Abstract
Simultaneously visualizing the decision and objective space of continuous multi-objective optimization problems (MOPs) recently provided key contributions in understanding the structure of their landscapes. For the sake of advancing these recent findings, we compiled all state-of-the-art visualization methods in a single R-package (moPLOT). Moreover, we extended these techniques to handle three-dimensional decision spaces and propose two solutions for visualizing the resulting volume of data points. This enables – for the first time – to illustrate the landscape structures of three-dimensional MOPs.
However, creating these visualizations using the aforementioned framework still lays behind a high barrier of entry for many people as it requires basic skills in R. To enable any user to create and explore MOP landscapes using moPLOT, we additionally provide a dashboard that allows to compute the state-of-the-art visualizations for a wide variety of common benchmark functions through an interactive (web-based) user interface.
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Notes
- 1.
Note that we focus here on the case where the box constraints are inactive. Some discussion of how to handle the decision boundary can be found, e.g., in [20].
- 2.
A level set of a function \(f:\mathbb {R}^n\rightarrow \mathbb {R}\) w.r.t. value \(c\in \mathbb {R}\) is the set of points \(\{(x_1,\dots ,x_n)\in \mathbb {R}^n:f(x_1,\dots ,x_n) =c\}\). The isosurface is a 3D level set.
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The authors acknowledge support by the European Research Center for Information Systems (ERCIS) .
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Schäpermeier, L., Grimme, C., Kerschke, P. (2021). To Boldly Show What No One Has Seen Before: A Dashboard for Visualizing Multi-objective Landscapes. In: Ishibuchi, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2021. Lecture Notes in Computer Science(), vol 12654. Springer, Cham. https://doi.org/10.1007/978-3-030-72062-9_50
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