  Constraint violation has been a building block to design evolutionary
multi-objective optimization algorithms for solving constrained multi-objective
optimization problems. However, it is not uncommon that the constraint
violation is hardly approachable in real-world black-box optimization
scenarios. It is unclear that whether the existing constrained evolutionary
multi-objective optimization algorithms, whose environmental selection
mechanism are built upon the constraint violation, can still work or not when
the formulations of the constraint functions are unknown. Bearing this
consideration in mind, this paper picks up four widely used constrained
evolutionary multi-objective optimization algorithms as the baseline and
develop the corresponding variants that replace the constraint violation by a
crisp value. From our experiments on both synthetic and real-world benchmark
test problems, we find that the performance of the selected algorithms have not
been significantly influenced when the constraint violation is not used to
guide the environmental selection.
