to correctly predict the best individuals. The method achieves a substantial reduction of fitness evaluations on a set of benchmarks not only in comparison to a standard evolution strategy but also with respect to other model assisted optimization schemes. I

Institut für Theoretische Informatik Automated Theorem Proving in Interactive Proof Construction

The main contribution of this thesis is the application of the first-order theorem prover DARWIN, the implementation of the Model Evolution calculus, to software verification problems. It is attempted to embed the theorem prover as a decision procedure in the KEY system for formal specification and verification. As a true first-order calculus, Model Evolution does not have to rely on ground instantiations, giving it an advantage in reasoning with quantifiers and uninterpreted function symbols that is required for the class of proof obligations that are examined. This work is also a first approach towards satisfiability modulo theories in Model Evolution. It gives a heuristic implementation that is shown to be successful for a number of examples and discusses alternative possibilities to lift ground procedures of satisfiability modulo theories to the first-order calculus.

Memory Consolidation and the Hippocampal Complex

und Rosy; Menschen, an welche sich nur positive Erinnerungen konsolidierten. Christian Mühl Memory Consolidation 3 The hippocampal complex, is widely accepted as the structure supporting the acquisition of declarative memories. Another less unanimously shared position is that the same structures, which are necessary for the acquisition of declarative memories, are involved in the maintenance of them in the period after the initial learning occurred. Evidence from amnesic patients that suffered damage to the hippocampal complex suggests, that the retrievability of memories acquired prior to the trauma causing amnesia is similarly affected as the capability to form new memories. As remote memories are frequently found preserved, a process of consolidation is assumed, which makes declarative memories gain independence from the hippocampal complex with time. Two theories currently are in the centre of the debate about consolidation. The “Standard Model of Memory Consolidation ” (SM) assumes the temporally-limited dependency of all kinds of declarative memories on the hippocampal complex until the consolidation process is complete. Th

Physica A: Statistical Mechanics and its Applications

und als Manuskript vervielfältigt worden. Bonn, März 2008“Synchronizability of stochastic network ensembles in a model of interacting dynamical units

gedruckt. Evolutionary Optimization of Dynamic Multiobjective Functions

Abstract. Many real-world problems show both multiobjective as well as dynamic characteristics. In order to use multiobjective evolutionary optimization algorithms (MOEA) efficiently, a systematic analysis of the behavior of these algorithms in dynamic environments is necessary. Dynamic fitness functions can be classified into problems with moving Pareto fronts and Pareto sets having varying speed, shape, and structure. The influence of the dimensions of the objective and decision space is considered. The analysis will focus on standard benchmark functions and newly designed test functions. Convergence and solution distribution features of modern MOEA, namely NSGA-II, SPEA 2 and MSOPS using different variation operators (SBX and Differential Evolution), will be characterized using Pareto front metrics. A new path integral metric is introduced. Especially the ability of the algorithms to use historically evolved population properties will be discussed.