The space allocation problem
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In the domain of architecture and planning, the space allocation problem (SAP) is a general class of computable problems which is employed by numerous design processes to assist in the generation of spaces of a layout and simultaneously satisfy design objectives. The SAP has eluded automation due to combinatorial complexity and geometric intractability. This thesis describes a computational framework for solving the SAP across multiple scales and domains of the application using reinforcement learning algorithms that generate spatial solutions with optimal space-activity relations. In this research, a broad range of computable problems are addressed across three scales of design processes, namely, space planning, site planning, and interactive networks of city blocks. This is achieved by identifying the role of SAP in generating the spatial output of a design process and compartmentalizing the SAP into computable tasks. Each task is mapped to a spatial model that consists of a set of geometric operations driven by optimization algorithms or numerical relations. These techniques are referred to as the space allocation techniques or SAT and developed as autonomous modules. Each spatial model invokes a specific set of SAT modules, in sequence, and the models can be connected to solve the desired SAP. The spatial models are integrated into a framework after considering the exclusivity of the task accomplished by the models, common methods, data structures, and the flow of information between models. It is proposed that the spatial output of large design processes is approximated by creating workflows of connected elemental models. A workflow can be reused to solve project-specific design problems by updating the inputs such as site boundary or project requirements and bylaws. The workflows support design exploration and provide iterative user interaction such that for a given problem, it is possible to study entirely different solutions, explore the downstream propagation of a design decision, generate alternatives or determine an exact solution. The workflow permits re-usability to evolve the design solutions over numerous similar projects. These features of the proposal lead to an explicit design process that helps in preserving the information regarding design decisions. The proposal provides a semi-automation environment that allows users to develop spatial solutions, interactively, where the geometric or topological inputs can be altered at runtime and the system generates the solution. To evaluate this proposal, several features of a standard solution are identified to address their usability in design processes, the generalization of SAP across geometric and topologically variant problems, and the diverse scales of design processes. These features aid in the development of an alternative design environment where the potential for semi-automation is explored. The case studies and test-cases presented in this thesis illustrate the interaction between the designer and the software where the user can alter basic inputs on a spreadsheet or change the governing shapes at runtime and the workflow dynamically updates the internal organization of spaces and their activities. A prototype, namely, Integrated Design Framework or IDF, is implemented to demonstrate the applications of the proposed computational framework. It is anticipated that the development of SAP will support several activities related to architectural practice and research including design in practice, analytical research, and the development/deployment of building systems and subsequent processes such as the design of mechanical systems and structural design.