Abstract
Multi-objective optimization problems (MOP) are frequently encountered in practice. In some cases, different computationally expensive analyses may be independently used for computing different objectives of the MOP. Additionally, the analyses may be executed to obtain estimates with different fidelity, typically higher fidelity requiring a longer run-time. For instance, in automotive design, the aerodynamic drag is computed using computational fluid dynamic (CFD) analysis and its crashworthiness/strength is assessed using finite element analysis (FEA). Both the objectives can be independently computed and the underlying fidelity of each analysis can also be controlled using different mesh sizes/thresholds on the residual errors. While there exist a number of generic MOP benchmark problems in the literature, there is scarce work on constructing MOPs with multi-fidelity (MF) analyses to support the development of multi-fidelity, multi-objective optimization algorithms. The existing MF benchmarks are limited to unconstrained, single-objective optimization problems only. Towards addressing this gap, in this paper, we introduce a test suite for multi-objective, multi-fidelity optimization (MOMF). The problems are derived by combining existing unconstrained, multi-objective design optimization problems with resolution/stochastic/instability errors that are common manifestations of MF simulations. The method allows for the construction of any number of low-fidelity functions with desired level of correlations for a given high-fidelity objective function. We hope that the test suite would motivate novel algorithmic developments to support optimization involving computationally expensive and independently evaluable objectives.
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Notes
- 1.
To conserve space, the following shorthand is used in this paper: \({[k] = \{1,2,\dots ,k\}}\) and \([k^*] = \{0,1,\dots ,k-1\}\). As is conventional, [i, j] indicates the real interval between (and including) endpoints i and j.
- 2.
It is helpful to think of the index to \(\varPhi \) as indicating the degree of noise introduced, e.g., \(\varPhi _0\) has no noise and thus the highest fidelity, whereas \(\varPhi _3\) has a more noise and thus lower fidelity.
- 3.
We use \(\varPhi _3\) as a baseline here, because we have 4 levels of fidelity. If 5 levels of fidelity were required, the baseline would be \(\varPhi _4=5000\).
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The authors acknowledge the support from the Australian Research Council through the Discovery Project grant DP190101271.
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Kenny, A., Ray, T., Singh, H.K., Li, X. (2023). A Test Suite for Multi-objective Multi-fidelity Optimization. In: Emmerich, M., et al. Evolutionary Multi-Criterion Optimization. EMO 2023. Lecture Notes in Computer Science, vol 13970. Springer, Cham. https://doi.org/10.1007/978-3-031-27250-9_26
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