Automated floorplanning or space layout planning has been a long-standing NP-hard problem in the field of computer-aided design, with applications in integrated circuits, architecture, urbanism, and operational research. In this paper, we introduce GenFloor, an interactive design system that takes geometrical, topological, and performance goals and constraints as input and provides optimized spatial design solutions as output. As part of our work, we propose three novel permutation methods for existing space layout graph representations, namely O-Tree and B*-Tree representations. We implement our proposed floorplanning methods as a package for Dynamo, a visual programming tool, with a custom GUI and additional evaluation functionalities to facilitate designers in their generative design workflow. Furthermore, we illustrate the performance of GenFloor in two sets of case-study experiments for residential floorplanning tasks by (a) measuring the ability of the proposed system to find a known optimal solution, and (b) observing how the system can generate diverse floorplans while addressing given a constant residential design problem. Our results indicate convergence to the global optimum is achieved while offering a diverse set of solutions of a residential floorplan corresponding to local optimums of the solution landscape.