Abstract
Computationally expensive simulations play an increasing role in engineering design, but their use in multi-objective optimization is heavily resource constrained. Specialist optimizers, such as ParEGO, exist for this setting, but little knowledge is available to guide their configuration. This paper uses a new implementation of ParEGO to examine three hypotheses relating to a key configuration parameter: choice of scalarising norm. Two hypotheses consider the theoretical trade-off between convergence speed and ability to capture an arbitrary Pareto front geometry. Experiments confirm these hypotheses in the bi-objective setting but the trade-off is largely unseen in many-objective settings. A third hypothesis considers the ability of dynamic norm scheduling schemes to overcome the trade-off. Experiments using a simple scheme offer partial support to the hypothesis in the bi-objective setting but no support in many-objective contexts. Norm scheduling is tentatively recommended for bi-objective problems for which the Pareto front geometry is concave or unknown.
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Acknowledgments
This work was supported by Jaguar Land Rover and the UK-EPSRC grant EP/L025760/1 as part of the jointly funded Programme for Simulation Innovation. The authors thank Joshua Knowles for discussions on ParEGO and surrogate-based optimization that helped inspire the research directions in this paper.
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Aghamohammadi, N.R., Salomon, S., Yan, Y., Purshouse, R.C. (2017). On the Effect of Scalarising Norm Choice in a ParEGO implementation. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_1
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