  The goal of constrained multiobjective evolutionary optimization is to obtain
a set of well-converged and welldistributed feasible solutions. To complete
this goal, there should be a tradeoff among feasibility, diversity, and
convergence. However, it is nontrivial to balance these three elements
simultaneously by using a single tradeoff model since the importance of each
element varies in different evolutionary phases. As an alternative, we adapt
different tradeoff models in different phases and propose a novel algorithm
called ATM-R. In the infeasible phase, ATM-R takes the tradeoff between
diversity and feasibility into account, aiming to move the population toward
feasible regions from diverse search directions. In the semi-feasible phase,
ATM-R promotes the transition from "the tradeoff between feasibility and
diversity" to "the tradeoff between diversity and convergence", which can
facilitate the discovering of enough feasible regions and speed up the search
for the feasible Pareto optima in succession. In the feasible phase, the
tradeoff between diversity and convergence is considered to attain a set of
well-converged and well-distributed feasible solutions. It is worth noting that
the merits of reference points are leveraged in ATM-R to accomplish these
tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is
developed to generate promising solutions beneficial to different evolutionary
phases. Systemic experiments on a wide range of benchmark test functions
demonstrate that ATM-R is effective and competitive, compared against five
state-of-the-art constrained multiobjective optimization evolutionary
algorithms.
