Klaus Ambrosi

Acceleration of the A*-Algorithm for the Shortest Path Problem in Digital Road Maps

Using the A*-algorithm to solve point-to-point-shortest path problems, the number of iterations depends on the quality of the estimator for the remaining distance to the target. In digital maps of real road networks, iterations can be saved by using a better estimator than the Euclidian estimator. An approach is to integrate Segmentation Lines (SegLine) into the map modelling large obstacles. An auxiliary graph is constructed using the Seg-Lines wherein a shortest path is calculated yielding a better estimate. Some computational results are presented for a dynamic version of this approach.

Approach for Dynamic Problems in Clustering

In cluster analysis, a variety of methods has been developed for different areas of application (e.g. economic, ecology, medicine, psychology), some of which were implemented in data evaluation software packages (e.g. SPSS x , SAS). In many scenarios, particularly economic and ecological ones, special methods are required in order to analyze the development of clusters over time. While there are such methodical extensions for factor analysis and multidimensional scaling, hardly any dynamic approaches exist in the field of cluster analysis.

Contraction Hierarchies with A* for digital road maps

One of the most successful recent approaches for solving single source - single destination problems in graphs is the Contraction Hierarchies (CH) algorithm, originally published by [3]. The general algorithm consists of two phases: Firstly, a total order on the nodes in the graph is calculated. Secondly for queries, a modified bi-directional Dijkstra-search is performed on the hierarchy implied hereby. Relying on Dijkstra’s algorithm, CH makes no use of the geometric information contained within digital road maps. We propose A*-like modifications of the original query algorithm that double query speed. Results are presented in a benchmark using a map from the OpenStreetMap project.

Shortest-Path Algorithms and Dynamic Cost Changes

Shortest-path algorithms are used to find an optimal way through a network. These networks often underlie dynamic changes, e.g. in a road network we find congestions or road works. These dynamic changes can cause a previously calculated route to be not up-to-date anymore. A shortest-path algorithm should react on these changes and present a new route without much overhead in time and space. The simplest way would be to calculate the whole route again. Dynamic shortest path algorithms with different features have been developed avoiding a full re-calculation. This paper describes the advantages of dynamic algorithms and provides an overview.

Detecting Changes in Statistics of Road Accidents to Enhance Road Safety

Finding significant changes in multidimensional data is a crucial task for several use cases. With change mining on frequent itemsets, alterations in the statistics of personal injury road accidents can be detected. Since a lot of factors determine the situation of an accident, the statistical data consists of too many dimensions to detect changes in their frequencies manually. Hence, we propose an automated approach based on Frequent Itemset Mining using known algorithms, such as Apriori, to detect significant changes within the data. Firstly, the 1.8 million records of Great Britain’s road safety data openly published by the Department for Transport are prepared and adjusted to match the algorithms’ requirements. Secondly, the most frequent itemsets for each time interval are filed and compared to the itemsets of the previous period and are split into classes of changing, stable and semi-stable itemsets. To build our framework we concentrate on the support of frequent itemsets and the changes between the months of two consecutive years.

Effects of Constraints in Residential Demand-Side-Management Algorithms—A Simulation-Based Study

Due to various challenges such as climatic changes or implementation of renewable energy generation, improvements in regulating energy grids are required. Demand-Side-Management (DSM) contributes to this progress by managing, shifting and controlling loads. However, many DSM algorithms make assumptions regarding load characteristics which do not consider real world conditions. Prior studies find a total of five constraints but so far no investigation shows the effects of these constraints on DSM algorithms. Hence, this research analyses the effects of several constraints of DSM algorithms by conducting a simulation. As a result, we can conclude that the constraints have an effect on the results. For example, the savings dropped about 7% when considering multiple constraints. The handling and the outcomes depend on several factors and might vary. As a logical conclusion, we postulate that these constraints should be considered in DSM algorithms.

A New Approach to Freight Consolidation for a Real-World Pickup-and-Delivery Problem

During courier and express providers’ operational scheduling, vehicles are assigned to customer orders. This task is complex, combinatorially comprehensive, and contains aspects that defy modeling within reasonable effort, e.g. due to a lack of structured data. Hence, a fully automated solution cannot be achieved. In practice, human dispatchers often use dialog-oriented decision support systems (DSS). These systems generate recommendations from which the human dispatchers select the most profitable one, while additionally taking into account domain-specific knowledge. Solutions that consolidate the freight of multiple customer orders onto a single vehicle are usually particularly favorable. Generally, consolidating leads to a higher degree of vehicle capacity utilization, which in turn increases cost effectiveness and lowers the resulting environmental damage. We present a new recursive heuristic for this scenario based on the well-known savings algorithm. A central parameter of the algorithm limits the number of interdependent single tours. Through the appropriate setting of this parameter, one can control the results’ complexity and ensure their transparency and acceptance by human dispatchers. Using real-world data benchmarks, we prove the effectiveness of our algorithm empirically.

Predicting Changes in Market Segments Based on Customer Behavior

In modern marketing, knowing the development of different market segments is crucial. However, simply measuring the occurred changes is not sufficient when planning future marketing campaigns. Predictive models are needed to show trends and to forecast abrupt changes such as the elimination of segments, the splitting of a segment, or the like. For predicting changes, continuously collected data are needed. Behavioral data are suitable for spotting trends in customer segments as they can easily be recorded. For detecting changes in a market structure, fuzzy-clustering is used since gradual changes in cluster memberships can implicate future abrupt changes. In this paper, we introduce different measurements for the analysis of gradual changes that comprise the currentness of data and can be used in order to predict abrupt changes.

Contraction Hierarchies with Turn Restrictions

For single-pair shortest path problems, Contraction Hierarchies (CH) provide very small query times together with a very low space overhead for the graph. During a preprocessing every node is assigned a distinct rank. Queries are performed using an alternating bidirectional Dijkstra search that only expands towards higher ranked nodes. In its original version CH do not take turn restrictions (TR) into account. This may lead to illegal routes whose length may considerably differ from legal ones. Incorporating TR widens the scope of application for CH, e.g., car navigation or precise traffic simulations. A way to consider TR is to switch from a node-based to an edge-based search, implicitly allowing nodes to be settled more than once. Compared to the original CH query this increases the size of the search trees substantially. A more space efficient adaptive algorithm combining node-based with on-demand edge-based search is presented, where nodes may only be settled multiply if the encountered path towards them traverses a (possible) TR. The number of iterations in this approach is at most as high as the edge-base search. Depending on the number of TR and the average node degree in the graph our approach outperforms the edge-based search by far.

Zur Entscheidungsunterstützung bei netzeffektbasierten Gütern

Fur marketingrelevante Fragestellungen und fur die strategische Bewertung von Technologiealternativen ist die Untersuchung des Diffusionsverlaufs bei Netzeffektgutern, wie z.B. Telekommunikationsdiensten, von hohem Interesse. Es wird ein Entscheidungsunterstutzungssystem vorgestellt, dass insbesondere Marketingvariable zur Ausgestaltung relevanter Merkmale von netzeffektbasierten Gutern unterstutzt. Ausgehend von dynamischen Nutzenfunktionen wird ein Modellansatz auf Grundlage der Mastergleichung der Physik bzw. den Mittelwertgleichungen vorgestellt, der Wechselwahrscheinlichkeiten zwischen den Produktalternativen ableitet. Die Anwendungsrelevanz des Modellansatzes wird durch entscheidungsrelevante What-If-Analysen verdeutlicht.