Self-Balancing Multimemetic Algorithms in Dynamic Scale-Free Networks

Evostar 2015 - The Leading European Event on Bio-Inspired Computation
Self-Balancing Multimemetic Algorithms in
Dynamic Scale-Free Networks
Rafael Nogueras Carlos Cotta
Departamento de Lenguajes y Ciencias de la Computación
Universidad de Málaga, Spain
EvoCOMPLEX 2015, Copenhagen, 8-10 April 2015
Self-Balancing MMAs in Dynamic Scale-Free Networks Universidad de Málaga 1 / 18

Introduction Model Description Experimental Analysis Conclusions
Parallel Computing & EAs
Use of parallel and distributed
models of EAs (GAs, MAs,
MMAs, etc.) to improve solution
quality and reduce computational
times.
The island model spatially
organizes populations into
partially isolated panmictic
demes.
island1
island2
island3
island4
migrants

Emergent Paralell Environments
Two emergent computational environments are offering new
opportunities to EAs:
I P2P networks: Equally privileged computing nodes carry out a
distributed computation without need for central coordination.
I Desktop Grids: Distributed networks of heterogeneous systems
which typically contribute computing cycles while they are
inactive (volunteer computing platforms).
Churn
The combined effect of multiple computing nodes leaving and
entering the system along time.

Scope
The connection topology of computing nodes is often fixed:
Goal
Study EAs running on unstable computational environments with
dynamic scale-free topology:
I Use of dynamic rewiring policies.
I Impact on performance and interplay with other
fault-tolerance techniques.

Network Topology
Scale-free networks are commonly observed in many natural
phenomena. They are characterized by a power-law distribution in
node degrees.
This kind of networks is often the result of processes driven by
preferential attachment.
1
2 3
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10
0
10
1
10
−2
10
−1
10
0
10
1
α=−1.9346
degree
P(degree)
Cumulative distribution function

Network Topology
Algorithm 1: Barabási-Albert Model
function BA-Model (↓ m, n : N) : Network
m0 ← min(n, m);
net ← CreateClique(m0);
δ[1 . . . m0] ← m0;
for i ← m0 + 1 to n do
net ← AddNode(net);
for j ← 1 to m do
k ← Pick(δ) // Sampling w/o replacement ∝ δ
δ[k] ← δ[k] + 1;
net ← AddLink(net, i, k);
end
δ[i] ← m;
end
return net

Instability
Algorithms must be executed on platforms with multiple
computing elements (processors)...
...but distributed platforms are prone to errors.
0 100 200 300 400 500 600 700 800 900 1000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
time
survival
probability
k=1
k=2
k=5
k=10
k=20
We assume node availability
follows a Weibull distributiona:
p(t1 | t0) = e
−
h
t1
β
η
−

t0
β
ηi
If the scale parameter η 1 the
hazard rate increases with time.
a
J Grid Comput, doi: 10.1007/s10723-014-9315-6, 2015

Coping with Instability
Computing in an unstable environment requires fault-tolerance.
Classical approaches are redundancy or checkpointing. Note that:
I These strategies require access to external safe storage and
possibly some central monitoring.
I As nodes go up and down, overall population size will
fluctuate.
An alternative strategy is used1:
I No central command required: decision making and
information exchange is done locally among neighboring
islands.
I Qualitative exchange of information among islands.
1
Comput Appl Math, doi: 10.1016/j.cam.2015.03.047

Self-Balancing
Node B
10
Node A
20
Node C
25
ping
pong
status?
status(10,3)
push(5)
15
15
ping
pong
status?
status(25,2)
request(5)
push(5)
20 20
msc Balancing routine for node A
Node B
16
Node A
40
status(16,4)
push(12)
28
28
30
ping
grow(7)
37
msc Resizing population upon neighbor failure
Compensate the loss of islands and balance population sizes2.
2
Comput Appl Math, 10.1016/j.cam.2015.03.047, 2015.

Dynamic Rewiring
When no rewiring, networks become more sparse and even
disconnected:
I Restricted flow of information via migration among islands.
I Disrupted functioning of balancing algorithms for frequent
reinitializations from scratch.
Rewiring strategy proceeds as follows:
I Inactive neighbors during balancing are forgotten.
I When the number of active neighbors of an island is below a
threshold, additional neighbors are searched.
I Rewiring is performed according to the BA model.

Dynamic Rewiring
Evolution of a volatile network (nι = 32, k = 10).
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32
t = 100
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t = 250
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t = 500
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t = 100
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30
t = 250
1
2
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22 23
30
t = 500

Benchmark and Settings
Parameters for island-based model:
I nι = 32 islands and µ = 16 individuals (at the beginning).
I m = 2 (BA model).
Node deactivation/reactivation:
I shape parameter η = 1.5.
I scale parameters β = −1/ log(p) for p = 1 − (knι)−1,
k ∈ {1, 2, 5, 10, 20, ∞}.
Problems used:
I Deb’s trap function (concatenating 32 four-bit traps).
I HIFF function (using 128 bits).
I MMDP (using 24 six-bit blocks).
25 runs @ 50,000 evaluations are performed for each problem and
algorithm.

Numerical Results
Approximation to the Optimum
Deviation from the optimum as a function of the churn rate. From
left to right: TRAP, HIFF and MMDP.
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
70
80
90
100
1/k
deviation
from
optimum
(%)
noB
noB
r
LBQ
LBQ
r
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
70
80
90
100
1/k
deviation
from
optimum
(%)
noB
noB
r
LBQ
LBQ
r
0 0.2 0.4 0.6 0.8 1
0
10
20
30
40
50
60
70
80
90
100
1/k
deviation
from
optimum
(%)
noB
noB
r
LBQ
LBQ
r
Performance degrades with increasing churn rates but not in the
same way for the different algorithms.

Numerical Results
Evolution of Best Fitness
Evolution of best fitness on the TRAP function for different churn
rates. From left to right: noB, LBQ and LBQr .
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10
4
14
16
18
20
22
24
26
28
30
32
evaluations
best
fitness
k=1
k=2
k=5
k=10
k=20
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10
4
14
16
18
20
22
24
26
28
30
32
evaluations
best
fitness
k=1
k=2
k=5
k=10
k=20
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10
4
14
16
18
20
22
24
26
28
30
32
evaluations
best
fitness
k=1
k=2
k=5
k=10
k=20
Rewiring increases performance for high churn rates.

Numerical Results
Spectral Analysis
10
0
10
1
10
−3
10
−2
10
−1
frequency
PSD
0 0.2 0.4 0.6 0.8 1
−1.8
−1.6
−1.4
−1.2
−1
−0.8
1/k
spectrum
slope LBQ
LBQr
The dynamics for increasing churn goes from Brown noise ∝ f −2
to pink noise ∝ f −1.

Numerical Results
Mean Size of Islands
k = 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10
4
16
18
20
22
24
26
28
30
32
34
evaluations
mean
popsize
LBQ
LBQr
k = 2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10
4
16
18
20
22
24
26
28
30
32
evaluations
mean
popsize
LBQ
LBQr
Rewiring in the presence of high churn results in decreasing island
sizes.

Conclusions
Performance in unstable computational environments requires
churn-aware strategies.
Rewiring policies keeping the global network connectivity pattern
result in increased resilience and better performance.
Future work:
I scalability analysis and study of the influence of network
parameters,
I analyze other rewiring strategies,
I design more complex fault-aware policies.

Thank You!
AnySelf Project
Please find us in Facebook
http://facebook.com/AnySelfProject
and in Twitter
@anyselfproject

Self-Balancing Multimemetic Algorithms in Dynamic Scale-Free Networks

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