This work demonstrates specific ways that the design of computer user interfaces can influence how individuals structure the problem solving process. In particular, an observational study of expert users of an image manipulation application indicates that current user interfaces make it difficult to explore sets of alternatives in parallel, despite this being a common problem solving practice. As a consequence, individuals tend to engage in highly linear problem solving processes. To address this problem, this work introduces the concept of a set-based interface, or an interface that facilitates the generation, manipulation, evaluation, and management of sets of alternative solutions. The concepts of a set-based interface are demonstrated in two tools, Side Views and Parallel Pies, both designed for use in the domain of image manipulation. Side Views automatically generates sets of previews for one or more commands and their parameters, enabling side-by-side comparison of alternatives. Parallel Pies streamlines the process of forking, or the act of creating new, standalone alternatives, and provides a visualization to evaluate results. Two controlled laboratory studies and a third think-aloud study reveal that these tools lead to users more broadly exploring the solution space and developing more optimal solutions for some types of tasks. These studies also show that the ability to broadly explore can initially be overused, adversely affecting solution quality if not enough time is spent maturing a single solution instance. This enthusiastic use of exploration tools is especially notable because such features are entirely optional to developing a solution. As such, these results suggest the need to further research ways user interfaces can support individuals in rapidly generating sets of alternative solutions. To support future research in this direction, this work contributes a set of metrics for quantifying breadth and depth of exploration; backtracking; and dead-ends in the problem solving process. A visualization called a process diagram aids in communicating these concepts.