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KNN-Averaging for Noisy Multi-objective Optimisation

Part of the Communications in Computer and Information Science book series (CCIS,volume 1439)

Abstract

Multi-objective optimisation is a popular approach for finding solutions to complex problems with large search spaces that reliably yields good optimisation results. However, with the rise of cyber-physical systems, emerges a new challenge of noisy fitness functions, whose objective value for a given configuration is non-deterministic, producing varying results on each execution. This leads to an optimisation process that is based on stochastically sampled information, ultimately favouring solutions with fitness values that have co-incidentally high outlier noise. In turn, the results are unfaithful due to their large discrepancies between sampled and expectable objective values. Motivated by our work on noisy automated driving systems, we present the results of our ongoing research to counteract the effect of noisy fitness functions without requiring repeated executions of each solution. Our method kNN-Avg identifies the k-nearest neighbours of a solution point and uses the weighted average value as a surrogate for its actually sampled fitness. We demonstrate the viability of kNN-Avg on common benchmark problems and show that it produces comparably good solutions whose fitness values are closer to the expected value.

Keywords

  • Multi-objective optimisation
  • Noisy fitness functions
  • Genetic algorithms
  • k-nearest neighbours
  • Cyber-physical systems

The authors are supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603), JST. Funding reference number: 10.13039/501100009024 ERATO. S. Klikovits is also supported by Grant-in-Aid for Research Activity Start-up 20K23334, JSPS.

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Notes

  1. 1.

    In this paper, we consider unconstrained MOO problems, meaning that \(f(\boldsymbol{x})\) always produces feasible output. For an introduction on constrained MOO see [8].

  2. 2.

    The implementation of our algorithm and the plots of all other experimental settings are available online https://github.com/ERATOMMSD/QUATIC2021-KNN-Averaging.).

  3. 3.

    https://www.mvstat.net/tduong/research/seminars/seminar-2001-05.

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Klikovits, S., Arcaini, P. (2021). KNN-Averaging for Noisy Multi-objective Optimisation. In: Paiva, A.C.R., Cavalli, A.R., Ventura Martins, P., Pérez-Castillo, R. (eds) Quality of Information and Communications Technology. QUATIC 2021. Communications in Computer and Information Science, vol 1439. Springer, Cham. https://doi.org/10.1007/978-3-030-85347-1_36

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  • DOI: https://doi.org/10.1007/978-3-030-85347-1_36

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