129. derivative-free global optimization method with inexact function evaluations

Department: Mechanical & Aerospace Engineering
Faculty Advisor(s): Thomas R. Bewley

Primary Student
Name: Shahrouz Alimohammadi
Email: salimoha@ucsd.edu
Phone: 858-822-7971
Grad Year: 2017

Student Collaborators
Muhan Zhao, muz021@ucsd.edu | Pooriya Beyhaghi, pbeyhagh@ucsd.edu

Abstract
Over the past decade, due to the availability of computer clouds and clusters computational power has dramatically increased and derivative-free optimization algorithms have become increasingly valuable for computer-aided designs (CADS). In this context, there is an ever-increasing demand for computational tools, that are compatible with cloud computers, and can identify optimal design parameters, while at the same time limiting the number of expensive evaluations of the model. In many practical problems, the calculation of the true objective function, for any feasible set of values of the parameters in the problem, is not exact. In some cases, the true objective function that we desire to minimize is given by the infinite-time average of a statistically stationary ergodic process. In such problems, any numerical or experimental approximation of this function is characterized by sampling error, which may be reduced by additional sampling. Delaunay-based optimization algorithms are very attractive in this context because they are efficient, and provably convergent derivative-free global optimization algorithms that are designed for a range of nonconvex optimization problems with expensive function evaluations with a handful of adjustable parameters. This work illustrates a computationally efficient Delaunay-based optimization combined with uncertainty quantification framework to be compatible with modern computer structures to solve a range of practical shape optimization problems. For the numerical validation, this framework is applied to a few benchmark test problems, and the result shows the new optimization framework substantially reduces the overall computational cost of the optimization process for this category of optimization problems.

Industry Application Area(s)
Aerospace, Defense, Security | Control Systems

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