IEEE Computational Intelligence Magazine - February 2022 - 11

a mapping from the continuous multidimensional
state space characterizing
vehicle positions and velocities to a
discrete set of actions in longitudinal
and lateral direction. It is obtained by
applying a customized version of the
double deep Q-network learning al -
gorithm. The main idea is to approximate
the DRL model with a set of
IF-THEN rules that provide an alternative
interpretable model, which is further
enhanced by visualizing the rules.
This concept is rationalized by the universal
approximation properties of the
rule-based models with fuzzy predicates.
The proposed approach includes
a learning engine composed of zeroorder
fuzzy rules, which generalize
locally around the prototypes by using
multivariate function models. The adjacent
(in the data space) prototypes,
which correspond to the same action,
are further grouped and merged into
the so-called MegaClouds reducing
significantly the number of fuzzy
rules. The input selection method is
based on ranking the density of the
individual inputs. Experimental results
show that the specific DRL agent can
be interpreted by approximating with
families of rules of different granularity.
The method is computationally
efficient and can be potentially extended
to addressing the explainability of
the broader set of fully connected deep
neural network models. "
A Generalized Fuzzy Extension Principle
and Its Application to Information
Fusion, by M. A. Islam, D. T.
Anderson, T. C. Havens, and J. E.
Ball, IEEE Transactions on Fuzzy Systems,
Vol. 29, No. 9, September
2021, pp. 2726-2738.
Digital Object Identifier: 10.1109/
TFUZZ.2020.3006574
" Zadeh's extension principle (ZEP)
is a fundamental concept in fuzzy set
(FS) theory that enables crisp mathematical
operation on FSs. A wellknown
short-coming of ZEP is that
the height of the output FS is determined
by the lowest height of the
input FSs. In this article, we introduce
a generalized extension principle (GEP)
that eliminates this weakness and provides
flexibility and control over how
membership values are mapped from
input to output. Furthermore, we provide
a computationally efficient pointbased
FS representation. In light of our
new definition, we discuss two approaches
to perform aggregation of FSs using
the Choquet integral. The resultant in -
tegrals generalize prior work and lay a
foundation for future extensions. Last,
we demonstrate the extended integrals
via a combination of synthetic and realworld
examples. "
IEEE Transactions on
Evolutionary Computation
Fast Immune System-Inspired Hypermutation
Operators for Combinatorial
Optimizations, by D. Corus, P. S.
Oliveto, and D. Yazdani, IEEE
Transactions on Evolutionary Computation,
Vol. 25, No. 5, October 2021,
pp. 956-970.
Digital Object Identifier: 10.1109/
TEVC.2021.3068574
" Various studies have shown that
immune system-inspired hypermutation
operators can allow artificial immune
systems (AIS) to be very efficient at
escaping local optima of multimodal
optimization problems. However, this
efficiency comes at the expense of considerably
slower runtimes during the
exploitation phase compared to the
standard evolutionary algorithms. We
propose modifications to the traditional
hypermutations with mutation potential
(HMP) that allow them to be efficient
at exploitation, as well as maintaining
their effective explorative characteristics.
Rather than deterministically evaluating
fitness after each bit-flip of a
hypermutation, we sample the fitness
function stochastically with a " parabolic "
distribution. This allows the stop at
the first constructive mutation (FCM)
variant of HMP to reduce the linear
amount of wasted function evaluations
when no improvement is found to a
constant. The stochastic distribution
also allows the removal of the FCM
More Trees or Larger Trees: Parallelizing
Monte Carlo Tree Search, by E. Steinmetz
and M. Gini, IEEE Transactions
on Games, Vol. 13, No. 3, September
2021, pp. 315-320.
Digital Object Identifier: 10.1109/
TG.2020.3048331
" Monte Carlo tree search (MCTS)
is being effectively used in many
domains, but acquiring good results
from building larger trees takes time
that can in many cases be impractical.
In this article, we show that parallelizing
the tree building process using
multiple independent trees (root parallelization)
can improve results when
limited time is available, and compare
these results to other parallelization
techniques and to results obtained
from running for an extended time.
We obtained our results using MCTS
in the domain of computer Go, which
has the most mature implementations.
Compared to previous studies, our
results are more precise and statistically
significant. "
FEBRUARY 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 11
mechanism altogether as originally
desired in the design of the HMP operators.
We rigorously prove the effectiveness
of the proposed operators for
all the benchmark functions, where the
performance of HMP is rigorously
understood in the literature. We validate
the gained insights to show linear
speed-ups for the identification of
high-quality approximate solutions to
classical NP-Hard problems from combinatorial
optimization. We then show
the superiority of the HMP operators
to the traditional ones in an analysis of
the complete standard Opt-IA AIS,
where the stochastic evaluation scheme
allows HMP and aging operators to
work in harmony. Through a comparative
performance study of other " fast
mutation " operators from the literature,
we conclude that a power-law distribution
for the parabolic evaluation scheme
is the best compromise in black-box
scenarios, where little problem knowledge
is available. "
IEEE Transactions on Games
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