"Exploiting Log-Convexity in Aircraft Design Optimization"
Abstract: Fast and efficient aircraft design optimization has been made possible through the use of Geometric Programming (GP). Despite many advantages, the underlying mathematics of the GP formulation impose a harsh limit on the types of models that can be used for discipline analyses like aerodynamics, structures, and propulsion. This work offers two new approaches to break through the fundamental limitation. First is a new class of surrogate models that can be fit to high fidelity data while remaining compatible with the Signomial Programming (SP) extension of Geometric Programming. Second is a new algorithm derived from Sequential Quadratic Programming (SQP) that allows an existing analysis model to be directly tied into the optimization algorithm with no need for a surrogate model. This talk will motivate the underlying mathematical theory of both new methods and show some initial applications to aircraft design optimization.
"Global Optimization using Optimal Decision Trees"
Abstract: Optimization is key to the conceptual design of aerospace systems. One major challenge in conceptual design is being able to optimize over constraints, functions or data that do not fit into certain forms. In increasing order of difficulty, design constraints may be mathematically inefficient (eg. non-convex constraints), inexplicit (eg. solutions of PDEs), or unqueriable (eg. results of non-repeatable experiments). The current state-of-the-art methods in aerospace design optimization are primarily gradient-based and heuristic methods. While these methods have seen their capabilities grow, they are limited to local and low dimensional optimization respectively, and struggle with a subset of the aforementioned constraint classes.
Leveraging the dramatic speed improvements in mixed-integer optimization (MIO) and recent research in machine learning (ML), I propose a new method to learn MIO-compatible approximations of difficult optimization problems using optimal decision trees. This approach only requires a bounded variable domain and data over unqueriable constraints, and can address all three difficult constraint classes. The MIO approximation is solved efficiently to find a near-optimal, near-feasible solution to the original optimization problem. Then, the solution is converged to a locally feasible and optimal solution using a series of projected gradient descent iterations. The method is tested on a number of numerical benchmarks from the literature as well as some real world design problems, demonstrating its promise in finding global optima efficiently.