IEEE Computational Intelligence Magazine - November 2022 - 60

a balanced task BTISTi
is constructed by
using the random oversampling technique.
To select the final assisting tasks
for ISTi, the best 10 individuals are
chosen from the population of each
candidate task in CaSISTi
, and these
individuals are evaluated on task ISTi.If
their average accuracy is higher than
that of task ISTi, then this candidate
task is considered to be helpful for ISTi,
and it is put into the final assisting task
set SISTi
selecting assisting task set SISTi for the
" ill-solved " task ISTi is described in
Algorithm 2.
C. Using SISTi to Assist the " ill-Solved "
Task ISTi
After obtaining the assisting task set SISTi
(assume its number is NISTi
), it is further
utilized to assist the task ISTi, which can
improve performance oftask ISTi.Specifically,
for each task ATi 2 SISTi
f1; .. .;NISTi g, its 10 individuals
Algorithm 1 The General Framework of EMT-MC
, i 2
(pATi1; ...;pATi10) with the highest accuracy
are chosen. Each individual pATik
ðk 2f1; .. .; 10gÞ makes N=10 copies,
where N is the population size of task
ISTi. By using the operations above, for
each assisting task ATi, an assisting population
PATi10 for task ISTi is constructed
which has the same population size as
ISTi. Then the populations PATi10 and
PISTi
use the crossover and mutation operations
suggested in NSGA-II to produce
offspring population P0
population set fP10
ISTi ; .. .; PISTi
g is
ISTi.Thus, for all of
obtained, fromwhich the non-dominated
sorting [47]isadopted,and thetop N
individuals are selected as the final population
for task ISTi.
It should be admitted that not all of
must creISTi
SISTi whose offspring are even
6:
7:
8:
9:
the assisting tasks in set SISTi
ate offspring with high quality. There
may exist an assisting task subset
SWorse
worse. For these assisting tasks, in
the next round, the assisting task set
SISTi
SISTi - SWorse
is updated by setting SISTi
ISTi which ensures the tasks in
SISTi to assist task ISTi.To be specific,
for each task ATi 2 SISTi , the accuracy
of its offspring population P0
10:
11:
12:
13:
14:
15:
ISTi is compared
with that of original PISTi.If
more than halfofthe offspring individuals
are worse than those of ISTi,it
the assisting tasks in set SISTi , an offspring
NISTi
Input: D: the original multiclass classification dataset;
maxgen: the maximum number of generations;
N: the population size of each task;
tD: the number of generations for independent evolution;
aD: the number of generations for assisting evolution;
z: a threshold that used to select the " ill-solved " tasks;
Output: FMC: the final multiclass classifier;
1: Obtain binary classification sub-problems withOVOstrategyfBC1; BC2; .. .; BCmðm1Þ=2g;
2: Initialize each population Pi (corresponding to a task Ti)
randomly with N individuals fpi1; .. .;piNg;
3: for i ¼ 1to maxgen do
4:
/*The first phase*/
5:
fP1; .. .; Pmðm1Þ=2g EvolvingIndependently
(P1; .. .; Pmðm1Þ=2, tD); //each population (Pi) evolves independently for tD
generations
/*The second phase*/
SIS Selecting " ill-solved " Tasks (P1; .. .; Pmðm1Þ=2, z);
//if the average accuracy of Pi is lower than z, then the corresponding task Ti is
put into set SIS
for each ISTi 2 SIS do
/*The third phase*/
SISTi SelectingAssistTasks (ISTi, z); //Selection of
assisting task set SISTi for the task ISTi
forj ¼ 1to aD do
/*The fourth phase*/
½ISTi; SISTi EvolvingAssist ðISTi, SISTi
//Using SISTi to assist task ISTi
end for
end foreach
16: end for
17: ½S the individual in population Pi with the highest value of
accuracy for each Ti;
18: FMC voting ([S]); //obtain the final multiclass classifier
by using voting technique in OVO strategy
19: return FMC; //output the final multiclass classifier
60 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2022
Þ;
indicates that the assistance of task ATi
may be useless. Therefore, in the next
round, the assisting task ATi will be
removed from set SISTi
.The whole
procedure of using the assisting task set
SISTi
in Algorithm 3.
. The whole procedure of
D. Time ComplexityAnalysis
In this section, the time complexity analysis
on the proposed method is presented.
To be specific, according to the framework
ofEMT-MC (see Algorithm 1), the
whole procedure ofthe proposed method
mainly includes four phases. In the first
phase, mðm 1Þ=2 sub-populations
evolve for tD generations. Suppose each
sub-population has N individuals, thus,
to aid the task ISTi can be found
the time complexity of the first phase is
OðN2 m2 tDÞ. The second phase is to
select the " ill-solved " tasks, which means
that there are mðm 1Þ=2 tasks to be
evaluated. Thus, the computational complexity
of the second phase is Oðm2Þ.In
the third phase, for each " ill-solved " task
ISTi, its assisting task set SISTi
is constructed.
It needs to consider Oðm2Þ tasks.
In the worst case, the time complexity of
thethird phaseis Oðm4Þ. The fourth phase
is to utilize the assisting task set SISTi
to
help task ISTi, and this procedure repeats
for aD generations. Thus, its time complexity
is OðN m2 aDÞ.In the worst
case, there are mðm 1Þ=2 " ill-solved "
tasks, and the worst time complexity of
the fourth phase is OðN m4 aDÞ.The

IEEE Computational Intelligence Magazine - November 2022

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