1. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Automatic Placement of Wireless Mesh
Nodes via Genetic Algorithms
Giuseppe De Marco
Department of Information System Engineering,
Toyota Technological Institute, Nagoya, Japan
NbiS2008, Turin, Italy
September 1 - 5, 2008
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
2. Mesh Networks Goal Graph Drawing Simulations Conclusion
Outline
1 Mesh Networks
2 Main Objective
3 Graph Drawing
GAMESH: Coding
GAMesh: Fitness function
4 Simulation
5 Conclusions
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
3. Mesh Networks Goal Graph Drawing Simulations Conclusion
Mesh Networks
• Profitable Ad hoc networks
• Extend Internet connectivity via radio links (last mile problem)
• Rural villages, communities, nomadic users
• Very cost effective: installation/area/bps
Antenna type Cost
Omnidirectional 10k ∼ 100k × km2
Directional 1k ∼ 10k × km2
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
4. Mesh Networks Goal Graph Drawing Simulations Conclusion
Mesh Networks
Mesh Node (MN)
Mesh Portal
Internet connection
Test Point (TP) or Mesh Client
Usually divided in backhaul and access network:
• Backhaul has different channels/ tx. power
• Bakchaul can have different spatial reuse
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
5. Mesh Networks Goal Graph Drawing Simulations Conclusion
Our goals
• How to displace the mesh nodes?
• Some Theoretical results
• Gupta & Kumar and al. → nodes density vs. transmission power
• Extended to directive antennae [H-N. Dai et al., INFOCOM2008]
• Which constraints do matter?
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
6. Mesh Networks Goal Graph Drawing Simulations Conclusion
Our goals
• How to displace the mesh nodes?
• Some Theoretical results
• Gupta & Kumar and al. → nodes density vs. transmission power
• Extended to directive antennae [H-N. Dai et al., INFOCOM2008]
• Which constraints do matter?
• Connectivity of backhauls
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
7. Mesh Networks Goal Graph Drawing Simulations Conclusion
Our goals
The displacement problem can be defined as follow.
Definition
In general, the problem is like a vertex-covering problem. Given a set Vacc
of m Test Points (TP), and a set V of m MNs to be deployed in A, find
the best arrangement of MNs s.t. the graph G(V, E) is connected and
every v ∈ Vacc has a link to an u ∈ V (covering)
TP
MN
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
8. Mesh Networks Goal Graph Drawing Simulations Conclusion
Related work
• Choose a set of Candidate Site (CS) and find the minimum subset
• Linear/Mixed Programming with some constraints1
• Cons: consider only a subset of available points. Measurement
campaign is needed
• Our Contribute: Consider all available CS and use a simpler
modeling
1
E. Amaldi, A. Capone, M. CESANA, I. Filippini, F. Malucelli, Optimization Models
and Methods for Planning Wireless Mesh Networks, Computer Networks, Elsevier, Vol.
52, Issue 11, August 2008, Page(s) 2159-2171
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
9. Mesh Networks Goal Graph Drawing Simulations Conclusion
To our aim, we use GA. Why?
• Linear Programming unfeasible.
• Other techniques (force-directed drawing) hard to adapt to constraints
GAMesh synopsis:
• coding based on 2D-square of nodes
• cross-over based on squares-content swapping
• several mutation methods
• constraints via penalty functions
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
11. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Cross-over
1
1
8
8
2
5
3
6
7 4
1
6
5
3
4
6
5
5
3
6
3
1
1
4
4
7
2
2
7
1
7
2
rect1 rect1
rect2 rect2
parent 1 parent 2
child 1 child 2
Standard cross-over mechanisms (string based) not work (similar to TSP
problem).
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
12. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Mutation
1 SingleMutate: picks up a single node and move it in a random
position in the plane.
2 RectMutate: picks up two squares in the plane and move the content
of one square to the other one.
3 SmallMutate: picks up a single node and move it by a fixed step (=3).
4 SmallRectMutate: picks a square of nodes and move it by a fixed step
(=3).
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
13. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Fitness function
GAMesh uses combinatorial optimization, i.e. the optimization is tied to
the combination of nodes. What function to optimize?
Hints (constraints)
1 The network must be connected
2 The network must cover all TPs
3 The network should satisfy other constraints
• Minimum interference
• Minimum installation cost, K
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
14. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Fitness function
Some notes
• Giant component C0 of G(V, E) → the largest connected component
• Degree Di = j aij
Figure: |C0| = 5
8
i
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
15. Mesh Networks Goal Graph Drawing Simulations Conclusion
GAMesh: Fitness function
It’s very simple to recognize that the key parameter is maxi(D) and C0
• ↓ maxi(D) ⇒↓ K
• For omnidirectional antenna
• ↓ maxi(D) ⇒↓ Di ⇒↓ Interference
• For directive antenna we suppose that interference is neglectable
We can set also contraints on D to make redundant the network (not a
tree)
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
16. Mesh Networks Goal Graph Drawing Simulations Conclusion
Fitness function
We use a threshold Th on C0: bad individuals have C0 < 1
We can derive the fitness function by imposing that
−
max(D)
n − 1
+ w(p0) > 1 (1)
∂w
∂p0
< 0 (2)
f(s) =
|C0|
n , if |C0| < Th
−max(D)
n−1 + 2(2 − p0)2, if |C0| ≥ Th
(3)
n number of MNs
p0 = #isolated
m
Th threshold
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
17. Mesh Networks Goal Graph Drawing Simulations Conclusion
Constraints
Use of a penalty function
f(s) = −
max(D)
n − 1
+ 2(2 − p0)2
+
O
i=1
ǫiΦi , |C0| ≥ Th (4)
In this work:
• Constraint on the access network capacity, θi
• Constraint on the backhaul network capacity, ρij
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
18. Mesh Networks Goal Graph Drawing Simulations Conclusion
By assuming perfect scheduling and ρij = ρ, θi = θ:
Φ1 =
1 −
1
ρnD (i,j)∈E
(fi + fj)
Φ2 = 1 −
λ0d
θ
where fi is the traffic demand of access net.
Di=2
id =5
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
19. Mesh Networks Goal Graph Drawing Simulations Conclusion
Simulation
Table: GAMesh parameters
Initial pop. Mutation rate Crossover square(m) Grid step(m)
50 0.02 8 20
Table: Simulation parameters. Bit rates are in Mbps.
Service Area(m2) Position of TPs n MPs λ0 θ ρ
L2 = 8002 l1 = L
2 , l2 = L 15 1 0.5 11 54
User traffic demand λ0, access trafficf = λ0θd. GAMesh uses a
termination condition based on relative improvements.
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
20. Mesh Networks Goal Graph Drawing Simulations Conclusion
Simulations: Other parameters
Radio parameters
L ≤ LTh Pt − PRX ,
where PRX is the sensitivity of the receiver end.
We set LTh = 55dB and LTh = 48dB, for the BN and the AN, respectively.
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
23. Mesh Networks Goal Graph Drawing Simulations Conclusion
0 20 40 60 80 100 120 140 160 180 200
0
10
20
30
40
50
60
70
80
90
100
%
iteration
min(n
0
)
Median n
0
Median(1−Tav
)
Median(1−T
v
)
Table: GAMesh iterations
(ite) for different values of
the grid size.
grid size ite Var(ite)
50 158.60 42.3089
80 180 80.1
100 179 60.0462
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
24. Mesh Networks Goal Graph Drawing Simulations Conclusion
Conclusions
In this work, we presented GAMesh, a framework for wireless mesh
network design
• Algorithm features
• Graph combination through single objective function
• GAMesh explores all points in the plane
• The running time depends on n and pop. size
• It does not depend on the grid size!
• Multiple constraints embedded in f(s)
• In regard to wireless mesh net
• Few parameters, D and p0, can describe the problem (interference,
cost, traffic...)
• No need to make measurements (in theory)
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco
25. Mesh Networks Goal Graph Drawing Simulations Conclusion
Conclusions
Further investigations
• Consider the Digital Elevation Map of the area...
• ...consider also the height of the MN
• Abstract model of radio propagation
• Flow graph (for testing routing feasibility)
• Multiobjective, vertex-covering + GAMesh, i.e. automatic setting of
the minimum of n
GAMesh: Automatic Placement of Wireless Mesh Nodes via Genetic Algorithms Giuseppe De Marco