IEEE Computational Intelligence Magazine - February 2021 - 27

established high-quality schedules from past problems to bias
the search for new traveling salesman problems (TSPs). In addition to reusing past optimized solutions, Roberto et al. [53]
proposed the transfer of structural information from subproblems to bias construction of the aggregation matrix of the estimation of distribution algorithm (EDA) for solving a
multi-marker tagging single-nucleotide polymorphism (SNP)
selection problem. Based on semidefinite programming, [54]
and [55] proposed a homogeneous and heterogeneous transfer
learning approach to speed up the evolutionary optimization of
vehicle routing via knowledge transferred from the solved
vehicle routing and arc routing problems, respectively. Chaabani
et al. [56] integrated a co-evolutionary decomposition-based
algorithm with transfer learning to enhance the EA search for
solving bi-level production-distribution problems in supply
chain management. Tan et al. [19] proposed an adaptive knowledge transfer framework for surrogate-assisted evolutionary
search of computationally expensive problems based on the
idea of multiproblem surrogates, which enables EAs to acquire
and spontaneously transfer the learned models across problems
towards efficient global optimization.
From these approaches, we can observe that the success of
ETO for complex optimization relies greatly on finding
simpler and related problems of the encountered complex

was proposed in [18], where a weighted l1 norm-regularized
learning process is formulated to adapt customer distributions
across vehicle routing problems for the transfer of high-quality
routing solutions during the search process. Through an independent transfer component, the design of learning and transfer of knowledge can be developed in ETO for enhanced
multitask optimization performance. In [48], Ma et al. introduced a two-level transfer learning method for evolutionary
multitasking, for which the upper-level implements inter-task
knowledge transfer learning via genetic crossover and the lower-level performs intra-task transfer learning based on information transfer of decision variables.
It is worth noting that the correlation between tasks is essential to achieve positive knowledge transfer for MTOPs. As discussed in Section II-A, the search in EAs is an iterative process,
and the guidance of the search towards areas of high-quality
solutions is time-dependent. Therefore, the usefulness of knowledge transfer across tasks may vary at different stages of the evolutionary search, i.e., the evaluation of correlation in MTOPs is
dynamic rather than a static problem. To utilize the availability
of today's cloud computing, the design of ETO approaches
capable of solving a large number of tasks simultaneously is also
an interesting topic to be explored.
C. ETO for Complex Optimization

Many real-world applications involve
complex optimization problems, e.g.,
non-convex problems (e.g., Fig. 6(a)),
problems possess many constraints (e.g.,
Fig. 6(b) and Fig. 6(d)), problems cannot be solved in polynomial time (e.g.,
Fig. 6(b)), problems contain many local
optima (e.g., Fig. 6(c)), and extremely
computationally expensive problems
(e.g., Fig. 6(d)). To address the complexity of these problems, many features have
been proposed in EAs to improve the
search efficiency, such as new search
operators [20], adaptive mechanisms [49],
and new search space construction [50].
By learning and transferring useful
knowledge from related and simpler
problem domains, ETO can help to
deal with complex optimization problems. In [51], Louis et al. presented
a study to acquire problem specific
knowledge to aid the search in a genetic algorithm (GA) via case-based reasoning. Instead of starting anew on each
problem, appropriate intermediate solutions drawn from similar problems
solved previously are periodically
injected into the GA population. In
[52], Cunningham and Smyth applied
knowledge transfer in the form of

Output :

Optimized
Solution
for Task 1

Optimized
Solution
for Task 2

Optimized
Solution for
Task n

Knowledge
Learning and
Transfer

Reproduction

Selection

Input :

Task 1

Task 2

Task n

FIGURE 5 Illustration of multitask optimization.

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