IEEE Computational Intelligence Magazine - November 2019 - 55

within the horizontal box. A population
of solutions, when gets operated by an
EA's operators, a flexible or restrictive
implicit parallelism gets set within EA's
population for creation of widely or
narrowly distributed set of new solutions, respectively. Early EA researchers
[1], [2] have argued that due to the use
of a population, a large number of partially good sub-solutions can get parallelly processed in every iteration, thereby
providing population-based EAs an
"implicit parallelism" for quickly arriving at better regions for an efficient
search. As mentioned, the extent of
implicit parallelism depends largely on
the designed operators. Some operators
may constitute a broad parallel search,
thereby creating very different population members from their parents making
a flexible search. On the other hand,
some search operators may introduce a
restricted search, thereby not allowing a
too diverse population to be created
from generation to generation. The
extent of search created by an algorithm
may be too flexible or restrictive for
efficiently solving a specific problem.
Therefore, an explicit control on the
effect of induced implicit parallelism is
an important concept that every EA
designer must understand. This is depicted in Figure 1, in which EA operators
are externally controlled in order to
induce an adequate extent of search
through a more flexible or a more
restrictive implicit parallelism mechanism. In the context of multi- and
many-objective optimization, implicit
parallelism is actually an inner feature of
EMO algorithms, which makes it possible to find a set of trade-off Pareto-optimal solutions simultaneously. An explicit
control of the extent of their search can
be introduced by restrictions or relaxations on normalization, selection,
recombination, mutation, and migration
procedures within an EMO algorithm.
Figure 2 presents a sketch explaining
the qualitative levels of explicit control
introduced in a few existing multi- and
many-objective optimization algorithms.
Classical generating methods [33], in
which each Pareto-optimal solution is
attempted to be found independently by

scalarizing the problem into a single
objective, introduce least implicit parallelism in terms of finding a set of welldistributed Pareto-optimal solutions.
Thus, this method has the maximum
explicit control on the part of the user.
In the decomposition-based EMO algorithms, the population is divided into
different subpopulations and they can
either evolve independently or collaboratively within an algorithm. The division
process and the ensuing interactions can
be controlled explicitly by the user. For
example, in M2M, the population is
decomposed into a number of subpopulations describing each subproblem. In
this sense, the M2M method is considered to have a reduced explicit control
compared to the classical generating
methods. In MOEA/D, the recombination procedure is confined within a
neighborhood of a decomposition vector, but the selection is not restricted
within the same neighborhood, thereby
making the process less explicitly controlled than M2M. NSGA-III, on the
other hand, is not restrictive in its

recombination operator, but restricts its
niching operation within associated
members of every reference line.
Although, it introduces a smaller explicit
control than MOEA/D or M2M due to
its global dominance check, EMO algorithms, such as, NSGA-II, SPEA2, and
others, possess the smallest level of
explicit control without any restriction
on selection or recombination operations. It is important to note and as highlighted before that a smaller explicit
control does not mean that the algorithm is more efficient. Every problem
requires a good setting of explicit control
so that a requisite implicit parallelism can
get set up within the search process.
It is evident from the above discussion that an algorithm's implicit parallelism gets set by explicit control of its
operators. If the search power generated
by the induced implicit parallelism
mechanism is adequate for a problem
class to be solved efficiently, the algorithm with its set explicit control will be
successful to solve the specific problem
class. It is then important for an algorithm

No Explicit Control
Population

Evolutionary
Algorithm

Implicit
Parallelism

Extent
of
Search

Explicit
Control

FIGURE 1 Explicit control of EA operators establishes a regulated implicit parallelism resulting
in a controlled extent of search.

Decomposition-Based Methods
Classical
Generating
Methods
MOEA /D-M2M

Large

MOEA /D

NSGA-III

Medium

NSGA-II
SPEA2,...
Small

Extent of Explicit Control
FIGURE 2 Levels of explicit control of implicit parallelism in different decomposition-based
multi- and many-objective optimization algorithms.

NOVEMBER 2019 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

IEEE Computational Intelligence Magazine - November 2019

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