Robust design via geometric and signomial programming

Solving convex optimization problems has become extremely efficient and reliable after the recent development of polynomial-time algorithms and advancement in computing power. Geometric Programming (GP) and Signomial Programming (SP) has been proven successful in optimizing multidisciplinary designs due to exploiting the speed of convergence and the ability to model non-linear designs. However, an optimal solution of GPs and SPs can be sensitive to uncertainties in the parameters involved in the problem. In fact, robust optimization can incorporate the uncertainties in an optimization problem and solves for the worst-case scenario. Yet, robust geometric programs (RGPs) and robust signomial programs (RSPs) are not known to have a tractable formulation that current solvers can efficiently solve. In this thesis, approximate formulations of RGPs and RSPs are proposed. Recently, the curiosity regarding the deployment of GPs and SPs in model complex engineering systems has been growing. This awareness has motivated modeling the uncertainties that are fundamental to engineering design optimization. Consequently, RGPs and RSPs provide a framework for modeling and solving GPs and SPs while representing their ambiguities as belonging to an uncertainty set. The RGP methodologies presented here are based on reformulating the GP as a convex program and then robustifying it with methods from robust linear programming. The RSP methodology is based on solving sequential local RGP approximations. These new methodologies, along with previous ones from the literature, are used to robustify aircraft design problems, and the results of these different methodologies are compared and discussed.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Saab, Ali.

Advisor dc:contributor.advisor

• Karen Willcox.

• Computation for Design and Optimization Program.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/122319

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122319