Treat bbob-biobj-mixint as bound constrained?

[ttusar]

The issue we would like to avoid is to have parts of the Pareto set outside of [-5, 5]^n.

[nikohansen]

Possible ways to go about this

0. Keep the functions as is, thereby allowing the possibility that Pareto optimal solutions are outside of the bound domain (which is likely to happen in low dimension and unlikely in dimension >5)
1. raise an error outside the bounded domain
2. return NaN for out-of-bounds solutions (at no costs), forcing the algorithm to handle bounds
3. apply a sine-like transformation on the variables such that unbounded algorithms never evaluate solutions outside the bounded domain
4. add a penalty for out-of-bounds solutions which is large enough such that Pareto optimal solutions are only within the bounded domain.

We could also provide two or three test suites, e.g. 1.-3., which are all identical w.r.t. the performance assessment.

Rationales and observations

re. 1.: if an algorithm evaluates an out-of-bounds solution only rarely, this will lead to awkwardly broken runs

re. 2.: the performance can severely suffer from an inappropriate handling of NaN values even when no Pareto optimal solution is on the boundary. The risk for this to happen should be somewhat low-ish?

re. 3.: this changes the optimal solutions set (seen by the algorithm) where the transformation is not the identity and it changes the fitness landscape where the transformation is nonlinear. It doesn't need to change the bounded search domain (the transformation could be $x_i \mapsto \alpha x_i$ for $x_i \in [-4.9, 4.9]$ with $\alpha > 1$ and $x_i \mapsto x_i$ for $x_i \in \{ -5, 5\}$ and quadratic when $|x_i|\in[4.9, 5]$ such that it is continuous and differentiable).