Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

Hough, Patricia Diane ; Gray, Genetha Anne ; Castro, Joseph Pete, Jr. ; Giunta, Anthony Andrew

Sandia National Laboratories

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Ground Water;    Numerical Analysis.;    Computer Calculations;    58 Geosciences;   

DOI  :  10.2172/877137
RP-ID  :  SAND2005-7498
RP-ID  :  AC04-94AL85000
RP-ID  :  877137

美国|英语

来源: UNT Digital Library

【 摘 要 】

Many engineering application problems use optimization algorithms in conjunction with numerical simulators to search for solutions. The formulation of relevant objective functions and constraints dictate possible optimization algorithms. Often, a gradient based approach is not possible since objective functions and constraints can be nonlinear, nonconvex, non-differentiable, or even discontinuous and the simulations involved can be computationally expensive. Moreover, computational efficiency and accuracy are desirable and also influence the choice of solution method. With the advent and increasing availability of massively parallel computers, computational speed has increased tremendously. Unfortunately, the numerical and model complexities of many problems still demand significant computational resources. Moreover, in optimization, these expenses can be a limiting factor since obtaining solutions often requires the completion of numerous computationally intensive simulations. Therefore, we propose a multifidelity optimization algorithm (MFO) designed to improve the computational efficiency of an optimization method for a wide range of applications. In developing the MFO algorithm, we take advantage of the interactions between multi fidelity models to develop a dynamic and computational time saving optimization algorithm. First, a direct search method is applied to the high fidelity model over a reduced design space. In conjunction with this search, a specialized oracle is employed to map the design space of this high fidelity model to that of a computationally cheaper low fidelity model using space mapping techniques. Then, in the low fidelity space, an optimum is obtained using gradient or non-gradient based optimization, and it is mapped back to the high fidelity space. In this paper, we describe the theory and implementation details of our MFO algorithm. We also demonstrate our MFO method on some example problems and on two applications: earth penetrators and groundwater remediation.