A Generative Design System (GDS) allows for the generation and exploration of a wide number of design alternatives and for the automation of analysis and optimization processes. Algorithmic Design (AD) tools effectively support the development of GDSs, but they tend to be less appealing for the usage of such systems, as they rely on complex algorithmic descriptions of the design that quickly become overwhelming for less experienced programmers. The usage of GDSs is facilitated by Design Space Exploration Interfaces (DSEIs), which allows users to iteratively explore, visualize, and select design alternatives among the multidimensional design space defined by the GDS. DSEIs promote the collaboration between designers, clients, and end-users, making GDSs more interactive and more accessible. DSEIs rely on graphical user interfaces that relieve users from the burden of dealing with AD programs. The creation of such interfaces can be automated, so that they can be quickly created and modified. Although AD-based DSEIs exist for at least three decades, they have been more intensively researched and commercialized over the past eight years. In this article, existing AD-based DSEIs are reviewed, characterized, and compared according to several criteria, such as: navigation, visualization, search, ranking, grouping, filtering, and selection techniques. From this comparative study, a set of guidelines for the development of DSEIs is proposed.