IEEE Computational Intelligence Magazine - May 2022 - 57

optimization problem is further supplemented
with constraint functions to ensure
safe distance between UAVs, concurrence
with altitude boundaries, and prevention of
geofence breaches; refer to [84] for a
detailed description.
The ultimate goal of such a path planning
system is to enable real-time decision support. However, the
path-integral risk metric is computed via a numerical quadrature
scheme that becomes computationally expensive for
accurate risk estimation (i.e., when using a high-resolution
mesh). Hence, an MTO formulation was proposed in [84]
where cheaper low- and medium-fidelity auxiliary tasks
were generated (by means of lower-resolution meshes) and
combined with the main high-fidelity task at hand. The
high-, medium-, and low-fidelity tasks are denoted as
and T ,3
TT ,12
respectively.
Fig. 4 compares the optimization performance obtained by
a single-task multi-objective EA [85] (solving just the highfidelity
task) and a multi-objective version of MFEA-II (MOMFEA-II)
[84] solving {, }TT
12 or {, ,}.TTT The
123
hypervolume metric [86] is used to quantify convergence trends
in multidimensional objective space. As seen in the figure, both
MO-MFEA-II settings led to better hypervolume scores faster
than the conventional single-task approach. The speedup is
greater when given two auxiliary tasks (i.e., in the case of
MTO with {, ,}),TTT
123
transferring good solutions generated by lower-fidelity tasks to
quickly optimize the target problem instance.
D. Category 4: EMT in Complex Design
The evaluation of solutions in scientific and engineering design
domains often involves time-consuming computer simulation
or complex laboratory procedures to be carried out (such as
synthesizing candidate protein structures for protein optimization).
The need for active solution sampling and evaluation to
solve such tasks from scratch can thus become prohibitively
expensive. MTO provides an efficient alternative that has
begun to attract widespread attention; examples of practical
application have included finite element simulation-based system-in-package
design [87], finite difference simulation-based
optimization of well locations in reservoir models [88], parameter
identification of photovoltaic models [89], optimization of
active and reactive electric power dispatch in smart grids [90],
design of a coupled-tank water level fuzzy control system [91],
to name a few. The hallmark of EMT in such applications lies
in seeding transferred information into the search, hence building
on solutions of related tasks to enable rapid design
optimization. This attribute promises to particularly enhance
the conceptualization phase of design exercises, where multiple
concepts with latent synergies are conceived and assessed at the
same time [81], [92].
Take car design as an exemplar. In [93], [94], multifactorial
algorithms were applied to simultaneously optimize the design
parameters of three different types of Mazda cars-a sport
The transfer of solution building-blocks through the
learnt latent space not only opened up the possibility
of " out of the box " shape generation, but also yield ed
up to 38.95% reduction in drag force ...
demonstrating the advantage of
utility vehicle, a large-vehicle, and a small-vehicle-of different
sizes and body shapes, but with the same number of parts. (The
three problem instances were first proposed in [95], where the
structural simulation software LS-DYNA2 was used to evaluate
collision safety and build approximate response surface models.)
Each car has 74 design parameters representing the thickness of
the structural parts for minimizing weight while satisfying
crashworthiness constraints. The experimental results in [93]
showed that EMT was able to achieve better performance than
the conventional (single-task) approach to optimizing the car
designs. In another study, multitask shape optimization of three
types of cars-a pick-up truck, a sedan, and a hatchback-was
undertaken to minimize aerodynamic drag (evaluated using
OpenFOAM3 simulations) [29]. The uniqueness of the study
lies in using a 3D point cloud autoencoder to derive a common
design representation space (fulfilling the role of X in Eq.
(3)) that unifies different car shapes; a graphical summary of this
idea is depicted in Fig. 5. The transfer of solution buildingblocks
through the learnt latent space not only opened up the
possibility of " out of the box " shape generation, but also yielded
up to 38.95% reduction in drag force compared to a singletask
baseline given the same computational budget [29].
Not limited to structural and geometric design, EMT has also
been successfully applied to process design optimization problems.
In an industrial research [96], an adaptive multi-objective, multifactorial
2 https://www.lstc.com/products/ls-dyna
3 https://www.openfoam.com/
0.48
0.45
0.42
0.39
0.36
0.33
0.2
NSGA-II
MO-MFEA-II {T1, T2}
MO-MFEA-II {T1, T2, T3}
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Normalized Wall Clock Time
FIGURE 4 Convergence trends of NSGA-II and MO-MFEA-II on multiUAV
path planning. MO-MFEA-II incorporates lower-fidelity auxiliary
tasks to help optimize the high-fidelity target T1. Plots are obtained
from [84]. The shaded area spans 1/2 standard deviation on either
side of the mean performance.
MAY 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 57
Performance on T1 (Hypervolume)
https://www.lstc.com/products/ls-dyna https://www.openfoam.com/
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