While the utilization of robot arms has increased since the construction industry began to deploy robotic technologies for digital fabrication processes, a pipeline is missing for fabrication-aware design as the abstraction of complex, contradictory constraints for the designer is not evident. %the non-standard characteristics of building components still pose major challenges that require flexible and adaptable robotic fabrication strategies. Additional geometric complexity, material properties, etc. also contribute to the overall difficulties for fabricating the designated piece successfully without any collisions or structural failure. Through the development of two projects focusing on different aspects of robotic fabrication, this dissertation identifies various limitations related to the overall design-to-fabrication process and categorizes them into different types of constraints. It is observed that many of the constraints occurred within one fabrication task are usually intertwined and cannot be decoupled, which requires integrated computational strategies to resolve. By adopting available methods in the computer graphics field that address geometry and material, this dissertation presents a series of optimization-based strategies in the context of two specific research projects, targeting geometry processing and path planning for robotic fabrication. Its aim is to demonstrate the potential of using optimization methods to obtain achievable robotic fabrication solutions under sophisticated requirements. Focusing on geometry processing and path planning, respectively, this dissertation employs optimization approaches to assist with design aims, and develops a conceptual framework for solving fabrication-aware robotic fabrication tasks. The formulation of the optimization problems in this dissertation empowers the design processes to be fabrication-aware so as to be compatible with the selected fabrication technology. It provides a more mathematical and holistic perspective for looking at robotic fabrication technologies in the architectural domain.