Expensive multi-objective optimization of electromagnetic mixing in a liquid metal

Prinz, Sebastian; Thomann, Jana; Eichfelder, Gabriele; Boeck, Thomas; Schumacher, Jörg

doi:10.1007/s11081-020-09561-4

Cited by 5 publications

(3 citation statements)

References 38 publications

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“…Going forward, we would like to apply our algorithm to a real world application, similar to what has been done in [54]. Moreover, it would be desirable to obtain not just one but multiple Pareto critical solutions.…”

Section: Discussionmentioning

confidence: 99%

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Berkemeier

Peitz

2021

MCA

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We present a local trust region descent algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. Convergence to a Pareto critical point is proven. The method is derivative-free in the sense that derivative information need not be available for the expensive objectives. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar counterparts and complements multiobjective line-search algorithms. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points needed per iteration scales linearly with the decision space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives.

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Section: Discussionmentioning

confidence: 99%

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Berkemeier

Peitz

2021

MCA

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“…Going forward, we would like to apply our algorithm to a real world application, similar to what has been done in [51]. Moreover, it would be desirable to obtain not just one but multiple Pareto-critical solutions.…”

Section: Discussionmentioning

confidence: 99%

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Berkemeier,

Peitz

2021

Preprint

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We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective function that is computationally expensive. The method is derivative-free in the sense that neither need derivative information be available for the expensive objectives nor are gradients approximated using repeated function evaluations as is the case in finitedifference methods. Instead, a multiobjective trust region approach is used that works similarly to its well-known scalar pendants. Local surrogate models constructed from evaluation data of the true objective functions are employed to compute possible descent directions. In contrast to existing multiobjective trust region algorithms, these surrogates are not polynomial but carefully constructed radial basis function networks. This has the important advantage that the number of data points scales linearly with the parameter space dimension. The local models qualify as fully linear and the corresponding general scalar framework is adapted for problems with multiple objectives. Convergence to Pareto critical points is proven and numerical examples illustrate our findings.

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“…An expensive MO problem was also considered by Prinz et al (2021). More precisely, the authors consider the optimization of a mixing process in electrically conducting fluids.…”

Section: Overview Of the Special Issue Articlesmentioning

confidence: 99%

Multiobjective optimization and decision making in engineering sciences

Hakanen

Allmendinger

2021

Optim Eng

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Real-world decision making problems in various fields including engineering sciences are becoming ever more challenging to address. The consideration of various competing criteria related to, for example, business, technical, workforce, safety and environmental aspects increases the complexity of decision making and leads to problems that feature multiple competing criteria. A key challenge in such problems is the identification of the most preferred trade-off solution(s) with respect to the competing criteria. Therefore, the effective combination of data, skills, and advanced engineering and management technologies is becoming a key asset to a company urging the need to rethink how to tackle modern decision making problems. This special issue focuses on the intersection between engineering, multiple criteria decision making, multiobjective optimization, and data science. The development of new models and algorithmic methods to solve such problems is in the focus as much as the application of these concepts to real problems. This special issue was motivated by the 25th International Conference on Multiple Criteria Decision Making (MCDM2019) held in Istanbul, Turkey, in 2019.

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Expensive multi-objective optimization of electromagnetic mixing in a liquid metal

Cited by 5 publications

References 38 publications

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis Function Surrogate Models

Multiobjective optimization and decision making in engineering sciences

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