On the Consequences of the "No Free Lunch" Theorem for Optimization on the Choice of an Appropriate MDO Architecture

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 18241To link to this article: DOI : 10.2514/6.2017-3148 URL : https://doi.org/10. 2514/6.2017-3148 Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Multidisciplinary Design Optimization (MDO) based on high-fidelity models is challenging due to the high computational cost of evaluating the objective and constraints. To choose the best MDO architecture, a trial-and-error approach is not possible due to the high cost of the overall optimization and the complexity of each implementation. We propose to address this issue by developing a generic methodology that applies to any (potentially expensive) design optimization problem. The methodology consists in generating a scalable analytic replacement function that can be quickly computed, yet captures the structure and behavior of the original high-fidelity problem. One crucial characteristic of this replacement model is that the number of inputs and outputs can be set independently, making the problem scalable. This facilitates the evaluation of MDO architectures for the original MDO problem. The methodology is applied to two academic MDO test cases: a supersonic business jet design problem and a propane combustion problem. Well-known architectures (Multidisciplinary Feasible (MDF) and Individual Disciplinary Feasible (IDF)) are benchmarked on various instances to demonstrate the dependency between the performance of the architecture and the dimensions of the problem. The results show that the "no free lunch" theorem of optimization, which states that no particular optimization algorithm holds an advantage over another when considering all possible problems, also applies to the choice of the best suited MDO architecture for an MDO problem with scalable dimensions.

Benchmarking for Metaheuristic Black-Box Optimization: Perspectives and Open Challenges

“…Alternatively, to conventional data-based meta-models and surrogate models for optimization benchmarking, some new ideas related to feature-based surrogate models for benchmarking have been presented and investigated in [50], [51], [68]. The general idea behind these concepts is to construct computationally affordable representative benchmark problems, based on replacement or surrogate functions which capture the characteristics of the underlying high-fidelity simulation responses.…”

GEMS: A Python Library for Automation of Multidisciplinary Design Optimization Process Generation

“…In addition, for given disciplines, many different problems and associated processes are built in an industrial-scale development. Besides, MDO formulations exhibit different performances when the use case changes, since there is no "free lunch" for MDO formulations 6 . For given disciplines, changing the formulation completely changes the dataflow and the workflow.…”

“…• the performance of algorithms and formulations can be tuned on substitution problems thanks to the scalable methodology by Vanaret et al 6 3. Software architecture…”

“…The a priori selection of the most appropriate one is not straightforward. To this aim, GEMS supports the scalable MDO problem methodology proposed by Vanaret et al 6 . This methodology takes a reference set of disciplines and builds surrogate versions of them, using a small DOE.…”

“…Numerous formulations exist, and their respective performances depend on the addressed problem. For a given problem, their relative performances specially depend on the dimensions of the design variables, coupling variables, and constraints 6 . Besides, industrial applications invoke black box simulation codes that may not be modified or differentiated, or may involve discrete design variables, which restricts the set of potentially useful MDO formulations 1 .…”