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Hilbert Curves for Efficient Exploratory Landscape Analysis Neighbourhood Sampling

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Applications of Evolutionary Computation (EvoApplications 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14635))

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Abstract

Landscape analysis aims to characterise optimisation problems based on their objective (or fitness) function landscape properties. The problem search space is typically sampled, and various landscape features are estimated based on the samples. One particularly salient set of features is information content, which requires the samples to be sequences of neighbouring solutions, such that the local relationships between consecutive sample points are preserved. Generating such spatially correlated samples that also provide good search space coverage is challenging. It is therefore common to first obtain an unordered sample with good search space coverage, and then apply an ordering algorithm such as the nearest neighbour to minimise the distance between consecutive points in the sample. However, the nearest neighbour algorithm becomes computationally prohibitive in higher dimensions, thus there is a need for more efficient alternatives. In this study, Hilbert space-filling curves are proposed as a method to efficiently obtain high-quality ordered samples. Hilbert curves are a special case of fractal curves, and guarantee uniform coverage of a bounded search space while providing a spatially correlated sample. We study the effectiveness of Hilbert curves as samplers, and discover that they are capable of extracting salient features at a fraction of the computational cost compared to Latin hypercube sampling with post-factum ordering. Further, we investigate the use of Hilbert curves as an ordering strategy, and find that they order the sample significantly faster than the nearest neighbour ordering, without sacrificing the saliency of the extracted features.

Supported by the National Research Foundation of South Africa Thuthuka Grant Number 138194/TTK210316590115.

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Notes

  1. 1.

    https://pypi.org/project/pflacco/.

  2. 2.

    Python’s time.perf_counter.

  3. 3.

    This leave-one-instance out approach is used instead of the leave-one-problem out approach due to the small number of classes.

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Author information

Authors and Affiliations

  1. University of Pretoria, Pretoria, South Africa

    Johannes J. Pienaar & Anna S. Boman

  2. University of South Africa, Pretoria, South Africa

    Katherine M. Malan

Authors
  1. Johannes J. Pienaar
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  2. Anna S. Boman
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  3. Katherine M. Malan
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Correspondence to Katherine M. Malan .

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Editors and Affiliations

  1. University of York, York, UK

    Stephen Smith

  2. University of Coimbra, Coimbra, Portugal

    João Correia

  3. University of Málaga, Málaga, Spain

    Christian Cintrano

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Pienaar, J.J., Boman, A.S., Malan, K.M. (2024). Hilbert Curves for Efficient Exploratory Landscape Analysis Neighbourhood Sampling. In: Smith, S., Correia, J., Cintrano, C. (eds) Applications of Evolutionary Computation. EvoApplications 2024. Lecture Notes in Computer Science, vol 14635. Springer, Cham. https://doi.org/10.1007/978-3-031-56855-8_18

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  • DOI: https://doi.org/10.1007/978-3-031-56855-8_18

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