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Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package Flacco

Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

Choosing the best-performing optimizer(s) out of a portfolio of optimization algorithms is usually a difficult and complex task. It gets even worse, if the underlying functions are unknown, i.e., so-called black-box problems, and function evaluations are considered to be expensive. In case of continuous single-objective optimization problems, exploratory landscape analysis (ELA), a sophisticated and effective approach for characterizing the landscapes of such problems by means of numerical values before actually performing the optimization task itself, is advantageous. Unfortunately, until now it has been quite complicated to compute multiple ELA features simultaneously, as the corresponding code has been—if at all—spread across multiple platforms or at least across several packages within these platforms. This article presents a broad summary of existing ELA approaches and introduces flacco, an R-package for feature-based landscape analysis of continuous and constrained optimization problems. Although its functions neither solve the optimization problem itself nor the related algorithm selection problem (ASP), it offers easy access to an essential ingredient of the ASP by providing a wide collection of ELA features on a single platform—even within a single package. In addition, flacco provides multiple visualization techniques, which enhance the understanding of some of these numerical features, and thereby make certain landscape properties more comprehensible. On top of that, we will introduce the package’s built-in, as well as web-hosted and hence platform-independent, graphical user interface (GUI). It facilitates the usage of the package—especially for people who are not familiar with R—and thus makes flacco a very convenient toolbox when working towards algorithm selection of continuous single-objective optimization problems.

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Notes

  1. 1.

    In this context, an instance is the equivalent to an optimization problem, i.e., it maps the elements of the decision space \(\mathscr {X}\) to the objective space \(\mathscr {Y}\).

  2. 2.

    The authors intend to extend flacco by any feature set that has not yet been integrated into it.

  3. 3.

    In case of a 10-dimensional problem in which each input variable is discretized by three blocks, one already needs \(3^{10}\) \(=\) 59,049 observations to have one observation per cell—on average.

  4. 4.

    If a point is a local optimum the gradient is zero for all dimensions of a sample point, then the ratio of biggest and smallest gradient obviously cannot be computed and therefore results in a missing value (\(=\) NA).

  5. 5.

    The default classifiers are linear (LDA), quadratic (QDA) and mixture discriminant analysis (MDA) and the default threshold for dividing the data set into two groups are the 10%-, 25%- and 50%-quantile of the objective values.

  6. 6.

    Here, the “nearest better neighbor” is the observation, which is the nearest neighbor among the set of all observations with a better objective value.

  7. 7.

    The development version is available on GitHub: https://github.com/kerschke/flacco.

  8. 8.

    The stable release is published on CRAN: https://cran.r-project.org/package=flacco.

  9. 9.

    Link to the package’s tutorial: http://kerschke.github.io/flacco-tutorial/.

  10. 10.

    Link to the package’s GUI: https://flacco.shinyapps.io/flacco/.

  11. 11.

    Note that the shown numbers, especially the ones for the number of observations per cell, might be different on your machine, as the initial sample is drawn randomly.

  12. 12.

    The barrier tree features can only be computed if the total number of cells is at least two and the cell mapping convexity features require at least three blocks per dimension.

  13. 13.

    A more detailed step-by-step example can be found in the documentation of the respective flacco-function plotFeatureImportancePlot.

  14. 14.

    As many of the features are stochastic, it is highly recommended to compute the features multiple(\(=\) at least 5 to 10) times.

  15. 15.

    COSEAL is an international group of researchers with a focus on the Configuration and Selection of Algorithms, cf. http://www.coseal.net/.

  16. 16.

    The European Center of Information Systems (ERCIS) is an international network in the field of Information Systems, cf. https://www.ercis.org/.

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Acknowledgements

We acknowledge support by the ERCIS and thank Carlos Hernández (CINVESTAV, Mexico), Jan Dageförde, as well as Christian Hanster (University of Münster, Germany) for their valuable contributions to flacco and its GUI.

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Correspondence to Pascal Kerschke .

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Kerschke, P., Trautmann, H. (2019). Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package Flacco. In: Bauer, N., Ickstadt, K., Lübke, K., Szepannek, G., Trautmann, H., Vichi, M. (eds) Applications in Statistical Computing. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-25147-5_7

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