Contents I. Introduction
Recently, constrained multiobjective optimization [1] has attracted a lot of attention in the community of evolutionary computation. The fundamental reason is that many practical problems belong to constrained multiobjective optimization problems (CMOPs), which can be described as follows: \begin{equation*} {\textrm {min}}\mathbf {f}(\mathbf {\textbf {x}}) = (f_{1}(\mathbf {\textbf {x}}),f_{2}(\mathbf {\textbf {x}}),\ldots, f_{M}(\mathbf {\textbf {x}}))\tag{1}\end{equation*}
subject to
\begin{align*} \begin{cases} \mathbf {\textbf {x}} \in S \\ g_{n}(\mathbf {\textbf {x}}) \leq 0, & n=1, \ldots, l \\ h_{n}(\mathbf {\textbf {x}})=0, & n=l+1, \ldots, q \end{cases}\tag{2}\end{align*}
where is a -dimension solution in the decision space , is the set of objective functions, and are the th inequality constraint and the number of inequality constraints, respectively, and and () are the th equality constraint and the number of equality constraints, respectively. When a solution violates at least one constraint, it is infeasible; otherwise, it is feasible. When dealing with one CMOP, not only the objectives are needed to be optimized but also the constraints are required to be satisfied, thus finding a set of feasible Pareto-optimal solutions is the ultimate purpose. Feasible Pareto-optimal solutions refer to the Pareto-optimal solutions in the feasible regions, and they constitute a constrained Pareto front (CPF) in the objective space. Therefore, a well-converged and well-distributed CPF is desired when solving a CMOP.
