|Reducing the overlap of data points in 2D visualizations while preserving original positions is a challenging task. Traditionally, hand-crafted solutions have been proposed while more recently layout algorithms with a high degree of automation have been introduced. However, with a continuous parameter space, the number of alternative solutions is virtually infinite. So which one is best? This assessment can depend on many factors, coined by subjective human judgment as well as quantitative quality measures. Our approach follows the idea to have both humans and algorithms in control, to combine the strengths of both. We propose LayoutExOmizer, which stands for Layout Explorer and Optimizer. It is a visual analytics approach that guides users in finding meaningful solutions. LayoutExOmizer supports users in generating a preferred layout by discovering a corresponding set of input parameters. This parameter search is supported by visual interfaces (1) to directly steer the parameters of the layout optimization, (2) to assess the quality of layouts using quality measures, (3) to relate input and out space, and (4) to filter layouts by their quality. We demonstrate the usefulness of our approach in two usage scenarios with different quality measures, including the full set of Scagnostics measures.