8th IMACS Seminar on Monte Carlo Methods
August 29–September 2, 2011, Borovets, Bulgaria
Introduction
Metaheuristics:
• increasingly
popular in research
Generalized
Nets,and industry
• mimic natural metaphors to solve complex
Ant
Colony
Optimization
optimization
problems
Algorithms
• efficient and
effective to deliver satisfactory
solutions to large and complex problems in a
and
Genetic
Algorithms
reasonable time
• some of the most successful metaheuristics:
Vassia Atanassova
– Genetic
Algorithms
Stefka
Fidanova
– Ant Colony
Optimization
Ivan Popchev
Panagiotis Chountas
Generalized
IntroductionNets
Metaheuristics:
• Extension of Petri Nets and their modifications
• • increasingly
Apparatus for
popular
description
in research and industry
of parallel
processes
• mimic
natural
metaphors to solve complex
• optimization
Static structure:
problems
– Transitions
• efficient
and effective to deliver satisfactory
– Places
solutions
to large and complex problems in a
• reasonable
Dynamic structure:
time
– Tokens
• some
of the most successful metaheuristics:
– Predicate index matrices
– Genetic Algorithms
• Memory
– Ant Colony Optimization
• Time
try
cs:
Genetic
Generalized
Algorithms
Nets
• Parallel
Extension
global
of Petri
search
Netstechnique
and their that
modifications
emulates
natural
genetic
• Apparatus
foroperators
description
of parallel
processes
• GAs
are stochastic
search methods for
• Static structure:
exploring
complex problem space in order to find
– Transitions
optimal
solutions using minimal information
–
Places
• Population of individuals (tentative solutions)
• Dynamic structure:
• Fitness
function (individual’s suitability to problem)
– Tokens
•
•
•
•
•
– Predicate index matrices
Operators:
selection, crossover and mutation
Memory
Stop criterion (# iterations, finding of individual)
Time
Convergence towards a global solution
tions
try
cs:
Genetic
GN models
Algorithms
of GAs
• •Parallel
1. GA search
global search
procedure
technique
- in terms
thatofemulates
GNs
natural
genetic
operators
– The
GN model
simultaneously evaluates several
fitness functions, ranks the individuals per their FF
• GAs are
methodsthe
forproblem
and stochastic
chooses the search
best FF regarding
exploring complex problem space in order to find
• 2. Selection
tuning
of GAinformation
operators
optimal
solutionsand
using
minimal
– The GN model has the possibility to test different
• Population
individuals
(tentative
solutions)
groups of
of the
defined genetic
algorithm
operators
and choose the most appropriate combination
• Fitness
function (individual’s suitability to problem)
among them.
• Operators:
selection,
and mutation
– The developed
GN crossover
executes a genetic
algorithm
and implements tuning of the genetic operators, as
• Stop criterion
iterations,
finding
of individual)
well as the(#fitness
function,
regarding
to the
considered problem
• Convergence towards a global solution
tions
ates
try
o find
em)
ion
cs:
Ant
GN
Colony
models
Optimization
of GAs
• •1.ACO
GA search
is a new
procedure
metaheuristic
- in terms
method
of GNs
inspired
theGN
social
behaviour
of ants
in nature.
–byThe
model
simultaneously
evaluates
several
fitness functions, ranks the individuals per their FF
• It finds
good solutions
optimization
and chooses
the best FFfor
regarding
the problem
problems with restrictive constraints
• 2. Selection and tuning of GA operators
• Low level interaction between single agents
– The GN model has the possibility to test different
results
complex
behaviour
of the
whole
groupsinofathe
defined genetic
algorithm
operators
antand
colony
choose the most appropriate combination
among
them.path from food source to formicary
– Shortest
– The developed GN executes a genetic algorithm
– Communication via pheromone (distributed
and implements tuning of the genetic operators, as
numerical information), which ants use to
well as the fitness function, regarding to the
probabilistically construct solutions
considered problem
tions
sates
veral
try
heir FF
lem
o find
erent
rators
em)
on
ion
ithm
ors, as
cs:
AntGN
Colony
models
Optimization
of ACO
•• ACO
ACO issearch
a newprocedure
metaheuristic
– in method
terms ofinspired
GNs
by–the
social behaviour of ants in nature.
A GN was constructed, describing the ACO
algorithm.
• It finds
good solutions for optimization
problems
restrictive
constraints
– On thiswith
basis,
the opportunity
arose for
modification and improvement of the ACO
• Low algorithm.
level interaction between single agents
results in a complex behaviour of the whole
– GN models realizing the new modified versions of
ant colony
ACO were built.
– Shortest path from food source to formicary
– The test samples proved that these modifications,
– resulting
Communication
from thevia
application
pheromone
of (distributed
GNs, yield better
results
numerical
according
information),
to time.
which ants use to
probabilistically construct solutions
n
tions
spired
sates
e.
veral
try
heir FF
lem
o find
gents
erent
whole
rators
em)
on
ion
ary
ithm
ed
ors, as
cs:
o
GN
GNfor
models
hybridofACO/GA
ACO
•• ACO
Usually
search
metaheuristics
procedure are
– in combined
terms of GNs
with
local
search procedure or an exact method.
– A GN was constructed, describing the ACO
Ouralgorithm.
idea is to combine two metaheuristics.
– The GA starts with population which is closer to
– On
this basis,
the opportunity
optimal
solution.
Sometimes arose
after afor
number of
modification
and
improvement
of
the
ACO
iterations the GA goes to stagnation, the
algorithm.
population stop to be improved.
–– GN
Next,
models
the GA
realizing
solutions
the new
are provided
modifiedas
versions
input for
of
ACO
the ACO
werealgorithm
built.
and the pheromone is
updated accordingly.
– The test samples proved that these modifications,
– resulting
ACO with
updated
pheromone
is runyield
and thus
a
from
the application
of GNs,
better
new population
GA is generated
results
accordingfor
to time.
• Any ACO / GA version can be used,
depending on the problem solved.
n
tions
spired
sates
e.
veral
try
heir FF
lem
o find
gents
erent
whole
rators
em)
on
ion
ary
ithm
ed
ors, as
cs:
o
Constructing
GN for hybrid
theACO/GA
GN model
• • Usually
We describe
metaheuristics
ACO andare
GAcombined
with GNs with
(GACO
local
andsearch
GGA, respectively)
procedure orand
an using
exact them
method.
we
Our
prepare
idea isa to
GN
combine
describing
two the
metaheuristics.
hybrid ACO/GA
The problem
is coded
–algorithm.
The GA starts
with population
whichin
is G
closer
proc. to
optimal solution. Sometimes after a number of
• Both
GACO and
GGA
have
one inputthe
and one
iterations
the GA
goes
to stagnation,
output
places:
population
stop to be improved.
– Next, the GA solutions are provided as input for
the ACO algorithm and the pheromone is
updated accordingly.
– ACO with updated pheromone is run and thus a
new population for GA is generated
• Any ACO / GA version can be used,
depending on the problem solved.
n
A
tions
spired
swith
ates
ethod.
e.
veral
try
heir
FF
stics.
lem to
closer
o
find
mber of
e
gents
erent
whole
rators
input for
em)
on
s
Constructing
Constructing the
the GN
GN model
model
• We describe ACO and GA with GNs (GACO
and GGA, respectively) and using them we
prepare a GN describing the hybrid ACO/GA
algorithm. The problem is coded in Gproc.
•• Both
GACO
and
one input
and
Let token
 of
GNGGGA
enter place
l1 of the
GNone
with
prochave
initial characteristic
output
places: “current problem description
(graph of the problem, problem constraints, etc.”
ion
ary
ithm
d
edthus a
ors, as
cs:
o
where
WGA,2 = “a next iteration is necessary”,
WGA,3 = ¬ WGA,2,
where ¬ P is the negation of predicate P.
n
A
odel
tions
spired
swith
ates
(GACO
em
ethod.
e.
veral
try we
heir
FF
ACO/GA
stics.
lem to
G
closer
o
find .
PROC
mber
of
and one
e
gents
erent
whole
rators
input for
em)
on
s
ion
ary
ithm
d
edthus a
ors, as
cs:
o
Constructing
Constructingthe
theGN
GNmodel
model
•
Let token  of GN Gproc enter place l1 of the GN with
initial characteristic “current problem description
(graph of the problem, problem constraints, etc.”
• The -tokens from places l2 or l5 enter place iACO without a
new characteristic. It transfers through GN GACO and going
out of it (through place oACO) obtains the characteristic
where
WGA,2 = “a
next iteration
“current
solutionsis
ofnecessary”,
ACO-algorithm”.
WGA,3 = ¬ WGA,2,
where ¬ P is the negation of predicate P.
n
A
odel
odel
tions
spired
swith
ates
(GACO
em
ethod.
e.
veral
try we
heir
FF
ACO/GA
stics.
lem to
G
closer
o
find .
PROC
mber
of
and
one
e GN with
e
gents
iption
erent
whole
, etc.”
rators
input for
em)
on
s
ion
ary
ithm
d
edthus a
ors, as
cs:
o
P.
Constructingthe
theGN
GNmodel
model
Constructing
• where
WACO,4 = “The end-condition is satisfied”,
• The
-tokens
places l2 or l5 enter place iACO without a
WACO,5
= ¬ Wfrom
ACO,5
new characteristic. It transfers through GN GACO and going
• out
When
truth-value
WACO,4
is “true”,
token  enters
of it the
(through
place of
oACO
) obtains
the characteristic
place l4 with the characteristic “representation of the current
“current solutions
of ACO-algorithm”.
solutions (populations)
in appropriate
form of the GA”.
• Otherwise, it enters place l5 without a new characteristic.
model
n
A
odel
odel
tions
spired
swith
ates
(GACO
em
ethod.
e.
veral
try we
heir
FF
ACO/GA
stics.
lem to
G
closer
o
find .
PROC
mber
of
and
one
e GN with
e
gents
iption
erent
whole
, etc.”
rators
input for
em)
on
s
ion
iACO without a
ary
andagoing
ACO
ithm
d
thus
ed
racteristic
ors, as
cs:
o
Constructing
Constructingthe
theGN
GNmodel
model
• • where
Token from place l4 enters place iGA with the characteristic
WACO,4 = “The
end-condition
satisfied”, of the GA”.
“current
populationis(solutions)
WACO,5 = ¬ WACO,5
opulation
• When the truth-value of WACO,4 is “true”, token  enters
place l4 with the characteristic “representation of the current
solutions (populations) in appropriate form of the GA”.
P.
• Otherwise, it enters place l5 without a new characteristic.
model
model
n
A
odel
odel
tions
spired
swith
ates
(GACO
em
ethod.
e.
veral
try we
heir
FF
ACO/GA
stics.
lem to
G
closer
o
find .
PROC
mber
of
and
one
e GN with
e
gents
iption
erent
whole
, etc.”
rators
input for
em)
on
s
ion
iACO without a
ary
andagoing
ACO
ithm
d
thus
en  enters
ed
racteristic
ors,
as
cs:
on
of
the current
o
opulation
of
the GA”.
haracteristic.
P.
8th IMACS Seminar on Monte Carlo Methods
August 29–September 2, 2011, Borovets, Bulgaria
Constructing the GN model
Thank you
for your attention!
• Token
Vassia Atanassova
Fidanova
from place Stefka
l4 enters place
iGA with the characteristic
“current population
(solutions) of the GA”.
Ivan Popchev
Panagiotis Chountas
Acknowledgment to Grants DID-02-29 “Modeling Processes with Fixed Development Rules” and
DTK-02-44 “Effective Monte Carlo Methods for Large-Scale Scientific Problems” by
National Science Fund of Bulgaria, and Grant JP 100372 by Royal Society, UK
model
model
n
A
odel
odel
model
tions
spired
swith
ates
(GACO
em
ethod.
e.
veral
try we
heir
FF
ACO/GA
stics.
lem to
G
closer
o
find .
PROC
mber
of
and
one
e GN with
e
gents
iption
erent
whole
, etc.”
rators
input for
em)
he
characteristic
on
s
ion
the GA”.
iary
ACO without a
andagoing
ACO
ithm
d
thus
en  enters
ed
racteristic
ors,
as
cs:
on
of
the current
o
opulation
of
the GA”.
haracteristic.
P.
8th IMACS Seminar on Monte Carlo Methods
August 29–September 2, 2011, Borovets, Bulgaria
Thank you
for your attention!
Vassia Atanassova
Stefka Fidanova
Ivan Popchev
Panagiotis Chountas
Acknowledgment to Grants DID-02-29 “Modeling Processes with Fixed Development Rules” and
DTK-02-44 “Effective Monte Carlo Methods for Large-Scale Scientific Problems” by
National Science Fund of Bulgaria, and Grant JP 100372 by Royal Society, UK