arXiv subjects

Hendrik Richter

Publications and source records attributed to Hendrik Richter.

At least 19 recordsLinked to original sources

arXiv2026

Evolutionary Algorithms for Generating Graphs Matching Desired Laplacian Spectra

Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and configuration. However, constructing graphs that preserve high-level properties across a broad range of graph classes remains a challenging problem. We present a novel evolutionary approach to evolve graphs based on the Laplacian graph spectra descriptor. This descriptor can be used as part of a fitness function to evaluate graphs according to their desired high-level properties. Our evolutionary algorithm evolves graphs towards this descriptor in order to obtain graphs having properties that are consistent with it but are different from each other in terms of non-spectral graph metrics, such as path length, clustering coefficient and betweenness centrality. Our experimental results show that our approach is successful for different classes of graphs and a wide range of Laplacian graph spectra.

cs.NE↗

arXiv2024

Information flow and Laplacian dynamics on local optima networks

We propose a new way of looking at local optima networks (LONs). LONs represent fitness landscapes; the nodes are local optima, and the edges are search transitions between them. Many metrics computed on LONs have been proposed and shown to be linked to metaheuristic search difficulty. These have typically considered LONs as describing static structures. In contrast to this, Laplacian dynamics (LD) is an approach to consider the information flow across a network as a dynamical process. We adapt and apply LD to the context of LONs. As a testbed, we consider instances from the quadratic assignment problem (QAP) library. Metrics related to LD are proposed and these are compared with existing LON metrics. The results show that certain LD metrics are strong predictors of metaheuristic performance for iterated local search and tabu search.

cs.NE↗

arXiv2023

Do Random and Chaotic Sequences Really Cause Different PSO Performance? Further Results

Empirical results show that PSO performance may be different if using either chaotic or random sequences to drive the algorithm's search dynamics. We analyze the phenomenon by evaluating the performance based on a benchmark of test functions and comparing random and chaotic sequences according to equality or difference in underlying distribution or density. Our results show that the underlying distribution is the main influential factor in performance and thus the assumption of general and systematic performance differences between chaos and random appears not plausible.

cs.NE↗

arXiv2023

Do Random and Chaotic Sequences Really Cause Different PSO Performance?

Our topic is performance differences between using random and chaos for particle swarm optimization (PSO). We take random sequences with different probability distributions and compare them to chaotic sequences with different but also with same density functions. This enables us to differentiate between differences in the origin of the sequences (random number generator or chaotic nonlinear system) and statistical differences expressed by the underlying distributions. Our findings (obtained by evaluating the PSO performance for various benchmark problems using statistical hypothesis testing) cast considerable doubt on previous results which compared random to chaos and suggested that the choice leads to intrinsic differences in performance.

physics.soc-ph↗

arXiv2023

Model based MIN/MAX override control of centrifugal compressor systems

We consider an application-oriented nonlinear control of centrifugal compressors. Industrial applications require the compressor system to adjust to variable process demands and to be restricted to the valid operation range (e.g. surge limit). We modify a compressor model of Gravdahl and Egeland to account for characteristic features of industrial compressors and combine the framework of nonlinear output regulation via the internal model principle with MIN/MAX-override control in order to implement trajectory tracking between given state constraints. Furthermore the switching scheme as well as the practical stability of the closed-loop MIMO system is analysed by the corresponding switched and impulsive error system. The override control is demonstrated by applying discharge pressure control, anti-surge control and maximum discharge pressure limitation.

math.OC↗

arXiv2022

What is the Best Way to Optimally Parameterize the MPC Cost Function for Vehicle Guidance?

Model predictive control (MPC) is a promising approach for the lateral and longitudinal control of autonomous vehicles. However, the parameterization of the MPC with respect to high-level requirements such as passenger comfort as well as lateral and longitudinal tracking is a challenging task. Numerous tuning parameters as well as conflicting requirements need to be considered. This contribution formulates the MPC tuning task as a multi-objective optimization problem. Solving it is challenging for two reasons: First, MPC-parameterizations are evaluated on an computationally expensive simulation environment. As a result, the used optimization algorithm needs to be as sampleefficient as possible. Second, for some poor parameterizations the simulation cannot be completed and therefore useful objective function values are not available (learning with crash constraints). In this contribution, we compare the sample efficiency of multi-objective particle swarm optimization (MOPSO), a genetic algorithm (NSGA-II) and multiple versions of Bayesian optimization (BO). We extend BO, by introducing an adaptive batch size to limit the computational overhead and by a method on how to deal with crash constraints. Results show, that BO works best for a small budget, NSGA-II is best for medium budgets and for large budgets none of the evaluated optimizers is superior to random search. Both proposed BO extensions are shown to be beneficial.

eess.SY↗

arXiv2022

Spectral dynamics of guided edge removals and identifying transient amplifiers for death-Birth updating

The paper deals with two interrelated topics, identifying transient amplifiers in an iterative process and analyzing the process by its spectral dynamics, which is the change in the graph spectra by edge manipulations. Transient amplifiers are networks representing population structures which shift the balance between natural selection and random drift. Thus, amplifiers are highly relevant for understanding the relationships between spatial structures and evolutionary dynamics. We study an iterative procedure to identify transient amplifiers for death-Birth updating. The algorithm starts with a regular input graph and iteratively removes edges until desired structures are achieved. Thus, a sequence of candidate graphs is obtained. The edge removals are guided by quantities derived from the sequence of candidate graphs. Moreover, we are interested in the Laplacian spectra of the candidate graphs and analyze the iterative process by its spectral dynamics. The results show that although transient amplifiers for death-Birth updating are rare, a substantial number of them can be obtained by the proposed procedure. The graphs identified share structural properties and have some similarity to dumbbell and barbell graphs. Also, the spectral dynamics possesses characteristic features useful for deducing links between structural and spectral properties and for distinguishing transient amplifiers among evolutionary graphs in general.

q-bio.PE↗

arXiv2021

Wrong Colored Vermeer: Color-Symmetric Image Distortion

Color symmetry implies that the colors of geometrical objects are assigned according to their symmetry properties. It is defined by associating the elements of the symmetry group with a color permutation. I use this concept for generative art and apply symmetry-consistent color distortions to images of paintings by Johannes Vermeer. The color permutations are realized as mappings of the HSV color space onto itself.

cs.CV↗

arXiv2021

Designing color symmetry in stigmergic art

Color symmetry is an extension of symmetry imposed by isometric transformations and means that the colors of geometrical objects are assigned according to the symmetry properties of the objects. A color symmetry permutes the coloring of the objects consistently with their symmetry group. We apply this concept to bio-inspired generative art. Therefore, we interpret the geometrical objects as motifs that may repeat themselves with a symmetry-consistent coloring. The motifs are obtained by design principles from stigmergy. We discuss a design procedure and present visual results.

cs.NE↗

arXiv2020

Constructing transient amplifiers for death-Birth updating: A case study of cubic and quartic regular graphs

A central question of evolutionary dynamics on graphs is whether or not a mutation introduced in a population of residents survives and eventually even spreads to the whole population, or gets extinct. The outcome naturally depends on the fitness of the mutant and the rules by which mutants and residents may propagate on the network, but arguably the most determining factor is the network structure. Some structured networks are transient amplifiers. They increase for a certain fitness range the fixation probability of beneficial mutations as compared to a well-mixed population. We study a perturbation methods for identifying transient amplifiers for death-Birth updating. The method includes calculating the coalescence times of random walks on graphs and finding the vertex with the largest remeeting time. If the graph is perturbed by removing an edge from this vertex, there is a certain likelihood that the resulting perturbed graph is a transient amplifier. We test all pairwise nonisomorphic cubic and quartic regular graphs up to a certain size and thus cover the whole structural range expressible by these graphs. We carry out a spectral analysis and show that the graphs from which the transient amplifiers can be constructed share certain structural properties. The graphs are path-like, have low conductance and are rather easy to divide into subgraphs by removing edges and/or vertices. This is connected with the subgraphs being identical (or almost identical) building blocks and the frequent occurrence of cut and/or hinge vertices. Identifying spectral and structural properties may promote finding and designing such networks.

q-bio.PE↗

arXiv2020

Convergence analysis of particle swarm optimization using stochastic Lyapunov functions and quantifier elimination

This paper adds to the discussion about theoretical aspects of particle swarm stability by proposing to employ stochastic Lyapunov functions and to determine the convergence set by quantifier elimination. We present a computational procedure and show that this approach leads to reevaluation and extension of previously know stability regions for PSO using a Lyapunov approach under stagnation assumptions.

cs.NE↗

arXiv2019

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with $N \leq 14$ players

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. Using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with $N \leq 14$ vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.

q-bio.PE↗

arXiv2019

Analyzing symmetry and symmetry breaking by computational aesthetic measures

We study creating and analyzing symmetry and broken symmetry in digital art. Our focus is not so much on computer-generating artistic images, but rather on analyzing concepts and templates for incorporating symmetry and symmetry breaking into the creation process. Taking as a starting point patterns generated algorithmically by emulating the collective feeding behavior of sand-bubbler crabs, all four types of two-dimensional symmetry are used as isometric maps. Apart from a geometric interpretation of symmetry, we also consider color as an object of symmetric transformations. Color symmetry is realized as a color permutation consistent with the isometries. Moreover, we analyze the abilities of computational aesthetic measures to serve as a metric that reflects design parameters, i.e. the type of symmetry and the degree of symmetry breaking.

cs.NE↗

arXiv2019

Relationships between dilemma strength and fixation properties in coevolutionary games

Whether or not cooperation is favored over defection in evolutionary games can be assigned by structure coefficients for any arrangement of cooperators and defectors on any network modeled as a regular graph. We study how these structure coefficients relate to a scaling of dilemma strength in social dilemma games. It is shown that some graphs permit certain arrangements of cooperators and defectors to possess particularly large structure coefficients. Moreover, these large coefficients imply particularly large sections of a bounded parameter plane spanned by scaling gamble-intending and risk-averting dilemma strength.

q-bio.PE↗

arXiv2019

Fixation properties of multiple cooperator configurations on regular graphs

Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. Population structures can be expressed as configurations. Such configurations extend scenarios with a single cooperator among defectors to any number of cooperators and any arrangement of cooperators and defectors. Thus, as a single cooperator can be interpreted as a lone mutant, the discussion about fixation properties based on configurations also applies to multiple mutants. For interaction networks modeled as regular graphs and for weak selection, the emergence of cooperation can be assessed by structure coefficients, which are specific for a configuration and a graph. We analyze these structure coefficients and particularly show that under certain conditions the coefficients strongly correlate to the average shortest path length between cooperators on the evolutionary graph. Thus,for multiple cooperators fixation properties on regular evolutionary graphs can be linked to cooperator path length.

q-bio.PE↗

arXiv2018

Properties of interaction networks, structure coefficients, and benefit-to-cost ratios

In structured populations the spatial arrangement of cooperators and defectors on the interaction graph together with the structure of the graph itself determines the game dynamics and particularly whether or not fixation of cooperation (or defection) is favored. For a single cooperator (and a single defector) and a network described by a regular graph the question of fixation can be addressed by a single parameter, the structure coefficient. As this quantity is generic for any regular graph, we may call it the generic structure coefficient. For two and more cooperators (or several defectors) fixation properties can also be assigned by structure coefficients. These structure coefficients, however, depend on the arrangement of cooperators and defectors which we may interpret as a configuration of the game. Moreover, the coefficients are specific for a given interaction network modeled as regular graph, which is why we may call them specific structure coefficients. In this paper, we study how specific structure coefficients vary over interaction graphs and link the distributions obtained over different graphs to spectral properties of interaction networks. We also discuss implications for the benefit-to-cost ratios of donation games.

q-bio.PE↗

arXiv2018

Automatic Generation of Bounds for Polynomial Systems with Application to the Lorenz System

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an enclosure of attractors is proposed. The available software tools permit an algorithmizable process, which normally requires a good insight into the systems dynamics and experience. As a result we get an estimation of the attractor, whose conservatism only results from the initial choice of the Lyapunov candidate function. The proposed approach is illustrated on the well-known Lorenz system.

cs.SC↗

arXiv2018

Information content of coevolutionary game landscapes

Coevolutionary game dynamics is the result of players that may change their strategies and their network of interaction. For such games, and based on interpreting strategies as configurations, strategy-to-payoff maps can be defined for every interaction network, which opens up to derive game landscapes. This paper presents an analysis of these game landscapes by their information content. By this analysis, we particularly study the effect of a rescaled payoff matrix generalizing social dilemmas and differences between well-mixed and structured populations.

q-bio.PE↗