towards a 2-dimensional self-organized framework for structured population-based metaheuristics
DESCRIPTION
Presentation of the paper "Towards a 2-dimensional Self-organized Framework for Structured Population-based Metaheuristics". IEEE International Congress on Complex Systems, Agadir, Morocco, 2012TRANSCRIPT
Towards a 2-dimensional Self-organized Framework for Structured Population-based Metaheuristics
Carlos M. Fernandes1,2
J.L.J. Laredo3
J.J. Merelo1
Carlos Cotta4
Agostinho C. Rosa2
1Department of Computers Architecture and Technology, University of Granada, Spain
2 LaSEEB-ISR-IST, Technical Univ. of Lisbon (IST), Portugal3 University of Luxembourg
4 University of Malaga
2
Objectives and Motivation
ICCS 2012, Agadir, Morocco
Objective: describe the properties of a swarm of simple entities that interact (communicate) on a 2-dimensional heterogeneous environment.
Motivation: improve the state-of-the-art on dynamic population structures for bio-inspired algorithms.
Local rulesStigmergySelectionStochastic no central coordination
3
Non-panmictic Evolutionary Algorithms (Eas)
ICCS 2012, Agadir, Morocco
Island Models
Cellular EAs
EAs are based on the selection, recombination and mutation of populations of solutions
Panmictic EAs
Non-Panmictic EAs
4
Particle Swarm Optimization
ICCS 2012, Agadir, Morocco
Bio-inspired: bird flocks and fish schools.
Topology: ring, star,...
5
The System
ICCS 2012, Agadir, Morocco
Habitat: 2-dimensional toroidal grid of nodes with size N×N
Swarm: population of n particles (p) with a random fitness value [0,1].
Initialization: the particles are randomly distributed in the grid
Dynamics: particles move to neighboring sites
Communication: particles leave marks (m) with their “status”
Evaporation: marks are erased after one iteration
Rules:check free nodes in Moore neighbourhood.if no free nodes → don’t moveif no marks → random siteif marks → move to more similar
P P P
P P P
P P P
P
P P P
m P P
P m
m
fitness
6
Self-Organization
ICCS 2012, Agadir, Morocco
Local rules → Global patterns
Dynamic, robust and displays power-laws
Self-Organized Criticality (SOC)
Edge of Chaos (EOC)
Highly Optimized Tolerance (HOT)
Self-Organized complex system?
No central coordination
No order, no chaos
7
Dynamic Behaviorone dimension
ICCS 2012, Agadir, Morocco
n=25
n=50
n=75
n=100
Space-time diagrams of a 1-dimensional habitat with 150 nodes
8
Dynamic Behaviortwo dimension
ICCS 2012, Agadir, Morocco
()
t = 0
t = 1
t = 0
t = 0
t = 0
t = 0
t = 0
t = 0
t = 0
t = 9
t = 10
t = 1000t = 500t = 250t = 100
k =4.02 k =4.02k =4.00k =3.77
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Dynamic Behavior2D: clustering degree and distance
ICCS 2012, Agadir, Morocco
0 75 1502253003754505256006757508259009752.5
3
3.5
4
4.5
iteration t
k
0 75 1502253003754505256006757508259009750
0.05
0.1
0.15
0.2
0.25
iteration t
d
1 10 100 1000 100000.01
0.1
1
10
100
1000f(x) = 2553.98182 x^-1.1750431R² = 0.742468825507372
k
frequency
inte
nsi
ty
1 10 100 1000 100000.01
0.1
1
10
100
1000
f(x) = 77.9227875 x^-0.9867793R² = 0.700408288010165
d
frequency
inte
nsi
ty
k, average clustering degree (number of neighbours)
d , average distance (difference between fitness values) to neighbours
10
Dynamic Behavior2D: robustness
ICCS 2012, Agadir, Morocco
n:nodes→ 1:24 1:12 1:6 1:3 1:2 1:1.5 1:1.2
k1.18(0.76)
1.23(0.76)
1.23(0.76)
1.20(0.76)
1.07(0.70)
0.88(0.60)
0.56(0.60)
d0.82
(0.60)1.00(0.72)
0.97(0.68)
1.01(0.69)
1.00(0.69)
0.93(0.64)
0.42(0.60)
n→ 33 75 147 300 616 1200 2408 4800
k1.15
(0.72)1.29
(0.77)1.18
(0.75)1.22
(0.77)1.18
(0.74)1.20
(0.76)1.17
(0.74)1.18
(0.76)
d0.87
(0.62)1.04
(0.70)1.04
(0.71)1.10
(0.75)1.03
(0.70)1.01
(0.69)1.02
(0.69)0.97
(0.69)
n = 300 n = 600 n = 1200 n = 1800 n = 2400 n = 3000
Slope and r-squared of the power-laws
k =3.18 k =3.88k =3.92 k =4.58 k =6.27k =5.28d =0.038 d =0.076 d =0.243d =0.190d =0.144d =0.085
10000 iterations
11
Dynamic Behavior2D: fitness distribution
ICCS 2012, Agadir, Morocco
t = 0
t = 10000
Distribution of the fitness values on the the habitat (darker → higher fitness)
12
Dynamic Behavior
ICCS 2012, Agadir, Morocco
10481120
1140
1160
1180
1200
k=0k=2
k=4k=6
k=80
50100150200250300350400450
t=0
part
icle
s
k=0k=2
k=4k=6
k=80
50100150200250300350400450
t=1
k=0k=2
k=4k=6
k=80
50100150200250300350400450
t=2
part
icle
s
050
100150200250300350400450
t=1000
number of particles that move in each iteration.
number of articles classified according to the clustering degree
13
Conclusions
o Local rules lead to complex behavior
o Particles form highly dynamic clusters connected by paths
o The system’s output variables (degree of clustering and distance between neighboring particles) display a power-law relationship
o The system is robust
ICCS 2012, Agadir, Morocco
14
Future Research
o Study the model under different fitness distributions (normal, for instance) and under perturbations (remove particles, change fitness values, etc)
o Increase the memory of the system.
o Use the model for designing a cellular GA.
o Use the model as a basis for a dynamic PSO topology.
o Investigate if the model fits into a Self-Organization theory (SOC, EOC, HOT)
ICCS 2012, Agadir, Morocco
15
Questions?
ICCS 2012, Agadir, Morocco