IEEE Computational Intelligence Magazine - November 2021 - 39

algorithms, however, it suffers from negative
knowledge transfer among the tasks with low
correlation. To address this issue, in this study,
inter-task gene-similarity-based knowledge
transfer and mirror transformation are integrated
into MFEA (termed as MFEA-GSMT). In the
proposed inter-task gene-similarity-based
knowledge transfer, a probabilistic model is used to feature each
gene and the Kullback-Leibler divergence is employed to measure
the inter-task dimension similarity. Guided by the intertask
gene similarity, a selective crossover is used to reproduce
offspring solutions. The proposed inter-task knowledge transfer
is based on online gene similarity evaluation, instead of individual
similarity, to overcome the imprecise estimation of population
distributions in a high-dimensional space with only a small
number of samples. The proposed mirror transformation is an
extension of opposition-based learning to avoid premature convergence
and explore additional promising search areas. Experimental
results on both single-objective and multi-objective
multi-tasking problems demonstrate the effectiveness and efficiency
of the proposed MFEA-GSMT.
I. Introduction
M
ultitask optimization (MTO) [1]-[4] is an emerging
computational intelligence research topic dedicated
to solving multiple optimization tasks
simultaneously. It works under the assumption
that knowledge acquired from solving one task may help
solve other related tasks. In real-world applications, related
optimization tasks are ubiquitous [5], where there is ample
scope for MTO to show its abilities. MTO can be implemented
with different optimizers. Evolutionary MTO
(EMTO) algorithms have surfaced as one of the mainstream
MTO algorithms, featured by using population-based evolutionary
algorithms (EAs) as the optimizers.
EAs are a class of optimization metaheuristics stimulated by
the principles of survival of the fittest [6]. Unlike mathematical
programming methods, population-based EAs can obtain a set
of sufficiently good solutions in each run. EAs can also be
more effective in handling complex optimization problems
with black-box, multimodality, discontinuities, noise, and/or
dynamic properties [6], [7]. Conventional EAs were initially
designed for single-task optimization [7]. However, real-world
optimization tasks are seldom isolated and related tasks typically
contain common knowledge that can be used to significantly
assist the solving of each task. Inspired by transfer learning that
can utilize common knowledge of related source tasks to help
solve the target task [2], [8], previous studies [9]-[12] have
extended EAs to handle multiple optimization tasks simultaneously
via inter-task knowledge transfer, leading to EMTO.
EMTO acquires knowledge from the optimization process of
one task to facilitate the optimization of other tasks [8], [11].
The most representative EMTO algorithm is the multifactorial
evolutionary algorithm (MFEA) [11], where inter-task knowledge
transfer occurs
in vertical cultural
transmission and
Most MFEAs implicitly assume that inter-task
similarities exist, and they can facilitate the solving
of optimization tasks. However, inter-task similarities
are usually unknown in advance.
assortative mating. Recently, numerous studies [13]-[18] have
shown that MFEAs can outperform their counterpart singletask
EAs if the inter-task knowledge transfer is positive.
Most MFEAs implicitly assume that inter-task similarities
exist, and they can facilitate the solving of optimization tasks.
However, inter-task similarities are usually unknown in
advance. As a result, MFEAs might suffer from negative
knowledge transfer especially on the problems with low intertask
correlations. Developing an effective knowledge transfer
strategy is a key issue in MFEAs, and considerable efforts have
been devoted toward this task. For example, there are attempts
to explicitly transfer the individual(s) of one task as useful
knowledge to solve other tasks [11], [14]. Such individualtransfer-based
approaches are only suitable for MTO problems
whose optimal solutions are close to each other. To handle
problems with distant optima, some search-direction-transferbased
approaches [19]-[21] and linear-transformation-transferbased
approaches [22]-[24] have been proposed. These
approaches have achieved promising results, yet they are still
not efficient enough because the generated offspring are
around the subpopulation of the target task. To overcome the
above issue, online distribution-similarity-based knowledge
transfer was further introduced to MFEAs [25]-[29]. For
example, the works [26], [27] calculate the similarity among
tasks based on subpopulation distributions and Wasserstein distance
(WD) based on which suitable source tasks for knowledge
transfer are selected. A mixture modelling of multiple
task-related subpopulation distributions is used as the density
function to sample the offspring in [25]. Nevertheless, individual
distribution estimation can be very difficult and imprecise
especially in a high-dimensional space with only a small number
of samples [2].
To address the aforementioned issue, we present a new
MFEA equipped with inter-task gene-similarity-based knowledge
transfer and a mirror transformation, namely MFEAGSMT.
In the proposed inter-task knowledge transfers, a
normal distribution is used to approximate the subpopulation
distribution of a task on each dimension, and the KullbackLeibler
divergence (KLD) [30] is applied to estimate the intertask
gene similarity. Inter-task knowledge transfer is based on
the inter-task gene similarity to overcome negative knowledge
transfer. Moreover, an adaptive mirror transformation is introduced
to avoid premature convergence. The mirror transformation
is an extension of opposition-based learning and is
designed to explore more promising areas in an adaptive manner.
Experimental studies on benchmark and real-world problems
demonstrate that the proposed algorithm is more effective
than other state-of-the-art algorithms in terms of the obtained
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 39
IEEE Computational Intelligence Magazine - November 2021

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