Wolfgang Steitz

Edge Orientation and the Design of Problem-Specific Crossover Operators for the OCST Problem

In the Euclidean optimal communication spanning tree problem, the edges in optimal trees not only have small weights but also point with high probability toward the center of the graph. These characteristics of optimal solutions can be used for the design of problem-specific evolutionary algorithms (EAs). Recombination operators of direct encodings like edge-set and NetDir can be extended such that they prefer not only edges with small distance weights but also edges that point toward the center of the graph. Experimental results show higher performance and robustness in comparison to EAs using existing crossover strategies.

New insights into the OCST problem: integrating node degrees and their location in the graph

This paper considers the Euclidean variant of the optimal communciation spanning tree (OCST) problem. Researches have analyzed the structure of the problem and found that high quality solutions prefer edges of low cost. Further, edges pointing to the center of the network are more likely to be included in good solutions. We add to the literature and provide additional insights into the structure of the OCST problem. Therefore, we investigate properies of the whole tree, such as node degrees and the Wiener index. The results reveal that optimal solutions are structured in a star-like manner. There are few nodes with high node degrees, these nodes are located next to the graphs center. The majority of the nodes have very low node degrees. Especially, nodes with degree one are very common and located far away of the center. We exploit these insights to develop a construction heuristic, which builds spanning trees with similar properties. Experiments indicate a high solution quality for the OCST problem. In a next step, we seed the initial population of an evolutionary algorithm (EA) with solutions constructed with our method. An experimental study demonstrates the merits of using a biased initialization: the algorithm is faster, better compared to the same algorithm using random starting solutions.

Orientation matters: how to efficiently solve ocst problems with problem-specific EAs

The optimal communication spanning tree (OCST) problem is a well known

Inferring decision strategies from clickstreams in decision support systems: a new process-tracing approach using state machines

\mathcal{NP}

Using penalties instead of rewards: Solving OCST problems with guided local search

-hard combinatorial optimization problem which seeks a spanning tree that satisfies all given communication requirements for minimal total costs. It has been shown that optimal solutions of OCST problems are biased towards the much simpler minimum spanning tree (MST) problem. Therefore, problem-specific representations for EAs like heuristic variants of edge-sets that are biased towards MSTs show high performance. In this paper, additional properties of optimal solutions for Euclidean variants of OCST problems are studied. Experimental results show that not only edges in optimal trees are biased towards low-distance weights but also edges which are directed towards the graphs center are overrepresented in optimal solutions. Therefore, efficient heuristic search algorithms for OCST should be biased towards edges with low distance weight \emph{and} edges that point towards the center of the graph. Consequently, we extend the recombination operator of edge-sets such that the orientation of the edges is considered for constructing offspring solutions. Experimental results show a higher search performance in comparison to EAs using existing crossover strategies of edge-sets. As a result, we suggest to consider not only the distance weights but also the orientation of edges in heuristic solution approaches for the OCST problem.

New Heuristic Approaches for the Bounded-Diameter Minimum Spanning Tree Problem

Webstores can easily gather large amounts of consumer data, including clicks on single elements of the user interface, navigation patterns, user profile data, and search texts. Such clickstream data are both interesting to merchandisers as well as to researchers in the field of decision-making behavior, because they describe consumer decision-behavior on websites. This paper introduces an approach that infers decision-behavior from clickstream data. The approach observes clicks on elements of a decision-support-system and triggers a set of state-machines for each click. Each state-machine represents a particular decision-strategy which a user can follow. The approach returns a set of decision strategies that best explain the observed click-behavior of a user. Results of two experiments show that the algorithm infers strategies accurately. In the first experiment, the approach correctly infers most of the pre-defined decision-strategies. The second study analyzes the behavior of thirty-eight respondents and finds that the inferred mix of decision-strategies fits well the behavior described in the literature to date. Results show that using decision-support-systems on a web site and observing the user’s click-behavior make it possible to infer a specific decision strategy. The proposed method is general enough to be easily applied to both research and real-world settings, along with other decision-support-systems and strategies.

Guided local search for the optimal communication spanning tree problem

Abstract This paper considers the optimal communication spanning tree (OCST) problem. Previous work analyzed features of high-quality solutions and found that edges in optimal solutions have low weight and point towards the center of a tree. Consequently, integrating this problem-specific knowledge into a metaheuristic increases its performance for the OCST problem. In this paper, we present a guided local search (GLS) approach which dynamically changes the objective function to guide the search process into promising areas. In contrast to traditional approaches which reward promising solution features by favoring edges with low weights pointing towards the tree’s center, GLS penalizes low-quality edges with large weights that do not point towards the tree’s center. Experiments show that GLS is a powerful optimization method for OCST problems and outperforms standard EA approaches with state-of-the-art search operators for larger problem instances. However, GLS performance does not increase if more knowledge about low-quality solutions is considered but is about independent of whether edges with low weight or wrong orientation are penalized. This is in contrast to the classical assumption that considering more problem-specific knowledge about high-quality solutions does increase search performance.

Inferring Decision Strategies from Clickstreams in Decision Support Systems: A New Process-Tracing Approach using State Machines

Given a bound, the bounded-diameter minimum spanning tree (BDMST) problem seeks a spanning tree of minimum total weight with a diameter not exceeding the given diameter bound. Depending on the tightness of the bound, optimal solutions have different structures. For loose bounds, optimal solutions are similar to the much easier minimum spanning tree problem, and greedy heuristics perform best. In contrast, these approaches fail for tight diameter bounds. This paper investigates how the structure of good solutions, and in particular their backbones, change depending on the diameter bound. Two new heuristics are then designed to overcome the shortcomings of existing approaches; required parameters are investigated; and the paper presents performance results for Euclidean BDMST instances.

Solving OCST problems with problem-specific guided local search

This paper considers the optimal communication spanning tree (OCST) problem. Previous work analyzed features of high-quality solutions. Consequently, integrating this knowledge into a metaheuristic increases its performance for the OCST problem. In this paper, we present a guided local search (GLS) approach which dynamically changes the objective function to guide the search process into promising areas. In contrast to traditional approaches which reward promising solution features by favoring edges with low weights pointing towards the trees center, GLS penalizes low-quality edges with large weights that do not point towards the trees center.

Code-share connectivity within global airline alliances – How much potential is utilized?

Webstores can easily gather large amounts of consumer data, including clicks on single elements of the user interface, navigation patterns, user profile data, and search texts. Such clickstream data are both interesting to merchandisers as well as to researchers in the field of decision-making behavior, because they describe consumer decision-behavior on websites. This paper introduces an approach that infers decision-behavior from clickstream data. The approach observes clicks on elements of a decision-support-system and triggers a set of state-machines for each click. Each state-machine represents a particular decision-strategy which a user can follow. The approach returns a set of decision strategies that best explain the observed click-behavior of a user. Results of two experiments show that the algorithm infers strategies accurately. In the first experiment, the approach correctly infers most of the pre-defined decision-strategies. The second study analyzes the behavior of thirty-eight respondents and finds that the inferred mix of decision-strategies fits well the behavior described in the literature to date. Results show that using decision-support-systems on a web site and observing the user’s click-behavior make it possible to infer a specific decision strategy. The proposed method is general enough to be easily applied to both research and real-world settings, along with other decision-support-systems and strategies.