lecture 2: bio-inspired approaches - startseite tu ilmenau · lecture 2: bio-inspired approaches...

Bio-inspired Approaches

Dr.-Ing. Abdalkarim Awad

Prof. Dr.-Ing. habil. Andreas Mitschele-Thiel

Integrated Communication Systems Group

www.tu-ilmenau.de/ics

Lecture 2: Bio-inspired Approaches

Self-Organizing


20.10.2011






Lecture 1: Review

• Why Self-Organization

• Emergent Phenomena

• Direct and Indirect communication

• Feedback

• Decentralized Control






Characteristics of Biological Systems

• Complex behaviors on basis of limited set of basic rules

– Ant colony optimization

• Adaptive to the varying environmental circumstances

– Firefly synchronization

• Resilient to failures by internal or external factors

– Human Immune system

• Able to learn and evolve itself under new conditions

– Neural networks






Biological Models: Application Domains

• Application domains of bio-inspired solutions:

– Bio-inspired computing – a class of algorithms

focusing on efficient computing, e.g. for optimization processes and pattern recognition

– Bio-inspired systems – a class of system architectures for massively distributed and collaborative systems, e.g. for distributed sensing and exploration

– Bio-inspired networking – a class of strategies for efficient and scalable communication under uncertain network conditions, e.g. for autonomic organization in distributed network architectures






Biological Models: Application Domains

• Biological principles with application to

networking (examples):

– Ant Colony Optimization (ACO)

– Firefly Synchronization

– Artificial Immune System (AIS)

– Neural Networks (next week)






Swarm Intelligence (SI)

• Swarm Intelligence (SI) is

– computational techniques for solving distributed problems

inspired from biological examples provided by

• social insects such as ants, termites, bees, and wasps and

by swarm, herd, flock, and shoal phenomena such as fish

shoals (school of fish)

– Approaches to controlling and optimizing distributed

systems

– Resilient, decentralized, self-organized techniques






SI Organizing Principles

SI has the following notable features:

• Autonomy:

– The system does not require outside management or maintenance. Individuals are autonomous, controlling their own behavior both at the detector and effector levels in a self-organized way

• Adaptability:

– Based on local interaction, the system is able to adapt itself to changes

• Scalability:

– SI abilities can be performed using groups consisting of a few, up to thousands of individuals with the same control architecture.

• Flexibility:

– No single individual of the swarm is essential, that is, any individual can be dynamically added, removed, or replaced.






SI Organizing Principles

SI has the following notable features:

• Robustness:

– No central coordination takes place, which means that

there is no single point of failure

– It can recover form unexpected disruptions

• Massively parallel:

– Tasks can be performed by individuals within the group

same time.

• Emergence:

– The intelligence exhibited is not present in the individuals,

but rather emerges somehow out of the entire swarm..






SI Communication Forms

• Indirect communication

– Implicit communication that takes place between

individuals via the surrounding environment.

– Known as Stigmergy communication..

• Example

– Ants leave a chemical substance (pheromone )

• Direct Communication

– Explicit communication that can also take place between

individuals.

– Example:

• trophallaxis (food or liquid exchange

• , e.g. mouth-to-mouth food exchange)






Stigmergy

• Stigmergy: stigma (sign, mark) + ergon (work)

• Characteristics of stigmergy

– Indirect agent interaction modification of the environment

– The information is local: it can only be accessed by insects

that visit the locus in which it was released

– Work can be continued by any individual






SI: Main application

• SI principles have been successfully applied in a variety

of problem domains and applications:

Ant colony optimization (ACO),

• Which focuses on discrete optimization problems






• Ant Colony Optimization (ACO)






Ants

• Why are ants interesting?

– Ants solve complex tasks by simple local means

– Ants productivity is better than the sum of their single

activities

– Ants are grand masters in search and exploitation






Foraging behavior of Ants

• (Double bridge experiment)

Ants start with equal probability








The ant on shorter path has a shorter to-and-fro time from it’s nest to the food.








The density of pheromone on the shorter path is higher








The next ant takes the shorter route








Eventually, the shorter path is almost exclusively used






Travelling Salesman Problem (TSP)

• TSP description:

– Visit cities in order to make sales

– Save on travel costs

– Visit each city once (Hamiltonian circuit)

• A Hamiltonian cycle (or Hamiltonian circuit) is a cycle in an undirected graph which visits each vertex exactly once and also returns to the starting vertex.






From nature to computers

• The use of simple computational agents that work cooperatively

• In an iterative fashion, each ant moves from state Si to state Sj guided by two main factors:

1. Heuristic information:

A measure of the heuristic preference for moving from state Si to state Sj

This information is known a priori to the algorithm run, and is not modified during

2. Artificial pheromone trail(s):

A measurement of the pheromone deposition from ants previous transitions from state Si to state Sj

This information is modified during the algorithm run by the artificial ants






Ant Colony Optimization (ACO)

• Developed by Dorigo and Di Caro

• It is a population-based metaheuristic used to find

approximate solutions to difficult optimization problems

• ACO is structured into three main functions:

• AntSolutionsConstruct( )

– Performs the solution construction process

• PheromoneUpdate( )

– Performs pheromone trail updates

– Includes also pheromone trail evaporation

• DaemonActions( )

– An optional step in the algorithm which involves applying

additional updates from a global perspective






What is Metaheuristic?

• “A metaheuristic is a set of algorithmic concepts that can

be used to define heuristic methods applicable to a wide

set of different problems”

• In other words: “a metaheuristic is a general-purpose

algorithmic framework that can be applied to different

optimization problems with relatively few modifications”

…Dorigo, 1999

• Examples of metaheuristics:

– Tabu search

– Iterated local search

– …






Properties of the artificial ant

• Each artificial ant has an internal memory

• Starting in an initial state Sinitial each ant tries to build a feasible solution to the given problem, moving in an iterative fashion through its search space

• The guidance factors for ants movement take is a transition rule which is applied before every move from state Si to state Sj

• The amount of pheromone each ant deposits is governed by a problem specific pheromone update rule

• Pheromone deposition may occur at every state transition during the solution construction (pheromone trial update)

• Ants may retrace their paths once a solution has been constructed and only then deposit pheromone, all along their individual paths.






The original Ant System

• Developed by Dorigo et al. (1996)

• Ant system (AS)

– First ACO algorithm

– Pheromone updated by all ants in the iteration

• Travelling Salesman Problem (TSP) was used as a test-

bed for this algorithm.






PROBLEM DEFINITION

TSP:

Given a set of n cities, the Traveling

Salesman Problem requires a

salesman to find the shortest route

between the given cities and return

to the starting city, while keeping in

mind that each city can be visited

only once






TSP Problem

• Try all O(n!)

• 20 cities

• The resulting factorial of 20! is 19 digits long.

• 2432902008176640000 =2.4 e+18

• 100 cites

• The resulting factorial of 100! is 158 digits long.

• 933262154439441526816992388562667004907159682

643816214685929638952175999932299156089414639

761565182862536979208272237582511852109168640

000000000000000 00000000 =9.3 e+157

0 1

3 2

4






Solution for TSP

• A connected graph G=(V,E), where

– V is a set of vertices (cities)

– E is a set of edges (connection between cities)

• A variable called pheromone is associated with each edge and can be read and modified by ants

• Ant system is an iterative algorithm: at each iteration,

– A number of artificial ants are considered

– Each ant build a solution by walking from vertex to vertex

– Each vertex is visited one time only

– An ant selects the following vertex to be visited according to a

stochastic mechanism that is biased by the pheromone

• At the end, the pheromone values are updated on order to bias ants in the future iteration to construct solutions similar to the previously constructed






Ant System and the TSP

• The following steps is used to solve the TSP:

– Pheromone trail

– Memory

– Awareness of environment

– Probability function






Ant System and the TSP 1. Pheromone trail

– Iteration is defined as the interval in (t,t+1) where each of the N ants moves once

– Epoch n iterations (when each ant has completed a tour)

– Intensity of trail:

– Trail update function after each epoch:

– is the evaporation rate

– is the quantity of pheromone laid on path (i,j) by the ant k and is given by:

where is a constant and is the tour length of kth ant.

29

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Ant System and the TSP 2. Memory

– Prevents town repeats

– Tabu list

3. Awareness of environment

– City distance

– Visibility:

where

4. Probability function

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allowed if )( allowed

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ijij

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Ant System and the TSP

• Various improvements were made which gave rise to

several other ant algorithms which collectively form the

main ACO algorithms, such as:

– Max–Min Ant System

– Ant Colony System

– …..






Solving a Problem by ACO

Steps:

1. Represent the problem in the form a weighted graph, on

which ants can build solutions

2. Define the meaning of the pheromone trails

3. Define the heuristic preference for the ant while

constructing a solution

4. Choose a specific ACO algorithm and apply to problem

being solved

5. Tune the parameters of the ACO algorithm






Solving a Problem by ACO

• Scheduling

• Routing problems

– Traveling Salesman Problem (TSP)

– Vehicle routing

– Network routing

– …






TRAVELING SALESMAN PROBLEM (TSP)






REAL vs. ARTIFICIAL ANTS

• Discrete time steps

• Memory Allocation

• Quality of Solution

• Time of Pheromone

deposition

• Distance Estimation

REAL ANT ARTIFICIAL ANT






FLOWCHART OF ACO

Have all

cities been

visited

Have the

maximum

Iterations been

performed

START ACO

Locate ants randomly

in cities across the

grid and store the

current city

in a tabu list

Determine probabilistically

as to which city to visit next

Move to next city and

place this city in the

tabu list

Record the length of

tour and clear tabu list

Determine the shortest

tour till now and

update pheromone

NO

YES

STOP

ACO

YES NO






TSP-Example






Performance of TSP with ACO

heuristic

• Performs better than state-of-the-art TSP algorithms

for small (50-100) of nodes

• The main point to appreciate is that Swarms give us new algorithms for optimization






Firefly Synchronization







• Distributed precise synchronization hard to achieve

• Nature has surprising synchrony among independent actors

– Chirping crickets

– Flashing of fireflies

• Male fireflies flash to attract females (or meals!)

• Do not follow a leader

• Period between flashes is constant

– internal clock

• Flash at beginning of cycle

– initially random

• Each firefly is exposed to flashes of neighbors

– Resets the timing of flashes

– Self-organized synchrony






• Oscillators assume to interact by a simple

form of pulse coupling

– When a given oscillator fires, it pulls all the

other oscillators up by an amount , or pulls

them up to firing.

– Whichever is less







Firefly Synchronization - The Model

• New models inspired from synchronization principles of fireflies

• Firefly synchronization is based on pulse-coupled oscillators Integrate-and-fire oscillator → xi from 0 to 1 → oscillator fires when xi = 1, then xi comes back to 0

• Multiple oscillators interact in form of simple pulse coupling:

• When a given oscillator fires, it pulls the others up by a fixed amount, or brings them to the firing threshold, whichever is less:

• For almost all initial conditions the population evolves to a state in which all the oscillators are firing synchronously






• Generalize the integrate and fire dynamics

– Assume only that x evolves according to

– ƒ:[0,1][0,1] is smooth, monotonically increasing and concave down

– Here is a phase variable such that •

• Ф=0 when the oscillator is at its lowest state x=0

• Ф=1 at the end of the cycle when the oscillator reaches the threshold x=1.

Two Oscillators – The Model

d

dt

1

T, T is the cycle period

•ƒ satisfies ƒ(0)=0, ƒ(1)=1






• Example

– Here

–

– Consider Two oscillators governed by ƒ

• Interact by pulse coupling rule

Two Oscillators – The Model






• (a) Two Points on a fixed curve

• (b) Just before firing

• (c) Immediately After Firing

Two Oscillators – The Model cont…






Two Oscillators

• Strategy

– To prove that the two oscillators always become

synchronized, we first calculate the return map and

then show the oscillators are driven closer together

each time the map is iterated.

– Perfect Synchrony when the oscillators have gotten

so close together that the firing of one brings the

other to threshold.

– They remain synchronized thereafter because there

dynamics are identical.






How does it work!

• Return Map

– Two Oscillators A and B

– Consider the system just after A has fired

– Ф denotes the phase of B

– The return map R(Ф) is defined to be the phase of B

immediately after the next firing of A.






How does it work

• Observe that after a time 1-Ф oscillator B reaches threshold

• A moves from zero to an x-value given by xA= ƒ(1-Ф).






• An instant later B fires and xA jumps to ε+ƒ(1-Ф) or 1. whichever is less.

• If xA=1, we are done, the oscillators have synchronized.

How does it work






Immune System






Immune System

• Aim

– To provide responses to attacks from outside the body

• Antigen

– Any substance that elicits an immune response (e.g. virus,

bacteria)

• Self/Non-Self recognition

– Each cell has a marker (self)

– Cells without marker (non-self) are considered antigen

Immune system attacks antigen






Immune System

• Characteristics:

– Antigen-specific

– Systemic (throughout the body)

– Memory

• next attack recognized quicker

• level of response higher

• Dysfunctions

– Autoimmune disease

• System attacks self cells

– Allergies

• System attacks innocuous substances (allergen)






Immune System

• Agents of Immune System

– Lymphocites (white blood cells)

• Organs of lymphatic system: bone marrow, thymus gland,

spleen

• Lymph: colorless fluid transported by lymphatic vessels

– Lymphocites (B and T cells)

• Cells transported by blood and lymphatic vessels across the

whole body

• Cells exchanged between blood and lymphatic vessels

– Foreign organisms enter body through lymph nodes






Immune System






Immune System

– B cells (Bone)

• Produced by bone marrow / enter blood system

• Wait for antigen (in blood cells)

• Activation of B cells requires help of T cells when encounter antigen

• B cells replicate and release antibodies

• Antibodies circulate in the blood vessels for additional antigens to

mark

• B cells antibodies mark the antigen for destruction by other immune

system cells

– T cells (Thymus)

• Produced by bone marrow / initialised in thymus enter lymphatic

vessels

• Coordinate immune response + destroy infected body cells

• T cells replicate and create memory cells (for subsequent attacks)






Immune System

B

T

B

B

B

AB

AB

B

T

B

B

B

T

T

B and T cells circulate into body

Antigen enters body

B

B T

B cells recognise Antigen

T cell activates B cell

B cell replicates

B cells generate Antibodies (AB)

AB

AB

AB

T

AB marks Antigen as non-self

T cells destroy Antigen

AB






Immune System

• Innate immunity – Cells of immune system bind to specific antigen

• Pattern-recognition receptors • Passed from generation to generation • Evolution

• Acquired Immunity • Characteristics

– Distributed – No centralized control – Uses learning and memory – Tolerant of self

• Artificial Immune System (AIS) – an adaptive system inspired by theoretical and experimental immunology

• Aim: to efficiently detect changes in the environment or deviations from the normal system behavior in complex problems domains






Summary (what do I need to know)

• What make biological systems interesting ?

• What is ant colony optimization?

• How does it work?

• How can we achieve synchronization in a distributed

system?






References

• “Synchronization of Pulse-Coupled Biological Oscillators”, Renato E. Mirollo and Steven H. Strogatz, Siam Journal of Applied Mathematics, Vol. 50, No. 6 (Dec 1990), PP. 1645-1662

• M. Dorigo, V. Maniezzo & A. Colorni, Ant System: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B, 26(1):29-41,1996

• Slides “Adaptive Systems” by Giovanna Di Marzo Serugendo

• Slides“ Bio-Inspired Signal Processing” by Sergio Barbarossa

• Slides “Self-Organization in Sensor and Actor Networks” by Falko Dressler

• Slides “Synchronization of Pulse-Coupled Biological Oscillators” by Ramil Berner

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