Multi-Objective Optimization Utilizing Cluster Analysis Applied to Dimensional Transposed Problems

With respect to the importance of multi-objective optimization in the context of the today's information processing and analysis, as well as the limitation of current approaches to treat large and complex tasks in practical time and little adjustment costs, this work proposes a novel optimization concept, based on data domain transformations and subsequent cluster analyses to solve multi-objective optimization problems. The approach abstracts the transposition of large, high-dimensional and diverse data models to low-dimensional uniform equivalents within an independent framework, which is optimized regarding data similarity conservation, i.e. the semantic relations of the data items to each other are preserved, and low runtime complexity, i.e. linearly increasing model sizes also cause only linearly growing runtimes in spite of the consideration of all data relations. The cluster analysis step is represented by an enhanced version of the k-Means algorithm, which is designed to group large numbers of data items to large numbers of clusters with also linear time complexity. Applying and adapting these both components to generic segmentation and pattern recognition tasks as two representative multi-objective optimization problems, illustrate and prove the usability of the proposed concept, by solving these tasks with high qualities of results and low runtimes with virtually linear time complexities. The abstracted components, as well as their application extensions are tested and analyzed during full factorial design tests, utilizing artificial, scalable data models, to determine valid parameter ranges, qualities of results and runtimes, as well as to ensure repeatable and comparable tests."