arXiv subjects
Publications and source records attributed to Frank Neumann.
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more classical theories. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.
Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.
The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w.r.t. the number of fitness evaluations) of $Θ(n^{3.25}(\log n)^{0.25})$. In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely \emph{repair mechanisms} and \emph{parent selection}. We show that repairing infeasible offspring leads to an improved expected optimization time of $\mathord{O}(n^{3.2}(\log n)^{0.2})$. As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of $\mathord{O}(n^{3}\log n)$. Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms.
The placement of wind turbines on a given area of land such that the wind farm produces a maximum amount of energy is a challenging optimization problem. In this article, we tackle this problem, taking into account wake effects that are produced by the different turbines on the wind farm. We significantly improve upon existing results for the minimization of wake effects by developing a new problem-specific local search algorithm. One key step in the speed-up of our algorithm is the reduction in computation time needed to assess a given wind farm layout compared to previous approaches. Our new method allows the optimization of large real-world scenarios within a single night on a standard computer, whereas weeks on specialized computing servers were required for previous approaches.
The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences the runtime behavior. We consider generalizations of ORDER and MAJORITY and present a computational complexity analysis of (1+1) GP using multi-criteria fitness functions that take into account the original objective and the complexity of a syntax tree as a secondary measure. Furthermore, we study the expected time until population-based multi-objective genetic programming algorithms have computed the Pareto front when taking the complexity of a syntax tree as an equally important objective.
Generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds we define secondary theories and characteristic classes for smooth etale groupoids. As special cases we obtain versions of the groups of differential characters for smooth etale groupoids and for orbifolds.
We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild-Mitchell cohomology and those studied before by Watts, Roos, Quillen and others.
Wind energy plays an increasing role in the supply of energy world-wide. The energy output of a wind farm is highly dependent on the weather condition present at the wind farm. If the output can be predicted more accurately, energy suppliers can coordinate the collaborative production of different energy sources more efficiently to avoid costly overproductions. With this paper, we take a computer science perspective on energy prediction based on weather data and analyze the important parameters as well as their correlation on the energy output. To deal with the interaction of the different parameters we use symbolic regression based on the genetic programming tool DataModeler. Our studies are carried out on publicly available weather and energy data for a wind farm in Australia. We reveal the correlation of the different variables for the energy output. The model obtained for energy prediction gives a very reliable prediction of the energy output for newly given weather data.
Team pursuit track cycling is a bicycle racing sport held on velodromes and is part of the Summer Olympics. It involves the use of strategies to minimize the overall time that a team of cyclists needs to complete a race. We present an optimisation framework for team pursuit track cycling and show how to evolve strategies using metaheuristics for this interesting real-world problem. Our experimental results show that these heuristics lead to significantly better strategies than state-of-art strategies that are currently used by teams of cyclists.
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems with isolated program semantics. With this paper, we push forward the computational complexity analysis of GP on a problem with dependent program semantics. We study the well-known sorting problem in this context and analyze rigorously how GP can deal with different measures of sortedness.
Analyzing the computational complexity of evolutionary algorithms for binary search spaces has significantly increased their theoretical understanding. With this paper, we start the computational complexity analysis of genetic programming. We set up several simplified genetic programming algorithms and analyze them on two separable model problems, ORDER and MAJORITY, each of which captures an important facet of typical genetic programming problems. Both analyses give first rigorous insights on aspects of genetic programming design, highlighting in particular the impact of accepting or rejecting neutral moves and the importance of a local mutation operator.
With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length 'n'. Our investigations point out how the progress according to function values is stored in pheromone. We provide a general upper bound of O((n^3 \log n)/ ρ) for two ACO variants on all linear functions, where (ρ) determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called OneMax and BinVal and give additional insights using an experimental study.
We define secondary theories and characteristic classes for simplicial smooth manifolds generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds. As a special case we get versions of the groups of differential characters of Cheeger and Simons for simplicial smooth manifolds. Special examples include classifying spaces of Lie groups and Lie groupoids.
We describe the action of the different Frobenius morphisms on the cohomology ring of the moduli stack of algebraic vector bundles of fixed rank and determinant on an algebraic curve over a finite field in characteristic p and analyse special situations like vector bundles on the projective line and relations with infinite Grassmannians.
Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over $\bar{\Q}$ parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite group G of automorphisms, which comes with a fixed embedding in the mapping class group, such that in the associated complex analytic situation the action of G is precisely the differentiable action induced by this specified embedding of G in the mapping class group.