IEEE Computational Intelligence Magazine - November 2021 - 21

normalized attainment function is designed for better quantifying
convergence status, a multi-step nonlinear regression is proposed
to serve as a stable performance estimator, and the algorithmic
procedure of conventional resource allocation is refined for
flexibly adjusting resource allocation intensity and including
knowledge transfer information. It has been verified that the
GRA framework can enhance the overall performance of the
multi-objective EMTO algorithm in solving benchmark
problems, complex problems, many-task problems, and a
real-world application problem. Notably, the proposed
GRA framework served as a crucial component for the winner
algorithm in the Competition on Evolutionary Multi-Task
Optimization (Multi-objective Optimization Track) in IEEE
2020 World Congress on Computational Intelligence.
I. Introduction
M
ulti-objective optimization (MOO) is a prevalent
topic in real-world applications [1]-[5], which aims
at obtaining solutions with satisfactory performance
upon various criterion. Generally MOO can be
formulated as follows:
mi () (( ), ..., ())T
! X
nFX fX fX
.. X
= 1
st
n
(1)
where F(X) consists of n objective functions that often conflict
with one another, and Ω is the decision space. Owing to
the frequent occurrence of objective function confliction, the
optimal solutions of MOO are the set of the best trade-off
solutions called Pareto optimal solutions whose performance
on n objectives cannot be completely outperformed by any
other solution. By virtue of the population-based nature, evolutionary
algorithms (EAs) can generate MOO solutions naturally.
The ubiquitous EAs that are designed for MOO can be
broadly classified into three categories: dominance-based
algorithms that mainly employ the dominance relationships
to evolve solutions, such as NSGA-II [6] and SPEA2 [7],
decomposition-based algorithms that decompose MOO into
several single objective optimizations, such as MOEA/D [8]
and C-MOGA [9], and indicator-based algorithms that select
offsprings grounded on their contribution to a given performance
indicator, such as FV-MOEA [10] and IBEA [11].
Recent years have witnessed the surge of research on evolutionary
multitasking optimization (EMTO) [12], which is
intended to resolve multiple optimization problems simultaneously
through a unified chromosome representation [13].
EMTO can be formulated as follows:
(, , ...,) argmin(( ), (),..., ())
! X
XX XFXF XF X
.. X
12
KK
kk
=
st
12
(2)
where the EMTO problem consists of K distinct tasks, and the
aim is to figure out the best solution Xk for the k-th task within
each corresponding decision space Ωk. Using the EMTO
framework, by appropriately exploiting synergy among distinct
optimization tasks [14-16] and suppressing possible negative
transfer [17-19] during the concurrent optimization process,
multiple complementary optimization tasks can achieve
improved performance, which has been verified in numerous
real-world applications encompassing time series prediction
[20], machine learning hyperparameter tuning [21], fuzzy control
problems [22], software tests generation [23], and car architecture
design [24].
In light of the capability for handling several optimization
tasks concurrently, EMTO is widely adopted for multitasking
MOO problems. Broadly, EMTO algorithms on MOO problems
can be categorized into two groups, MOO-aware methods
that incorporate the characteristics of MOO into EMTO
algorithms, and MOO-agnostic methods that employ various
components for promoting the searching ability of EMTO
algorithms. In other words, the backbone of the MOOagnostic
methods can be directly employed on single objective
multitasking problems, but the backbone of MOO-aware
methods cannot. In detail, among the MOO-aware methods,
Lin et al. [25] proposed to select transferred individuals
according to its similarity with the historically effective transferred
solution for MOO; Yang et al. [26] clustered variables
into convergence-related variables and diversity-related variables,
and hereafter controlled each sort of variables with different
transfer
intensities; Lin et al. [27] applied a binary
incremental learning classifier to determine whether the
transferred individual can be a non-dominated solution and
employed the transferred results for retraining; Chen et al. [28]
quantified MOO solutions according to the dominance level
and brought into the heterogeneous domain adaptation techniques
from transfer learning [29]. Besides, among the MOOagnostic
methods, Liang et al. [30] discovered commonalities
among problems by measuring the multiplication of their
population distributions, and adjusted the knowledge transfer
magnitude according to the attained measurements; Chen
et al. [31] designed a multi-population framework with the
incorporation of JADE [32] and an adaptive local search to
facilitate better convergence performance; Liang et al. [33]
adopted opposition-based learning [34] for better exploration
in the decision space, and employed a simple transformation
mechanism to convert individuals from one domain to
another; Min et al. [21] solved single-task MOO by decomposing
MOO through the MOEA/D [8] framework, and
subsequently tackled various single-objective optimization
problems using the EMTO framework.
In spite of the progress on multitasking MOO by EMTO,
to the best of our knowledge, there has been little research
that considers the scenario where some MOO problems cannot
converge under restrictive computational budgets. Since
EMTO attempts to optimize several tasks simultaneously and
these tasks generally possess distinct attributes or, more crucially,
distinct optimization difficulties, it is urgent for EMTO
to allocate different computational resources towards all the
tasks based on their properties. The very first paper that covered
the concept of resource allocation in EMTO is
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 21
IEEE Computational Intelligence Magazine - November 2021

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - November 2021
