  Constrained multi-objective optimization problems (CMOPs) pervade real-world
applications in science, engineering, and design. Constraint violation has been
a building block in designing evolutionary multi-objective optimization
algorithms for solving constrained multi-objective optimization problems.
However, in certain scenarios, constraint functions might be unknown or
inadequately defined, making constraint violation unattainable and potentially
misleading for conventional constrained evolutionary multi-objective
optimization algorithms. To address this issue, we present the first of its
kind evolutionary optimization framework, inspired by the principles of the
alternating direction method of multipliers that decouples objective and
constraint functions. This framework tackles CMOPs with unknown constraints by
reformulating the original problem into an additive form of two subproblems,
each of which is allotted a dedicated evolutionary population. Notably, these
two populations operate towards complementary evolutionary directions during
their optimization processes. In order to minimize discrepancy, their
evolutionary directions alternate, aiding the discovery of feasible solutions.
Comparative experiments conducted against five state-of-the-art constrained
evolutionary multi-objective optimization algorithms, on 120 benchmark test
problem instances with varying properties, as well as two real-world
engineering optimization problems, demonstrate the effectiveness and
superiority of our proposed framework. Its salient features include faster
convergence and enhanced resilience to various Pareto front shapes.
