We consider visualization as a decision optimization tool in problems where the model and/or the objectives are not well defined. We investigate four specific problems representing different degrees of determination. The first problem concerns a smooth dynamic representation of data collected at fixed locations. In the example we want to minimize the deviations from a desired temperature over space and time. The second and third problems are the dynamic representation of observations in the form of averages over regions in space and time, and they are exemplified by epidemiological data. We are looking for spatial-temporal patterns that can suggest the most efficient ways of prevention and control. The fourth problem may be referred to as visual indexing. We perform exploratory analysis of a large collection of complex objects. The example is a dynamic index to a collection of 30,000 images. We search for the "most interesting" subsets of images via visual inspection of the index. In all cases we define appropriate techniques for the visual representation. We describe the software and hardware.