How parameters have been chosen in met
a
he
uristics
:
A survey
Eddy Janneth Mesa Delgado
Applied computation.
Systems
School.
Faculty of Mines.
National University of Colombia. Medellín.
Cra. 80 x Cl. 65. Barrio Robledo.
ejmesad@unal.edu.co
Abstract
:
Metaheuristics and heuristics use parameters to control
the
research
and
increa
se their flexibility. Heuristic
method’s
performance is
hold to the
set of parameters
chosen
. T
his paper is a survey of the theoretical approximation of the methods to
parameterize metaheuristics and
慮
example of
adaptive parameters to differential
evolution metaheuristic. A futures works are presented
⸠
Keywords
:
Global Optimization, Heuristic P
rogramming
, nonlinear programming,
parameters
.
1.
INTRODUC
TION
Direct methods are used to solve optimization
problem
s
, despite they can only guarantee a good
solution
. The first direct methods
developed
were
a
systematic
search over
solutions. They
evolve
d
to
be
more
and more effective
methods
until to arrive to
artific
ial intelligence
. Those new methods were
called
heuristics and
m
etaheuristics
(Himmelblau,
1972)
.
Heuristics mean “to find” or “to discover by trial and
error”. Metah
euristics mean a better way “to find”
(Yang, 2010)
. Besides to intelligence,
m
etaheuristics
differs from other
kind of
direct method
s
because
they
use parameters to adjust the search and the
strategy to enhance themselves. Parameters let
algorithms
to get
good answers
in a bigger spam of
problems that initial direct methods with less effort
(Zanakis
and
Evans, 1981; Zilinskas
and
T
ö
rn, 1989)
i
.e. evolutionary strategies are used to get an initial
solution for an unknown problem. By the way,
parameters are a
weakness too, because they need to
be tuning and controlling for every problem. So, a
wrong set of parameters can make metaheuristic
s fail
(Angeline, 1995; E. Eiben, et al., 1999; Kramer,
2008; Yang, 2010)
.
The aim of
this paper is
to
summarize the
information available for parameterization of
metaheuristics
, how them are controlled and tuned
and the effect over performance in some cases
. To do
tha
t, Initially, three key words (
parameters,
metaheuristics and
heuristics)
was used to search in
SCOPUS d
ata base. A
fter that,
a
filter
was made
manually including papers that
contain
:
Applied metaheuristics with adaptive and
self

adaptive parameters
Presentation and comparison of new
methods to adapt or to automate parameters.
Classifications and formalizati
on of methods
to control and tune parameters.
With these
criteria
49 papers w
ere
chosen
.
This paper is organized as follows
: p
arameters are
introduced in section 2.
The p
arameters classification
found
in the literature
are
describe
d
in section
3
and
Section
4
, the first
part present
the parameters
relevance in the heuristics to categorize the
parameters choice and the second
part
use
s
the
technique to choose the parameters to indicate the
type of setting.
An
example
of adaptation and self

adapta
tion are show
n
in Section
6
. Finally, general
conclusion
s
and future works
are presented
in section
7
.
2.
PARAMETERS
Stochastic methods
have not the same pathway
each
run of algorithms.
Also,
t
he intelligence immerse in
metaheuristics
change dynamical
ly
from the
characteristic
s
found in the
search
. Parameters
give
to
metaheuristics
robustness and flexibility
(Talbi,
2009)
.
To choose
parameters
is
not a simple task because a
wrong set of parameter
s would make that
metaheuristics have premature
convergence or even
no convergence at all
(B
ä
ck, 1996; Talbi, 2009)
.
Metaheuristic
s
need
to have enough parameters to be
flexible
,
but
each parameter increase the complexity
to the tune and control of the method and the
necessary changes to optimize a ne
w problem.
Each
metaheuristic is a complete different world, has
different parameters, and they influence the
metaheuristic in different ways. There is not a unique
right to choice parameters in metaheuristics. In
literature two points of view are related,
but they are
only for
Evolutionary C
omputing (EC).
Traditionally, EC includes genetic algorithms (GA)
,
evolution strategies
(ES), and evolutionary
programming (EP
). By the way, other metaheuristics
met the conditions propose by Angeline (1995) to be
a
n
E
C metaheuristic, method that iterated until
specific stopping criteria. So, we would extend this
classification to another metaheuristics and heuristics
in general, but they
do
no
t
use the same operators
that EC
( Fogel
,
D. B.
,
et al
, 1991)
. Specifically,
most
part of another heuristics
has
not operators
formalized as operators, they use a
complete rules
with parameters inside, so maybe it is not a direct
analogy
(Zapfel,
et al.
, 2010)
. In the next two
sections the formal parameter classification proposed
i
n literature was discussed and follow an example of
other heuristic adaptation are presented.
3
.
PARAMETERS
CLASSIFICATION
Each metaheuristic ha
s
a parameter’
s set to control
the search.
Although there
isn’t consensus
about a
unique classificat
ion to
metaheuristic parameters, one
ap
proximation had been developed for EC
(Angeline,
1995; Hinterding,
et al.
, 1997; Kramer, 2008)
.
According
with the definition provide
d
by Angeline
(1995) this classification
could be extended to others
paradigms.
The most complete classification
is
propose
d
by
Kramer
(2008) who links Angeline
(1995) point of
view and
Hinterding
et al
. (1997)
2.1.
Exogenous
.
These parameters are those
whose are
affect
ed by
metaheuristic
performan
ce, but they are external to it
,
fo
r example
: constrain changes, problems with parts
functions
.
2.2.
Endogenous
These are internal to the method and could be change
by the user or method itself. E
ven though
,
Endogenous parameters are our focus, we cannot
forget the exogenous ones
because they will affect
the choice.
Population level
:
In this level the parameters are
global for the optimization.
Operator of
EC
that use
this type or parameters control the next generation.
For example: population size, stopping criteria,
etc
.
Indi
vidual level
.
This kind of parameters only affects
each individual
, for example: It could be the pass for
each individual.
Component level
. In this level
,
the parameters affect
part of the individual like a gene
of a chromosome in
Generic Algorithms (GA).
Also, i
t is important to notice that, authors propose
this classification, but
they do not
talk about a right
or unique
manner to adapt and automatize each level
of parameters.
The techniques are addressed by next
classification.
4
.
PARAMETERS SETTING
S
In last section
,
parameters were changed according to
their level
of
sort in the metaheuristic
. In this case,
the parameters are chosen in two stages the first is
before to use metaheuristic, and it is called “to tune”
and the second one is called “to c
ontrol” and both
have different ways to
be
select.
2.1.
Tuning
.
Parameters are tuned b
efo
re to use metaheuristic.
Those initial parameters could be chosen by three
different levels accord Eiben, et al (1999).
Manually
:
The initial parameters could be chosen by
and expert
ad hoc
it is a right manner but lately are
not the most recommended
(Kramer, 2008; Talbi,
2009)
Design of experiments (DOE)
:
It implies design test
to show the behavior, and use
or define a
metric
analyz
e the result and take a decision about a value
or a range of values for each parameter.
(Kramer,
2008; Talbi, 2009)
.
Metaevolutionary
:
It means that parameters are
chosen by other metaheuristics, in literature a good
example is given by bacterial chemota
xis method
proposed
in
(M
ü
ller,
et al.
, 2000)
. Additionally,
Kramer (2008) extend this procedure to control like
in Hyper

metaheuristics
(Hamadi, et al., 2011)
2.2.
Control
Parameters can change while metaheuristic is
running.
Control process is this
change in “real
time”
. Accord to Hinterding
et al
. (1997) and Eiden
et al
(1999), Kramer
(2008) describe
s
and
discusses
about three methods to control parameters.
Deterministic
:
It could be static or dynamics. Statics
means there is no change at all and dynamic it
change with a specific rule like a dynamic penalty
than change with the distance to feasible zone
(Kramer, 2008; Mesa, 2010)
Adaptive
:
In this case, parameter changes
agree a rule
like if it happens, then do this. A classic example of
adaptive parameters is the 1/5
th
rule for mutation use
in ES
(B
ä
ck, 1996; Kramer, 2008)
.
Self

ada
p
tive:
In this type of control, p
arameters
evolves agree to the problem
for example the se
lf

adaptation of the mutation step

size with the
direction to mutation
(Kramer, 2008; Schwefel,
1995)
5
.
AN EXAMPLE
OF THE ADAPTATIVE AND
SELF

ADAPTATIVE PARAMETERS
FOR
DIFFERENTIAL EVOLUTION (DE)
.
Besides
the metaheuristic
s
covered
by
EC, there are
at least
twenty
different metaheuristics. Additionally,
they have
different approaches and hybrid
s
.
In
the
sake of brevity,
only Differential Evolution (DE)
parameters
adaptation is
review and
just
one
approach
of self

adaptation
is present.
DE is a metaheuristic
proposed by
Price
(
1996)
. It
was classified as evolutionary metaheuristic, but
DE
does not use formal operators
(crossover, mutation)
like other EC algorithms.
This metaheuristic have
certain characteristics that make a good example
to
study: conceptually are near to EC, have one
complete rule but they identify same operators that
have EC, mutation and crossover; have few
parameters, it is widely known and have self

adaptive parameter approach.
This
metaheuristic
(
DE
)
has different
versions
; five
classic
versions for this metaheuristics
are present in
(Mezura

Montes,
et al.
, 2006)
.
Brest,
et al.
( 2006)
use the
version
called
DE
/
rand/1/bin
to propose their
idea of self

adaptive parameters
.
DE parameters for
DE
/
rand/1/bin
version are:
Size of population
(population

level)
Scale factor
(Individual

level)
Crossover parameters
(component

level)
Minimal border
Maximal border
Number of generation
(population

level)
Dimensions
Trial vector
(individual

level)
Randomly chosen index
(an random integer
)
(
)
Random number
(
)
Figure 1 shows the pseudocode for DE,
is a
solution vector and
(
)
is the value of goal function.
Line 04 is mutation operator
(individual

level). L
ine
06
is
the complete heuristic rule. Lines 07

09 are a
borders handle when there a component outside the
feasible zone is forced to go in feasible solution
(
exogenous

level
)
.
01
Start
02
for
until
03
for
until
04
(
)
05
for
until
06
{
(
)
(
)
(
)
(
)
07
if
then
08
09
end if
08
09
end for
10
(
)
{
(
)
(
)
11
end for
12
end for
13
end algorithm
Fig
.
1
.
Pseudocode of DE.
Original algorithm tuned parameter manually based
on a few test,
they
recommended
,
the other
parameters are random or given by the problem.
The
parameters control deterministically (statics).
Later, o
ne of the
approaches
to
control
parameter
s
is
proposed
by
Ali
and
A. T
ö
rn
(
2004)
they fixed
, a
nd
and adapt
using:
{
(


)


(


)
(1)
Where
and
are the minimum and
maximum value found for current generation. And
is
the lower value feasible for
in this case
.
Brest,
et al.
( 2006)
proposed self

adaptive strategies
for
and
in this case, the values changes for each
individual. Initially a parent random vector are select
with size
.
For
a range between
[
,
0.9] are proposed
.
(2)
Where
. The best advantage presented
is the possibility to obtain the best result without run
the metaheuristics many times to
find the best
parameter to optimize each problem.
In the previous paragraphs indicated in parentheses
the
level of
slot to
the
different
parameters.
Although, it is not at exactly as in EC could be
possible extend
5
. CONCLUSION
S
T
here is
not
a general
categorization
for parameters
selection in metaheuristics. EC has a good
framework
for parameter setting. It is important to
notice that
the
se
metaheuristics
have a high
degree of
formalization.
In the previous
section
the
level of
slot to
the
different
parameters
was
indicated in parentheses.
Although, it is not at exactly as in EC could be
possible extend. The possibility to have a formal
framework to set the parameters is important because
it could help to determine which
parameters need
more
control
than other
s
before long tests.
Anyway,
this review just gives an initial idea of the
possibilities. There
is a lot of work
to do in this way.
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