IEEE Computational Intelligence Magazine - May 2023 - 20

The first category is the most widely used strategy that adopts
Pareto dominance-based strategies to ignore constraints to solve
an unconstrained helper problem. This category is suitable for
CMOPs whose constrained Pareto front (CPF) is the same as or
part oftheir unconstrained Pareto front (UPF) because searching
for the UPF by ignoring constraints could also find the CPF.
Tian et al. [6] proposed a coevolutionary framework including
two populations for the original problem and the unconstrained
helper problem, in which the two populations only exchange
information in environmental selection. Liu et al. [7] proposed a
bidirectional coevolutionary framework that employs one population
for the original problemto approach the CPF from feasible
regions and adopts the other population for the unconstrained
problem to approach the CPF from infeasible regions.
Li et al. [20] established a two-archive framework that employs
one convergence-related archive to solve the original problem
with priority for convergence and a diversity-related archive to
solve the unconstrained helper problem with a priority for diversity.
Tian et al. [21] proposed an auto-switch two-stage strategy
to solve the original problem in one stage and an unconstrained
helper problem in another stage when the population is stuck in
local feasible regions. Yu et al. [22] designed a dynamic selection
preference-assisted algorithm to dynamically adjust the selection
preference between feasibility and convergence (i.e., ignore constraints)
according to the population state. Liang et al. [23] used
the relationship between the CPF and the UPF to decide
whether an unconstrained helper problem is used. In order to
handle the relationships between constraints and objectives (i.e.,
constraint priority, objective priority, or the switch between
them), Xiang et al. [24] detected the problem type through the
relationship between the CPF and the UPF.
The second category adopts constraint relaxation-based
strategies2 to solve a constrained-relaxed helper problem. This
method is suitable for CMOPs whose CPF is near the UPF or
partially coincides with the UPF because feasible regions and
the CPF can be detected in the relaxed regions. Ming et al. [9]
proposed a dual-population-based algorithm that employs one
population to solve a constraint-relaxed helper problem by a
novel penalty function and the other population to solve the
unconstrained helper problem. Fan et al. [8] established a
push-pull search framework in which the push stage pushes
the population to the UPF by solving the unconstrained helper
problem and the pull stage pulls back the population by solving
the original problem via an " -constrained technique.
Zhu et al. [25] proposed a detect-and-escape strategy to detect
whether the population is stuck in local feasible regions and
employed the escape strategy to solve the unconstrained helper
problem to escape from the local feasible regions.
Sun et al. [26] separated the population into three subpopulations
(i.e., feasible, semi-feasible, and infeasible) and evolved
the semi-feasible subpopulation using a novel " -constrained
technique. Jiao et al. [27] transformed the original problem
2.The constraint relaxation methods mainly include " -constrained and penalty
function.
20 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2023
Evolutionary multitasking optimization
if a branch of evolutionary transfer
optimization. The idea of ETO is
extracted from the behaviors of human
beings since it is commonly seen for us
to exploit practical knowledge from
experiences to help solve related tasks
at hand.
into a dynamic MOP to change the feasibility priority and
relax the constraint dynamically.
The third category adopts the infeasible solution preservation
strategies to solve an even-search-guided helper problem. This
method is suitable for CMOPs whose CPF is not near the UPF.
The reason is that, when ignoring constraints or relaxation cannot
detect feasible regions and a CPF that is not near the UPF,
guiding an even search in promising regions in the objective
space can help find undetected feasible regions. Although this
category receives less attention, it can effectively handleCMOPs,
especially those with large infeasible regions and whose CPF is far
from the UPF. Yuan et al. [10] proposed an indicator based on
the cost value and an algorithm based on this indicator that could
preserve both infeasible and dominated solutions to achieve an
even search. Also, they proposed another approach [11] to evaluate
the potential value ofeach infeasible solution from different
aspects as a new constraint-handling technique (CHT). They
employed the CHT to preserve valuable infeasible solutions in
their algorithm. Zhou et al. [28] proposed an infeasible solutions
diversity maintenance " -constrained technique to preserve
" -infeasible solutions with good diversity in the objective space.
Zou et al. [29] proposed a dual-population algorithm based on
alternative evolution and degeneration where the secondary
population contains alternative evolution and degeneration
according to its state to utilize infeasible solutions.
B. RL Techniques in MOPs
In recent years, various studies have applied RL techniques in
handling MOPs. Nevertheless, the application of RL in
MOPs is just in its infant stage. Li et al. [30] developed an endto-end
framework for MOPs using the deep RL (DRL) technique.
The original MOP is first decomposed into a set ofsubproblems,
each of which is modeled as a neural network.
These networks are trained to generate Pareto optimal solutions
directly. The authors have applied their approaches to
solve multi-objective traveling salesman problems (MOTSOs).
Zhang et al. [31] proposed a concise meta-learning-based
DRL approach that first trains a meta-model by meta-learning
and constructs the submodels for each subproblem determined
using decomposition [32] to generate the Pareto front (PF).
The authors have employed their approach to solve MOTSPs
IEEE Computational Intelligence Magazine - May 2023

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