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Mixed-variable Bayesian optimization : application to aerospace system design

Julien Pelamatti 1, 2
2 BONUS - Optimisation de grande taille et calcul large échelle
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Within the framework of complex system design, such as aircraft and launch vehicles, the presence of computationallyintensive objective and/or constraint functions (e.g., finite element models and multidisciplinary analyses)coupled with the dependence on discrete and unordered technological design choices results in challenging optimizationproblems. Furthermore, part of these technological choices is associated to a number of specific continuous anddiscrete design variables which must be taken into consideration only if specific technological and/or architecturalchoices are made. As a result, the optimization problem which must be solved in order to determine the optimalsystem design presents a dynamically varying search space and feasibility domain.The few existing algorithms which allow solving this particular type of problems tend to require a large amountof function evaluations in order to converge to the feasible optimum, and result therefore inadequate when dealingwith the computationally intensive problems which can often be encountered within the design of complex systems.For this reason, this thesis explores the possibility of performing constrained mixed-variable and variable-size designspace optimization by relying on surrogate model-based design optimization performed with the help of Gaussianprocesses, also known as Bayesian optimization. More specifically, 3 main axes are discussed. First, the Gaussianprocess surrogate modeling of mixed continuous/discrete functions and the associated challenges are extensivelydiscussed. A unifying formalism is proposed in order to facilitate the description and comparison between theexisting kernels allowing to adapt Gaussian processes to the presence of discrete unordered variables. Furthermore,the actual modeling performances of these various kernels are tested and compared on a set of analytical and designrelated benchmarks with different characteristics and parameterizations.In the second part of the thesis, the possibility of extending the mixed continuous/discrete surrogate modeling toa context of Bayesian optimization is discussed. The theoretical feasibility of said extension in terms of objective/-constraint function modeling as well as acquisition function definition and optimization is shown. Different possiblealternatives are considered and described. Finally, the performance of the proposed optimization algorithm, withvarious kernels parameterizations and different initializations, is tested on a number of analytical and design relatedtest-cases and compared to reference algorithms.In the last part of this manuscript, two alternative ways of adapting the previously discussed mixed continuous/discrete Bayesian optimization algorithms in order to solve variable-size design space problems (i.e., problemscharacterized by a dynamically varying design space) are proposed. The first adaptation is based on the paralleloptimization of several sub-problems coupled with a computational budget allocation based on the informationprovided by the surrogate models. The second adaptation, instead, is based on the definition of a kernel allowingto compute the covariance between samples belonging to partially different search spaces based on the hierarchicalgrouping of design variables. Finally, the two alternatives are tested and compared on a set of analytical and designrelated benchmarks.Overall, it is shown that the proposed optimization methods allow to converge to the various constrained problemoptimum neighborhoods considerably faster when compared to the reference methods, thus representing apromising tool for the design of complex systems.
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Submitted on : Monday, January 18, 2021 - 3:37:12 PM
Last modification on : Thursday, March 24, 2022 - 3:42:59 AM


  • HAL Id : tel-03113542, version 1


Julien Pelamatti. Mixed-variable Bayesian optimization : application to aerospace system design. Discrete Mathematics [cs.DM]. Université de Lille, 2020. English. ⟨tel-03113542⟩



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