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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

0.1

0.2

0.3

0.4

0.5

0.6

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0.9

1

1

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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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

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0.7

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0.9

1

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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0.8

0.9

1

µ = 1/2 µ = 2

Bio-inspired network protocols

Objectives Ants Slime mold Physarum polycephalum Summary

Sample problems

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

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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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0.31

0.36

0.33

km

km

0

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1

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km

km

0

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1

Matlab Qualnet

Bio-inspired network protocols

Objectives Ants Slime mold Physarum polycephalum Summary

Sensor actor networks with µ = 2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

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1

0.27

0.40

0.33

km

km

0

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0 0.2 0.4 0.6 0.8 10

0.1

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0.27

km

km

0

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1

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

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