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From the above visualizations we report basic properties of the bbob-biobj-ext test functions and the corresponding Pareto set/front approximations that we provide for performance assessment. We investigate properties like continuous vs. discontinuous Pareto fronts and sets, the existence of nondominated points outside a certain region, and uni- or multimodality. Table 1 details these findings for the 2-variable instances 1–5 where search space related numbers correspond to the region [-5,5]n.

Table 1:

Selected properties of the bbob-biobj-ext test functions for the first five instances in dimension 2. The columns give the properties, from left to right, the number of distinct Pareto set parts (? = unclear), the number of distinct Pareto front parts, the (visual) convexity of the Pareto front (n = non-convex, y = convex), the existence of solutions within the best known Pareto set approximation that lie outside [-5,5]n (n = no such point, y = some points outside of the hyperbox), and finally the number of basins of attractions within [-5,5]n, induced visually from the plots described in the text.

 
 

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