Successful thesis proposal defense!
01 Apr 2020I have defended my thesis proposal titled Global Optimization in Engineering Design via Geometric Programming. My committee members are Prof. Mark Drela, Prof. Dimitris Bertsimas and Principal Research Engineer Robert Haimes. I hope to update the website with some of my accomplishments and future work soon! But here is the abstract:
There is a need to adapt and improve conceptual design methods through better optimization, to address the challenge of designing future engineered systems. Aerospace design problems are tightly-coupled multidisciplinary optimization (MDO) problems, and require all-at-once solutions methods for design consensus and global optimality. Although the literature on MDO has been growing, there are few tractable methods for simultaneous optimization in the aerospace field. I propose signomial programming (SP) as a tractable and practical way to formulate all-at-once engineering design optimization problems. SP extends geometric programming, which is a log-convex optimization formulation that can be solved efficiently using interior point methods. SP has been proposed for global solutions of large-scale aerospace problems such as transonic aircraft design, but has several shortcomings that it shares with other MDO formulations. Designs through SP are sensitive to uncertainty in parameters, and no tractable methods yet exist to solve optimization problems under uncertainty with probabilistic guarantees of constraint satisfaction. Furthermore, since signomial programs require explicit, SP-compatible constraints, they are restricted in their ability to accommodate data and/or black box functions. In this thesis, I enable conceptual engineering design under uncertainty by developing a robust SP framework for optimization over uncertain parameters. I leverage optimal regression trees to be able to generate SP-compatible constraints over arbitrary data and/or functions. I use the combination of SP-compatible constraints and constraint approximations to develop a global SP framework for engineering design. The proposed methods will solve engineering design problems efficiently and deterministically, and keep practical concerns for conceptual design in focus.