Mid-range metamodel assembly building based on linear regression for large scale optimization problems

Abstract

In this work an approach to building a high accuracy approximation valid in a larger range of design variables is investigated. The approach is based on an assembly of multiple surrogates into a single surrogate using linear regression. The coefficients of the model assembly are not weights of the individual models but tuning parameters determined by the least squares method. The approach was utilized in the Multipoint Approximation Method (MAM) method within the mid-range approximation framework.The developed technique has been tested on several benchmark problems with up to 1000 design variables and constraints. The obtained results show a high degree of accuracy of the built approximations and the efficiency of the technique when applied to large-scale optimization problems.

Sub-space approximations for MDO problems with disparate disciplinary variable dependence

“…Available approximation techniques include approximation assemblies by Polynkin and Toropov (2012), where intrinsically linear and rational functions are assembled into a single approximation using linear regression, the moving least squares method (Lancaster and Salkauskas 1981) and kriging based on a computationally efficient hyper-parameter optimisation method by Mortished et al (2016).…”

Implementation of Discrete Capability into the Enhanced Multipoint Approximation Method for Solving Mixed Integer-Continuous Optimization Problems

“…These approximat ion functions have a relatively s mall number (N +1 where N is number of design variables) of regression coefficients to be determined and the corresponding least squares problem can be solved easily. This feature of such approximations allo ws applying them to large scale optimization problems with the number of design variables in the order of hundreds [6].…”

“…The MAM is based on the building of mid-range appro ximations [4][5][6] and is suitable to solve large-scale optimization problems by producing better quality approximations that are sufficiently accurate in a current trust region and inexpensive in term of co mputational costs required for th eir building. These approximat ion functions have a relatively s mall number (N +1 where N is number of design variables) of regression coefficients to be determined and the corresponding least squares problem can be solved easily.…”

“…This approach has been influenced by the previous work [1][2][3] on two-point approximation methods. This was later generalized to multi-point approximations [4][5][6].…”

“…Therefore, the tuning parameters of the assembly model are not restricted to a positive range but may have negative values as well . In the current work, following the previous research for a case of continuous variables [6], this approach is utilized in the MAM for design optimizations with integer-continuous variables.…”