[Question] Multiobjective optimization where one target has no optimization direction (but required range)

[Abrikosoff]

I have a multiobjective optimization scenario where, for one of the targets, I do not have a preferred optimization direction, but I do have a range into which the output values from the optimizer should fall. Previously this situation has been dealt with in an ad hoc manner by simply dropping that particular target, but this doesn't seem correct and not really in the spirit of performing MOBO; also the range constraint cannot be enforced.

In general this situation could be corrected by defining a function that maps all values outside of the required range back into the support of that target, and then setting the optimization direction to be minimization (for example, map function could be defined to be quadratic within the range), but I am unsure where I should put this map function. My idea is to define a custom metric which outputs the evaluation result of this map function, but this would:

1. require use of the Developer API;
2. run into the situation where Metrics (in my understanding) are used in way they are not meant to be, i.e., after this mapping the output of the Metric is no longer the direct evaluation result.

Any ideas or suggestions would be really appreciated!