On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling

Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of evolutionary algorithms for a dynamic variant of a classical combinatorial optimization problem, namely makespan scheduling. We study the model of a strong adversary which is allowed to change one job at regular intervals. Furthermore, we investigate the setting of random changes. Our results show that randomized local search and a simple evolutionary algorithm are very effective in dynamically tracking changes made to the problem instance.Comment: Conference version appears at IJCAI 201

Gradients in urban material composition: A new concept to map cities with spaceborne imaging spectroscopy data

To understand processes in urban environments, such as urban energy fluxes or surface temperature patterns, it is important to map urban surface materials. Airborne imaging spectroscopy data have been successfully used to identify urban surface materials mainly based on unmixing algorithms. Upcoming spaceborne Imaging Spectrometers (IS), such as the Environmental Mapping and Analysis Program (EnMAP), will reduce the time and cost-critical limitations of airborne systems for Earth Observation (EO). However, the spatial resolution of all operated and planned IS in space will not be higher than 20 to 30 m and, thus, the detection of pure Endmember (EM) candidates in urban areas, a requirement for spectral unmixing, is very limited. Gradient analysis could be an alternative method for retrieving urban surface material compositions in pixels from spaceborne IS. The gradient concept is well known in ecology to identify plant species assemblages formed by similar environmental conditions but has never been tested for urban materials. However, urban areas also contain neighbourhoods with similar physical, compositional and structural characteristics. Based on this assumption, this study investigated (1) whether cover fractions of surface materials change gradually in urban areas and (2) whether these gradients can be adequately mapped and interpreted using imaging spectroscopy data (e.g. EnMAP) with 30 m spatial resolution. Similarities of material compositions were analysed on the basis of 153 systematically distributed samples on a detailed surface material map using Detrended Correspondence Analysis (DCA). Determined gradient scores for the first two gradients were regressed against the corresponding mean reflectance of simulated EnMAP spectra using Partial Least Square regression models. Results show strong correlations with R2 = 0.85 and R2 = 0.71 and an RMSE of 0.24 and 0.21 for the first and second axis, respectively. The subsequent mapping of the first gradient reveals patterns that correspond to the transition from predominantly vegetation classes to the dominance of artificial materials. Patterns resulting from the second gradient are associated with surface material compositions that are related to finer structural differences in urban structures. The composite gradient map shows patterns of common surface material compositions that can be related to urban land use classes such as Urban Structure Types (UST). By linking the knowledge of typical material compositions with urban structures, gradient analysis seems to be a powerful tool to map characteristic material compositions in 30 m imaging spectroscopy data of urban areas

3-Objective Pareto Optimization for Problems with Chance Constraints

Evolutionary multi-objective algorithms have successfully been used in the context of Pareto optimization where a given constraint is relaxed into an additional objective. In this paper, we explore the use of 3-objective formulations for problems with chance constraints. Our formulation trades off the expected cost and variance of the stochastic component as well as the given deterministic constraint. We point out benefits that this 3-objective formulation has compared to a bi-objective one recently investigated for chance constraints with Normally distributed stochastic components. Our analysis shows that the 3-objective formulation allows to compute all required trade-offs using 1-bit flips only, when dealing with a deterministic cardinality constraint. Furthermore, we carry out experimental investigations for the chance constrained dominating set problem and show the benefit for this classical NP-hard problem

Rigorous analyses for the combination of ant colony optimization and local search

Ant colony optimization (ACO) is a metaheuristic that produces good results for a wide range of combinatorial optimization problems. Often such successful applications use a combination of ACO and local search procedures that improve the solutions constructed by the ants. In this paper, we study this combination from a theoretical point of view and point out situations where introducing local search into an ACO algorithm enhances the optimization process significantly. On the other hand, we illustrate the drawback that such a combination might have by showing that this may prevent an ACO algorithm from obtaining optimal solutions

Aspects of guaranteed error control in CPDEs

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretisation error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bounds (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects. First, the variational crimes from a nonconforming finite element discretisation and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB. Second, the reliable approximation of the discretisation error on curved boundaries and, finally, the reliable bounds of the error with respect to some goal-functional, namely, the error in the approximation of the directional derivative at a given point

Aspects of quaranteed error control in CPDEs

Whenever numerical algorithms are employed for a reliable computational forecast, they need to allow for an error control in the final quantity of interest. The discretisation error control is of some particular importance in computational PDEs (CPDEs) where guaranteed upper error bounds (GUB) are of vital relevance. After a quick overview over energy norm error control in second-order elliptic PDEs, this paper focuses on three particular aspects. First, the variational crimes from a nonconforming finite element discretisation and guaranteed error bounds in the discrete norm with improved postprocessing of the GUB. Second, the reliable approximation of the discretisation error on curved boundaries and, finally, the reliable bounds of the error with respect to some goal-functional, namely, the error in the approximation of the directional derivative at a given poin

On the influence of pheromone updates in ACO algorithms

The runtime analysis of randomized search heuristics is a growing field where, in the last two decades, many rigorous results have been obtained. These results, however, apply particularly to classical search heuristics such as Evolutionary Algorithms (EAs) and Simulated Annealing. First runtime analyses of modern search heuristics have been conducted only recently w. r. t. a simple Ant Colony Optimization (ACO) algorithm called 1-ANT. In particular, the influence of the evaporation factor in the pheromone update mechanism and the robustness of this parameter w. r. t. the runtime have been determined for the example function OneMax. This paper puts forward the runtime analysis of the 1-ANT on example functions. With respect to EAs, such analyses have been essential to develop methods for the analysis on more complicated problems. The proof techniques required for the 1-ANT, unfortunately, differ significantly from those for EAs, which means that a new reservoir of methods has to be built up. Again, the influence of the evaporation factor is analyzed rigorously, and it is proved that its choice can be very crucial to allow efficient runtimes. Moreover, the analyses provide insight into the working principles of ACO algorithms and, in terms of their robustness, describe essential differences to other randomized search heuristics