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222 results on '"Kathrin Klamroth"'

1. SCORE Band Visualizations: Supporting Decision Makers in Comparing High-Dimensional Outcome Vectors in Multiobjective Optimization

Author

Bhupinder S. Saini, Kaisa Miettinen, Kathrin Klamroth, Ralph E. Steuer, and Kerstin Dachert

Subjects
Multiple criteria optimization, interactive visualization, correlated objectives, parallel coordinate plots, Pareto optimality, Electrical engineering. Electronics. Nuclear engineering, TK1-9971
Abstract

Clearly arranged visualizations are needed in multiobjective optimization problems with a large number of objective functions, when a large number of Pareto optimal outcome vectors (vectors of objective function values) must be compared during the decision making processes. This paper contributes to visualizing such outcome vectors independent of how they have been generated. Parallel coordinate plots are a widely used visualization technique to represent different outcome vectors.We propose a novel visualization technique called SCORE bands to be used with parallel coordinate plots to support the decision maker in simultaneously identifying patterns in outcome vectors and correlations among the objective functions in a meaningful way. To do so, amongst others, we change the ordering of objective functions and modify the distances among them in parallel coordinate plots. SCORE bands also have interactive capabilities allowing the decision maker to first study general trends among the outcome vectors as bands and then zoom-in and move about different groups of outcome vectors of interest. The novelty of our approach lies in proposing a visually appealing way to support the decision maker in dealing with large amounts of information. We demonstrate the benefits of SCORE bands with different examples.

Published
2024
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32. GivEn - Shape Optimization for Gas Turbines in Volatile Energy Networks.

Author

Jan Backhaus, Matthias Bolten, Onur Tanil Doganay, Matthias Ehrhardt 0001, Benedikt Engel, Christian Frey, Hanno Gottschalk, Michael Günther 0005, Camilla Hahn, Jens Jäschke, Peter Jaksch, Kathrin Klamroth, Alexander Liefke, Daniel Luft, Lucas Mäde, Vincent Marciniak, Marco Reese, Johanna Schultes, Volker Schulz 0001, Sebastian Schmitz, Johannes Steiner, and Michael Stiglmayr

Published
2020

43. Event-based MILP models for ridepooling applications

Author

Michael Stiglmayr, Kathrin Klamroth, and Daniela Gaul

Subjects
Mathematical optimization, Information Systems and Management, General Computer Science, Optimization algorithm, Computer science, Event (computing), Event based, Management Science and Operations Research, Flow network, Industrial and Manufacturing Engineering, Time windows, Modeling and Simulation, Spatial representation, Benchmark data
Abstract

Ridepooling services require efficient optimization algorithms to simultaneously plan routes and pool users in shared rides. We consider a static dial-a-ride problem (DARP) where a series of origin-destination requests have to be assigned to routes of a fleet of vehicles. Thereby, all requests have associated time windows for pick-up and delivery, and may be denied if they can not be serviced in reasonable time or at reasonable cost. Rather than using a spatial representation of the transportation network we suggest an event-based formulation of the problem, resulting in significantly improved computational times. While the corresponding MILP formulations require more variables than standard models, they have the advantage that capacity, pairing and precedence constraints are handled implicitly. The approach is tested and validated using a standard IP-solver on benchmark data from the literature. Moreover, the impact of, and the trade-off between, different optimization goals is evaluated on a case study in the city of Wuppertal (Germany).

Published
2022
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45. Biobjective optimization problems on matroids with binary costs

Author

Jochen Gorski, Kathrin Klamroth, and Julia Sudhoff

Subjects
FOS: Computer and information sciences, Control and Optimization, Optimization and Control (math.OC), Applied Mathematics, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), Management Science and Operations Research, Mathematics - Optimization and Control, MathematicsofComputing_DISCRETEMATHEMATICS
Abstract

Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. In this paper, we consider biobjective optimization problems on matroids where one of the objective functions is restricted to binary cost coefficients. We show that in this case the problem has a connected efficient set with respect to a natural definition of a neighborhood structure and hence, can be solved efficiently using a neighborhood search approach. This is, to the best of our knowledge, the first non-trivial problem on matroids where connectedness of the efficient set can be established. The theoretical results are validated by numerical experiments with biobjective minimum spanning tree problems (graphic matroids) and with biobjective knapsack problems with a cardinality constraint (uniform matroids). In the context of the minimum spanning tree problem, coloring all edges with cost 0 green and all edges with cost 1 red leads to an equivalent problem where we want to simultaneously minimize one general objective and the number of red edges (which defines the second objective) in a Pareto sense.

Published
2022
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