Applied
Soft
Computing
35
(2015)
541–557
Contents
lists
available
at
ScienceDirect
Applied
Soft
Computing
j
ourna
l
h
o
mepage:
www.elsevier.com/locate/asoc
A
self-adaptive
multi-objective
harmony
search
algorithm
based
on
harmony
memory
variance
Xiangshan
Dai,
Xiaofang
Yuan
∗
,
Zhenjun
Zhang
College
of
Electrical
and
Information
Engineering,
Hunan
University,
Changsha
410082,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
5
December
2014
Received
in
revised
form
20
May
2015
Accepted
12
June
2015
Available
online
9
July
2015
Keywords:
Multi-objective
optimization
Pareto
front
(PF)
Harmony
search
(HS)
Self-adaptive
parameter
setting
Self-adaptive
bandwidth
a
b
s
t
r
a
c
t
Although
harmony
search
(HS)
algorithm
has
shown
many
advantages
in
solving
global
optimization
problems,
its
parameters
need
to
be
set
by
users
according
to
experience
and
problem
characteristics.
This
causes
great
difficulties
for
novice
users.
In
order
to
overcome
this
difficulty,
a
self-adaptive
multi-
objective
harmony
search
(SAMOHS)
algorithm
based
on
harmony
memory
variance
is
proposed
in
this
paper.
In
the
SAMOHS
algorithm,
a
modified
self-adaptive
bandwidth
is
employed,
moreover,
the
self-
adaptive
parameter
setting
based
on
variation
of
harmony
memory
variance
is
proposed
for
harmony
memory
considering
rate
(HMCR)
and
pitch
adjusting
rate
(PAR).
To
solve
multi-objective
optimiza-
tion
problems
(MOPs),
the
proposed
SAMOHS
uses
non-dominated
sorting
and
truncating
procedure
to
update
harmony
memory
(HM).
To
demonstrate
the
effectiveness
of
the
SAMOHS,
it
is
tested
with
many
benchmark
problems
and
applied
to
solve
a
practical
engineering
optimization
problem.
The
experimen-
tal
results
show
that
the
SAMOHS
is
competitive
in
convergence
performance
and
diversity
performance,
compared
with
other
multi-objective
evolutionary
algorithms
(MOEAs).
In
the
experiment,
the
impact
of
harmony
memory
size
(HMS)
on
the
performance
of
SAMOHS
is
also
analyzed.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
The
majority
of
real-world
optimization
problems
consist
of
multiple
objectives
which
usually
conflict
with
each
other,
the
so
called
multi-objective
optimization
problems
(MOPs).
MOPs
gen-
erate
a
set
of
optimal
solutions
instead
of
a
single
solution,
largely
known
as
Pareto
optimal
set
[1].
The
efficiency
to
find
multiple
solu-
tions
of
most
classical
optimization
algorithms
is
low
since
these
optimization
algorithms
usually
achieve
only
one
Pareto
optimal
solution
in
one
run,
therefore,
these
algorithms
have
to
be
run
many
times
to
acquire
the
Pareto
optimal
set.
In
the
last
few
decades,
evolutionary
algorithms
have
attracted
great
attention
among
researchers
to
solve
MOPs,
many
multi-
objective
evolutionary
algorithms
(MOEAs)
have
been
developed,
such
as
NSGA-II
[1],
PESA-II
[2],
SPEA2
[3]
and
M-PAES
[4].
The
rea-
son
for
the
fast
development
of
MOEAs
is
that
these
algorithms
are
able
to
find
multiple
Pareto
optimal
solutions
in
just
one
single
execution.
Harmony
search
(HS)
algorithm,
inspired
by
the
music
improvisation
process,
is
a
new
kind
of
meta-heuristic
algorithm
[5].
The
HS
algorithm
has
been
applied
to
solve
a
wide
variety
of
optimization
problems
[6–9]
as
it
has
several
advantages
including:
∗
Corresponding
author.
Tel.:
+86
13873195923.
E-mail
address:
yuanxiaofang126@126.com
(X.
Yuan).
(a)
HS
has
fewer
control
parameters
and
the
initial
value
setting
of
decision
variables
is
unnecessary
and
(b)
HS
is
easy
to
be
imple-
mented
and
understood.
Recently,
there
are
several
attempts
to
extend
the
HS
to
solve
MOPs.
Literature
[10]
has
used
HS
to
solve
multi-objective
optimization
of
time-cost
trade-off,
while
this
algorithm
has
little
diversity
of
non-dominated
solutions
as
it
only
uses
dominated-based
comparison
and
ignores
diversity
comparison.
The
multi-objective
harmony
search
algorithm
proposed
by
Siva-
subramani
et
al.
[11]
is
able
to
converge
to
Pareto
optimal
solutions,
however
it
has
low
convergence
rate
and
needs
a
large
number
of
iterations.
This
low
convergence
rate
can
be
attributed
to
the
use
of
an
improved
harmony
search
(IHS)
algorithm
[12]
whose
convergence
rate
is
far
from
fast.
Two
detailed
proposals
for
apply-
ing
basic
HS
algorithm
to
solve
MOPs
have
been
proposed
by
Ricart
et
al.
[13],
however
these
algorithms
show
poor
performance
in
terms
of
convergence
and
diversity.
Pavelski
et
al.
[14]
have
investigated
four
variants
of
HS
algorithm
for
solving
MOPs.
How-
ever,
these
four
variants
cannot
generate
true
and
well-distributed
Pareto
optimal
solutions.
The
poor
performance
of
all
aforemen-
tioned
multi-objective
HS
algorithms
can
be
attributed
to
the
fact
that
these
algorithms
have
poor
search
abilities
for
MOPs.
More-
over,
the
control
parameters
of
these
multi-objective
HS
algorithms
need
to
be
set
by
users
according
to
experience
and
problem
char-
acteristics.
As
a
result,
this
causes
great
burden
to
new
users,
and
http://dx.doi.org/10.1016/j.asoc.2015.06.027
1568-4946/©
2015
Elsevier
B.V.
All
rights
reserved.
剩余16页未读，继续阅读
资源评论
