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The goal of constrained multiobjective evolutionary optimization is to obtaina set of well-converged and welldistributed feasible solutions. To completethis goal, there should be a tradeoff among feasibility, diversity, andconvergence. However, it is nontrivial to balance these three elementssimultaneously by using a single tradeoff model since the importance of eachelement varies in different evolutionary phases. As an alternative, we adaptdifferent tradeoff models in different phases and propose a novel algorithmcalled ATM-R. In the infeasible phase, ATM-R takes the tradeoff betweendiversity and feasibility into account, aiming to move the population towardfeasible regions from diverse search directions. In the semi-feasible phase,ATM-R promotes the transition from "the tradeoff between feasibility anddiversity" to "the tradeoff between diversity and convergence", which canfacilitate the discovering of enough feasible regions and speed up the searchfor the feasible Pareto optima in succession. In the feasible phase, thetradeoff between diversity and convergence is considered to attain a set ofwell-converged and well-distributed feasible solutions. It is worth noting thatthe merits of reference points are leveraged in ATM-R to accomplish thesetradeoff models. Also, in ATM-R, a multiphase mating selection strategy isdeveloped to generate promising solutions beneficial to different evolutionaryphases. Systemic experiments on a wide range of benchmark test functionsdemonstrate that ATM-R is effective and competitive, compared against fivestate-of-the-art constrained multiobjective optimization evolutionaryalgorithms.

ATM-R: An Adaptive Tradeoff Model with Reference Points for Constrained Multiobjective Evolutionary Optimization