IEEE Computational Intelligence Magazine - November 2021 - 50

MFEA-GSMT vs. MFEA-GS, and MFEA-MT vs. MFEAOBL.
It can be seen from Table II that:
❏ The proposed MFEA-MT and MFEA-GSMT perform the
best in most tasks.
❏ The performance of MFEA-MT in the majority of tasks
completely surpasses that of MEFA. MFEA-GSMT performs
better than or similar to MFEA-GS on 16 out of 18
tasks. MFEA-OBL also outperforms MFEA on most tasks.
These results imply that OBL is an effective strategy introduced
into the MFEA.
❏ MFEA-MT outperforms MFEA-OBL on 17 out of 18
tasks, which suggests that the proposed mirror transformation
strategy could perform better than the classical OBL.
C. Effects of Gene-Similarity-Based
Inter-Task Transfer Strategy
This section explores the effects of the proposed gene-similaritybased
inter-task transfer strategy. The term MFEA-GS is adopted
to denote MFEA with only the adaptive gene-similarity-based
inter-task transfer strategy, i.e., without using the mirror transformation
strategy. MFEA-GS is compared with the MFEA-KLD,
i.e., an MFEA selecting the most similar source-tasks based on
the subpopulation similarity, instead of gene similarity, for intertask
knowledge transfer. In MFEA-KLD, the KLD value of two
subpopulation distributions in the evolution process is used to
measure the similarity between tasks. In assortative mating, the
most similar source subpopulation is selected to mate with the
target subpopulation. MFEA-GS and MFEA-KLD are also compared
with MFEA and MFEA-GSMT to show the effects of the
proposed gene-similarity-based inter-task transfer strategy.
Many-tasking optimization problems are selected for the
benchmark test suite here, since it is more challenging for
inter-task transfer strategies. Table III presents the experimental
results of the compared algorithms on a five-tasking optimization
test suite proposed in the WCCI2021 Competition on
Evolutionary Multi-task Optimization, which contains 10 test
problems named MaT1-MaT10. The experimental results with
the best average objective values are highlighted in bold font.
The following observations are obtained on the results:
❏ MFEA-GS and MFEA-GSMT perform the best in most
many-tasking optimization problems, which implies that the
similarity-based inter-task transfer strategy can promote the
positive transfer of knowledge.
❏ MFEA-GS performs better than or similar to MFEA-KLD
on 45 out of 50 tasks, which suggests that the proposed
gene-similarity-based inter-task transfer can handle the
many-tasking problems better than the population-similarity-based
inter-task transfer.
❏ The performance of MFEA-GSMT is similar to that of
MFEA-GS, which indicates that the gene-similarity-based
inter-task transfer plays a dominant role in the improvement
of the algorithm on many-tasking problems. The mirror
transformation strategy might be less effective in dealing with
many-tasking problems, where the partition of the search
areas could be too coarse to favor the search of any task.
50 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
D. Results on Real-World Problems
In this part, the well-known parameter optimization in back propagation
(BP) of neural networks is taken as a representative realworld
problem to challenge the proposed algorithm. BP adjusts
the connection weights and thresholds of the network to optimize
the loss between the actual output of the network and the target
output. Particularly, two three-layer BP neural networks are optimized
at the same time to show the effectiveness of multi-tasking
optimization. The training and testing data of the neural network
are the housing information data in the suburbs of Boston, Massachusetts
(http://archive.ics.uci.edu/ml/machine-learning
-databases/housing/housing.data). The number of nodes in the
input layer of the two networks are both set to 13. The numbers
of the output layer nodes are both set to 1. The numbers of the
hidden layer nodes of the two models are set to 10 and 20,
respectively. As such, there are 151(=13)10+10+10+1) parameters
in the first network model and 301(=13)20+20+20+1)
parameters in the second network model to optimize. The L1
norm loss function is used as the fitness evaluation function.
To reflect the differences in the performance of the compared
algorithms, the gradient descent method is not used to
update the weights and thresholds of the models during the
evolution. Once the evolution ends, we use the optimal solution
obtained by the compared algorithms as the initial parameters of
the models and then train the models using the gradient descent
method. Table IV shows the mean and standard deviation of the
loss of the models in the training data during the evolution, test
data during the evolution, and test data using the EA optimal
solution as the initialization parameter for the gradient descent
method. Figure 5 shows the convergence trend of the model
error on the training data during the iteration process. It can be
http://archive.ics.uci.edu/ml/machine-learning(http://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data http://archive.ics.uci.edu/ml/machine-learning(http://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
IEEE Computational Intelligence Magazine - November 2021

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