The field of information visualization tries to find graphical representations of data to explore regions of interest in potentially large data sets. Additionally, the use of algorithms to obtain exact solutions, which cannot be provided by basic visualization techniques, is a common approach in data analysis. This work focuses on optimization, distance computation and data estimation algorithms in the context of information visualization. Furthermore, information visualization is closely connected to interaction. To involve human abilities in the computation process, the goal is to embed these algorithms into an interactive environment. In an analysis dialog, the user observes the current solution, interprets the results and then formulates a strategy of how to proceed. This forms a tight loop of interaction, which uses human evaluation to improve the quality of the results. Optimization is a crucial approach in decision making. This work presents an interactive optimization approach, exemplified by parallel coordinates, which are a common visualization technique when dealing with multi-dimensional problems. According to this goal-based approach, multi-dimensional distance computation is discussed as well as a data estimation approach with the objective of approximating simulations by the analysis of existing values. All these approaches are integrated in an existing visual analysis framework and deal with multi-dimensional goals, which can be defined and modified interactively by the user. The goal of this work is to support decision makers to extract useful information from large data sets.