IEEE Computational Intelligence Magazine - May 2022 - 62

Program A
Program B
while
xn y
m ny x
y
y 1
Knowledge
Transfer
Block
y
m
y
y
y
1
FIGURE 9 Two programs A and B concerning different tasks but with similar abstract syntax tree representations are depicted. Knowledge encoded
in common subtrees could be efficiently transferred and reused through EMT to enhance the performance of an imagined automated program
generator.
In what follows, we delve into a specific use-case in software
testing that precisely fits the MTO problem setting with a
set of objective functions and a set of corresponding solutions
being sought.
1) Case study in software test data generation [32]
In [32], the ability of EMT to guide the search in software
branch testing by exploiting inter-branch information was
explored. Each task in MTO represented a branch of a given
computer program, with the objective of finding an input
such that the control flow on program execution (resulting
from that input) would bring about the branch. Successfully
achieving this is referred to as branch coverage. Hence, the
overall problem statement, given multiple branches, was to
find a set of test inputs that would maximize the number of
branches covered. (Optimal coverage could be less than
100% since certain branches could be infeasible, and hence
never covered.)
In the experimental study, 10 numerical calculus functions
written in C, extracted from the book Numerical Recipes in C:
TABLE III The coverage percentage obtained by MTEC-one,
MTEC-all and single-task EA over 20 independent runs. Best
values are marked in bold. Reported results are obtained
from [32].
PROGRAM BRANCHES MTEC-ONE MTEC-ALL
plgndr
gaussj
toeplz
bessj
bnldev
des
fit
laguer
sparse
adi
20
42
20
18
26
16
18
16
30
44
100
97.62
85
100
80.77
93.44
97.5
91.25
81.33
59.09
100
97.62
85
100
80.77
91.88
97.5
90.94
90
59.09
SINGLETASK
EA
99.58
97.62
84.75
100
76.92
93.44
92.78
85
88
56.25
The Art of Scientific Computing [116], were considered. The
inputs to these functions are of integer or real type. Two EMT
algorithm variants (labelled as MTEC-one and MTEC-all,
indicating the number of tasks each candidate solution in a
population is evaluated for) that seek to jointly cover all
branches of a program were compared against a single-task EA
tackling each branch independently. Table III contains the
averaged coverage percentage obtained by all algorithms over
20 independent runs, under uniform computational budget.
The table reveals that MTEC, by virtue of leveraging inter-task
information transfers, achieved competitive or superior coverage
performance than the independent search approach on the
majority of programs.
IV. Forging a Future for EMT in Multi-X Problems
The discussions heretofore provided an overview of EMT
methodologies, and examples where these methods have been
explored in real-world contexts. A representative set of applications
from the literature were summarized in half-dozen broad
categories, spanning topics in data science, complex engineering
design, operations research, etc., offering a bird's eye view
of the potential impact of EMT. This section looks toward the
future of the field. An admittedly inexhaustive list of recipes is
presented by which problem formulations of general interest-
cutting across different application domains-could be newly
cast in the light of EMT. The formulations fall under the
umbrella of multi-X EC [4], since they stand to gain from the
implicit parallelism of EAs in sampling, evaluating and processing
multiple candidate solutions at once. It is hoped that our
discussions will spark future efforts on pushing the envelope of
population-based search further with both implicit and explicit
EMT strategies.
A. EMT in Multi-Objective,
Multi-Constrained Problems
Over recent decades, the solving of multi-objective optimization
problems (MOPs) has greatly benefited from the capacity
of EAs to generate approximations to a full Pareto set in a
single run [85]. The universality of MOPs in decision-making
62 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
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