IEEE Computational Intelligence Magazine - February 2021 - 31

encountered, search experiences obtained from these alternate
formulations may lead to better problem-solving for the target
problem [26]. Instead of performing evolutionary search on the
original problem formulation with a complicated search space,
the search may be conducted based on alternate formulations
containing simpler search spaces. By transferring useful knowledge obtained in the simpler search space back to the original
space, the search can be guided to regions of high-quality solutions for better optimization performance.
In practice, there are several ways to construct different formulations of a given optimization problem, such as changing
the constraints, altering the structure of objective function(s),
and reducing the number of control variables. However, it is
often difficult to ascertain whether the constructed formulation
is useful. Moreover, it is also a challenge to conduct knowledge
transfer across different formulations effectively. Potential
research topics include the following:
❏❏ Design of useful alternate problem formulations in the context of single- and multi-objective optimization, constrained
optimization, etc.
❏❏ Design of ETO algorithms capable of automatically generating and configuring different formulations of a given problem.
❏❏ Efficient allocation of computational resources for conducting
evolutionary search based on different problem formulations.
C. ETO for Deep Learning

Deep learning has been applied to many real-world applications, such as image classification [63], speech recognition [80],
and recommendation systems [81]. However, the success of
deep learning often relies on the " deep " architecture of neural
networks to learn representations from data such as images,
video or text automatically, without introducing hand-coded
rules or human domain knowledge [63]. Currently, state-ofthe-arts deep neural networks are often manually designed
with expertise from deep learning and problem-to-be-solved.
To make deep learning more accessible and to reduce the
need for human expertise, a number of dedicated EAs have
been proposed for the automatic design of deep neural architectures. In [82], Zhang et al. integrated multi-objective evolutionary search with ensemble learning to optimize the
configuration of a deep belief network. In [83], Liu et al. introduced a layerwise method based on multi-objective evolutionary optimization for structural learning of deep neural
networks. Sun et al. applied a genetic algorithm to automatically design a deep convolutional neural network for image classification [64]. Traditional EAs usually require a large amount of
computational cost to find an acceptable deep neural architecture. On the other hand, the transfer of knowledge, such as
neural architectures [84], deep features [85], and internal representations [86], across deep learning models can often improve
the deep learning performance. Designing effective ETO
methods for automatic deep learning is thus a potential
research direction. Such ETO algorithms should learn and
transfer success from well-designed deep learning models to
enhance the evolutionary search of new deep learning models.

Potential research topics include 1) the design of ETO algorithms for deep neural network architecture searches with
knowledge transfer across neural network models in the form
of small neural nets, learned deep features, etc.; 2) the design of
ETO algorithms for fast hyper-parameters optimization in
deep neural network architectures based on hyper-parameters
of trained networks across problem domains; 3) the design of
ETO approaches with unified knowledge space across different
deep learning models; and 4) the design of graphics processing
unit (GPU)-based ETO approaches for fast and efficient automatic design of deep neural network architectures.
D. ETO in Complex Data Environment

Modern applications often contain data with complex properties, such as noise, imbalanced information, and limited labels.
For instance, the tag noise in an image may be generated by
unreliable labeling using a fast framework such as Amazon
Mechanical Turk [87]. The breast cancer dataset usually contains
a large number of benign samples and a small number of malignant samples, leading to an imbalance classification problem
[88]. In logistics, there may exist vehicle routing tasks involving
customers ranging from hundreds to thousands, and often there
is no label information to relate one customer to another [89].
As improper knowledge transfer across problems is undesirable,
designing ETO approaches to handle complex data properties
for positive knowledge transfer is important. A number of
approaches have been proposed for knowledge transfer in realistic scenarios with complex data properties. In particular, Ge
et al. considered the issue of negative transfer and imbalanced
data distributions in [90], while Yu et al. focused on TL designs
in cases where label noises exist [91]. Cao et al. presented a
study on adaptive TL design, which can automatically estimate
the similarity between source and target tasks [92].
Potential research topics for ETO in complex data environment include 1) the design of robust ETO algorithms for positive knowledge transfer from noisy data; 2) the design of online
ETO algorithms for positive knowledge transfer across problem
domains where the data for learning and transfer appear in
sequential or batch order; 3) the design of ETO algorithms for
positive knowledge learning and transfer across problems having imbalanced data or without labels; and 4) the design of
ETO approaches for efficient knowledge transfer in cases
where the problem property changes in dynamic environments.
E. Theoretical Study of ETO

Despite the increasing interest in designing new ETO algorithms, there is a lack of rigorous theoretical studies on ETO.
Although there are some theoretical analyses of knowledge
transfer between classification tasks [93], [94], such analyses do
not directly apply to EAs. There are a few studies on the similarity measure between optimization problems for positive
knowledge transfer in evolutionary search [95]-[98]. To have a
better understanding of how and when ETO works, more theoretical studies and analyses of ETO are necessary. Possible topics of research include the following:

FEBRUARY 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

IEEE Computational Intelligence Magazine - February 2021

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