IEEE Computational Intelligence Magazine - November 2021 - 36

One of the major contributions of GRA lies in the
adjustable resource allocation intensity.
Agricultural crops
(GHISA)8
collected by United States
Geological Survey (USGS) is applied as dictionary A. Since
the original dictionary A for GHISA is of size 125 × 6988,
to reduce the optimization complexity, we randomly select
100 spectral signatures from the total 6988 signatures and
form a new dictionary Au
of size 125 × 100. The target vecYYY
and all
,,,
tor of image pixels includes three vectors 123
the vectors are based on the dictionary Au with Gaussian
noise vector N with zero mean and standard deviation of
0.05, which takes the equation (20):
YAXN
ii
=+
(20)
where the detailed information for abundance vector Xi is
illustrated in Table XII. Moreover, in terms of the mechanism
details to solve such a multi-objective optimization, one can
refer to the original paper [50].
For comparative studies in the problem of hyperspectral
unmixing, algorithms involving the proposed GRA,
MOMFEA, MOMFEA-II, and EMTIL introduced in
Section IV.C are taken into account. According to the
characteristics of the application problem, the population
size of all the methods is set to 50 and the maximum
evaluation rounds are set to 60,000. Since the algorithms
are all designed for continuous problems and the mechanism
to solve the hyperspectral unmixing problem is
based on discrete optimization, all the algorithms convert
the continuous vector in the domain [, ]01 N
into a 0/1
TABLE XII The detailed information for abundance vector.
ABUNDANCE
VECTOR
X1
X2
X3
NON-ZERO
INDICES
1-20
7-26
21-40
ZERO INDICES
21-100
1-6, 27-100
1-20, 41-100
SPARSITY
20
20
20
vector by a threshold of 0.5. In GRA, for
this problem, RAI is set to 0.30, rmp is set to
0.10, and the nonlinear regression step size
M is set to 3. Furthermore, the local search
designed for continuous optimization is also
converted into the permutation-based local search (i.e., the
selected dimension flips from 1/0 to 0/1). To evaluate the
optimization performance, the hypervolume indicator [41]
is applied for comparison, and the reference point
is 1%
larger than the corresponding nadir point in every component,
where the nadir point is constructed from the worst
objective function [52].
The comparison results on hyperspectral unmixing are
showcased in Table XIII. Since the three reconstruction tasks
have certain similarity relationships, the algorithm of MOMFEA-II
can outperform the MOMFEA counterpart since it
can adaptively capture the rmp value during the evolution
process. Since EMTIL is initially designed for continuous
optimization, the discrete decision boundary for the binary
classification [27] in the adaptive control component may be
detrimental for the overall optimization framework. Conversely,
owing to the searching ability of the base optimizer
and the allocation ability of the proposed resource allocation
component, the proposed GRA can outperform all the algorithms
significantly.
TABLE XIII Median hypervolume results for hyperspectral
unmixing problems over 30 independent runs.
METHODS
MOMFEA
MOMFEA-II
EMTIL
GRA
TASK 1
0.760054
0.928598
0.711637
0.947609
TASK 2
0.786264
0.93659
0.717955
0.946317
TASK 3
0.757077
0.9299
0.686035
0.951624
8 https://cmr.earthdata.nasa.gov/search/concepts/C1629302681-LPDAAC_ECS.html
V. Conclusion
In this paper, a generalized resource allocation component
(GRA) is proposed to flexibly allocate resources for different
tasks on EMTO problems in multi-objective settings. The
proposed GRA is based on MTO-DRA, whose behavior
and motivation have been analyzed theoretically in this
paper. To extend MTO-DRA into MOO settings, an attainment
function performance metric and a multi-step nonlinear
regression have been designed based on the proposed
theoretical framework. To redeem the deficits that MTODRA
cannot flexibly adjust resource allocation intensity
when encountering more tasks, a novel allocation framework
is proposed for better controlling allocation intensity, and for
incorporating transfer information during the evolution process.
The comprehensive comparative studies have been conducted
on benchmark problems, complex problems, and
many-task problems of multitasking MOO problems, to confirm
the superiority of the proposed resource allocation
framework. In the case study on a real-world application, the
proposed GRA also possesses satisfying performance for
hyperspectral unmixing.
Recall that, in the sensitivity analysis section of Section
IV.E, it is pointed out that for different EMTO problems, different
RAP values can achieve the best performance accordingly.
Albeit the selected parameter has relatively stable
performance, in the future, we still look forward to developing
an adaptive component to better control the allocation intensity,
thereby hopefully improving the performance of GRA to
a higher level.
36 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
https://cmr.earthdata.nasa.gov/search/concepts/C1629302681-LPDAAC_ECS.html
IEEE Computational Intelligence Magazine - November 2021

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