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Objectives Ants Slime mold Physarum polycephalum Summary
Bio-inspired network protocols
Department of Mathematical SciencesUniversity of Delaware
Supported byArmy SBIR A072-074-1669, NSF CCF-0726556 and CCF-0829748
November 5, 2013
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Graduate students
Wei Chen
Rui Fang
Zequn Huang
Jeremy Keffer
Ke Li
Claudio Torres
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is swarm intelligence?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Modeling and analysis objectives
Construct a complete mathematical model of a basicant-based routing protocol (BARP) and slime mold basedsensor network protocols.
Analyze the model to extract design principles.
Compare with QualNet simulations.
Refine/improve the model.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Individual ant properties
Lifespan: 1-2 years.
Individually inept.
Nearly blind.Fast movers and carriers.Can lay chemical trails of pheromones and detecttrails.Can consume food and regurgitate food throughantennation.
Very simple programming.earching for food (foraging), carrying food,recruiting others, alarm, attack.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Individual ant properties
Lifespan: 1-2 years.
Individually inept.
Nearly blind.Fast movers and carriers.Can lay chemical trails of pheromones and detecttrails.Can consume food and regurgitate food throughantennation.
Very simple programming.earching for food (foraging), carrying food,recruiting others, alarm, attack.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Individual ant properties
Lifespan: 1-2 years.
Individually inept.
Nearly blind.Fast movers and carriers.Can lay chemical trails of pheromones and detecttrails.Can consume food and regurgitate food throughantennation.
Very simple programming.earching for food (foraging), carrying food,recruiting others, alarm, attack.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Individual ant properties
Lifespan: 1-2 years.
Individually inept.
Nearly blind.Fast movers and carriers.Can lay chemical trails of pheromones and detecttrails.Can consume food and regurgitate food throughantennation.
Very simple programming.Searching for food (foraging), carrying food,recruiting others, alarm, attack.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Ant colony properties
Lifespan: 10’s of years.
No central control!
Robust. Resilient to environmental changes.
Capable to solving sophisticated problems such as finding theminimum path between the hive and food sources withmultiple barriers and obstacles.
Inspiration for “swarm” algorithms.
Ants account for 15% - 20% of the terrestrial animal biomasson Earth. In tropical climates, estimates are closer to 25%.By this assessment, they are the most successful animals onEarth!
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
Random noisy exploration
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
HmmmHmmm
Stimergy (deposition of pheromone).
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
???
Evaporation.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
Nonlinear reinforcement.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A heuristic for swarm optimization
Food
Nest
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Forward ant propagation
pij =(τij)
α (ηij)β (ψij)
γ∑h∈Ni
(τih)α (ηih)β (ψih)β,
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Forward ant propagation
pij =(τij)
β∑h∈Ni
(τih)β,
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Forward ant propagation
pij =(τij)
β∑h∈Ni
(τih)β,
Ideal communication: ~y (n+1) = P(n)(β)~y (n), P(n) = [pij ].
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Timescales
There are three critical timescales.
h1: time interval over which pheromone evaporates.
h2: time interval at which ants are released into the network.
h3: typical time required to make a single hop.
We assume h3 � h1 ≤ h2 and m = h2/h1.
τ(n+1)ij = (1− h1κ1)mτ
(n)ij + h2κ2
∞∑k=1
1
kp̃sdij (k)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Nonlinear dynamics
~y (n+1) =P(β)~y (n),
~τ (n+1) =(1− h1κ1)m2τ(n)ij + h2κ2
∞∑k=1
1
kp̃sdij (k),
Goal: Identify stationary states of this system, and dynamicresponse to perturbations.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Nonlinear dynamics
Λτij =∞∑k=1
1
kp̃sdij (k), Λ = κ1/κ2.
Goal: Identify stationary states of this system, and dynamicresponse to perturbations.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Model prediction versus Qualnet Simulations
n1
n2
(2.5688,2.5884,2.6098)
n3
(0.2275,0.2199,0.2142)
n4
(0.1456,0.1344,0.1334) n5
(0.0819,0.0854,0.0809)
(0.2275,0.2199,0.2142)
(0.0000,0.0000,0.0000)
(0.0819,0.0854,0.0809)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Experiments on a simple 5 node network
The structure of stable solutions varies based on the routingexponent β:
Example
S1: β = 0.5, Λ = 0.3,
multi-route solution
S5: β = 2, Λ = 0.3,
single-route solution
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Trials with varying β
The multi-route solution is dynamically connected to the single-route solution
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Varying β
After ramping up β from 0.5 to 2 by time step h3, multiple routesolutions will gradually shift to the stable single route solution:
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Design principles for larger networks
Time of Simulation 199.99N 200β 0.5→ 2Λ 0.3h1 1h2 1h3 0.01
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Large 50-node networks
Following are some parameters we used Matlab and Qualnetparameters:
Simulation time 200N 200β 0.5→ 2Λ 0.3h1 1h2 1h3 0.01
Random initial conditions.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 0 (β = 0.5)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 30 (β = 0.5)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 50 (β = 0.5→ 2)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 65 (β = 0.5→ 2)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 80 (β = 0.5→ 2)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Exploiting the dynamics
T = 100 (β = 2)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Hop count versus time
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Statistical comparison
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Problem: Sensor networks
Given an ad-hoc network of data sources, relay nodes (data sourceswithout data) and a data sink, how do we move the data from thesources to the sink?
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
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Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is Physarum polycephalum?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is Physarum polycephalum?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is Physarum polycephalum?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is Physarum polycephalum?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
What is Physarum polycephalum?
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Mold solves hard problems
Steiner problems...
Slime mold solves the problems without central control.T. Nakagaki, A Tero. et al. Nature 407 (2000), Proc. Roy. Soc. 271 (2004), J. Theo. Bio. 244 (2007)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Mold solves hard problems
Steiner problems...
Slime mold solves the problems without central control.T. Nakagaki, A Tero. et al. Nature 407 (2000), Proc. Roy. Soc. 271 (2004), J. Theo. Bio. 244 (2007)
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Mold and singular potentials
Attack the problem with an electrostatic model.Application: Sensor/Actor networks.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
The Tero model for slime mold
Model the sensor network as a system of pipes.
qij =Dij
Lij(pi − pj),∑
j∈Ni
qij =mi ,
dDij
dt=f (|qij |)− rDij ,
where
f (x) = rDmaxa|x |µ
1 + a|x |µ.
p
p
p
1
3
2
i
p
qi1
qi2
qi3
mi
Note that we need to globally solve the pressure equation.m→ p → q.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
The pressure equation
p
p
p
1
3
2
i
p
qi1
qi2
qi3
mi
∑j∈Ni
Dij
Lij(pi − pj) = mi
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Synchronized wireless Jacobi iterations
∆ tsync
∆ tsync
∆ tsync
∆ tsync
∆ tsync
∆ tsync
∆ tsync
∆ tsync
∆ tsync
t=0
t=0
Solve ODE
Solve for p2
Solve ODE
Solve for p1
Node 1 time
Node 2 time
Real time
Sen
d p
, D
2
12
Sen
d p
, D1
12
Sen
d p
, D
212
Sen
d p
, D1
12
pi ←mi +
∑j∈Ni
Dij
Lijpj∑
j∈Ni
Dij
Lij
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A very small network
µ = 1/2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A very small network
µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
A very small network
Linear stability of stationary states in the network.
µ = 1/2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Sample problems
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µ = 1/2 µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Sample problems
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µ = 1/2 µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Robustness - degree distribution
10% sources
1 2 3 4 5 6 7 8 9 10 110
0.1
0.2
0.3
0.4
0.5
Node Degree (d)
P(d
)
µ = 0.5µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Robustness - degree distribution
30% sources
1 2 3 4 5 6 7 8 9 10 110
0.1
0.2
0.3
0.4
Node Degree (d)
P(d
)
µ = 0.5µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Robustness - degree distribution
50% sources
1 2 3 4 5 6 7 8 9 10 110
0.1
0.2
0.3
0.4
Node Degree (d)
P(d
)
µ = 0.5µ = 2
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Fault tolerance
10% 30% 50%
µ 0.5 2 0.5 2 0.5 2
1-fault 1 .9851 .9856 .9761 .9799 .9530
2-fault .9998 .9700 .9709 .9616 .9595 .9070
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Impact on performance
0 5 10 15 20µ=0.5
0
5
10
15
20µ=
2
10% sources20% sources30% sources40% sources50% sources
Expected hop count
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Extension to sensor actor networks
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Sensor actor networks with µ = 0.5
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0.33
km
km
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km
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Matlab Qualnet
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Sensor actor networks with µ = 2
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Matlab Qualnet
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Summary
Our model for ant-based and slime-based protocols capturesactual protocol behavior well.
Using pressure rather than pheromone poses special problemson ad-hoc networks that can be addressed with theasynchronous Jacobi algorithm.
Nonlinear dynamics helps us understand phase transitionswhen we vary the routing or flux exponent.
Design principles from small networks transfer to largenetworks.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Summary
Our model for ant-based and slime-based protocols capturesactual protocol behavior well.
Using pressure rather than pheromone poses special problemson ad-hoc networks that can be addressed with theasynchronous Jacobi algorithm.
Nonlinear dynamics helps us understand phase transitionswhen we vary the routing or flux exponent.
Design principles from small networks transfer to largenetworks.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Summary
Our model for ant-based and slime-based protocols capturesactual protocol behavior well.
Using pressure rather than pheromone poses special problemson ad-hoc networks that can be addressed with theasynchronous Jacobi algorithm.
Nonlinear dynamics helps us understand phase transitionswhen we vary the routing or flux exponent.
Design principles from small networks transfer to largenetworks.
Bio-inspired network protocols
Objectives Ants Slime mold Physarum polycephalum Summary
Summary
Our model for ant-based and slime-based protocols capturesactual protocol behavior well.
Using pressure rather than pheromone poses special problemson ad-hoc networks that can be addressed with theasynchronous Jacobi algorithm.
Nonlinear dynamics helps us understand phase transitionswhen we vary the routing or flux exponent.
Design principles from small networks transfer to largenetworks.
Bio-inspired network protocols