Biomimcry of Bacterial Foraging-For Distributed ion

8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion

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Biomimcry Of Bacterial Foraging Biomimcry Of Bacterial Foraging

for Distributed Optimization & for Distributed Optimization &

Control Control

Presented by : Presented by :-- Ankeeta Shah Ankeeta Shah

Electronics & Telecommunication Engg. Electronics & Telecommunication Engg.

Sec Sec ± ± A Gr A Gr -- 11

04012270230401227023



ContentsContents Introduction.Introduction.

Bacterial foraging.Bacterial foraging. Foraging theory.Foraging theory. Search strategies for foraging.Search strategies for foraging. Bacterial foragingBacterial foraging--E. Coli.E. Coli. Swimming & tumbling via flagella.Swimming & tumbling via flagella. E. coli swarm foraging for optimization.E. coli swarm foraging for optimization. Chemo taxis, Swarming, Reproduction,Chemo taxis, Swarming, Reproduction,

Elimination & DispersalElimination & Dispersal Nutrient hill climbing.Nutrient hill climbing. Bacterial Foraging Algorithm.Bacterial Foraging Algorithm. Foraging for Adaptive control.Foraging for Adaptive control. Autonomous Vehicle Guidance. Autonomous Vehicle Guidance. Conclusion.Conclusion.



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I ntroduction I ntroduction OptimizationOptimization isis oneone of of thethe acuteacute problemproblem inin

sciencescience && technologytechnology.. SeveralSeveral optimizationoptimization techniquestechniques areare therethere likelike::

11..GeneticGenetic algorithmalgorithm..

22..SimulatedSimulated analysisanalysis..33..TabuTabu searchsearch..

44..SwarmSwarm optimizationoptimization

55..Ant Ant colonycolony algorithmalgorithm etcetc....

Among Among thesethese wewe willwill concentrateconcentrate moremore oror lesslessonon BacterialBacterial ForagingForaging..



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Bacterial Foraging Bacterial Foraging

ForagingForaging-- searchsearch forfor foodfood (methods(methods forfor locating,locating,

handlinghandling && ingestingingesting food)food)..

A foraging animal takes actions to maximize theenergy obtained per unit time spent foraging, in

the face of constraints presented by its ownphysiology (e.g., sensing and cognitivecapabilities) and environment (e.g., density of prey, risks from predators, physical

characteristics of the search area).

After After manymany generationsgenerations poorpoor strategiesstrategies areareeithereither eliminatedeliminated oror redesignedredesigned..



44

Contd«Contd«

Logically, such evolutionary principles have ledscientists in the field of foraging theory to

hypothesize that it is appropriate to model theactivity of foraging as an optimization process.



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Foraging theoryForaging theory

Foraging theory animals maximizes theirenergy intake E per unit time T spent foragingi.e, E/T (or they maximize their long-termaverage rate of energy intake).

H ow optimisation is achieved?

Maximize long-term average rate of energy intakewhere only certain decisions and constraints areallowed.

Constraints due to incomplete information (e.g.,due to limited sensing capabilities) and risks(e.g., due to predators) have been considered.

Thus these approaches seek to construct an

optimal policy for making foraging decisions.



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Search strategies for foraging Search strategies for foraging

Cruise - forager moves continuously. Ambush- stationary and waits.

Saltatory-intermittently cruise & sit & wait

Search strategies for foraging animals



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Bacterial foraging Bacterial foraging--E . Coli E . Coli The E. coli has plasma membrane, cell wall &

capsule that contains the cytoplasm & nucleoid& flagella for locomotion.

Diameter - 1 m, length- 2 m, weighs - 1picogram & is about 70% water.

E . coli has a control system that enables it tosearch for food and try to avoid noxioussubstances

Its actuator (flagellum) is decision making,

sensors, & exhibits closed-loop behavior (i.e.,how it moves in various environmentsitsmotile behavior).

E . coli performs a type of saltatory search.



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Swimming &Tumbling via Swimming &Tumbling via

FlagellaFlagella Each flagellum is a left-handed helix connected

to the cell.

It rotates counterclockwise, viewed from freeend of flagellum toward the cell, it produces aforce against the bacterium so it pushes the cell.

If clockwise, it will pull at the cell.

We may think of each flagellum as a type of propeller & in control systems as actuator.



99

Contd«Contd«

From engineering perspective, the rotating shaft at the base of the flagellum seems to what biologists call a universal joint (so the rigidflagellum can point in different directions

relative to the cell). It shows two types of movement - swim &

tumble (for search of food)

Swim when anticlockwise movement.

Tumble when clockwise movement.



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Swimming & Tumbling of bacteria Swimming & Tumbling of bacteria

Swimming, Tumbling & Chemo tactic behavior of E. Coli



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E.Coli swarm foraging for E.Coli swarm foraging for

optimisationoptimisation

Suppose that we want to find the minimum of J (),

Rp

,where we do not have measurements or an analyticaldescription of the J ().

Here, we use ideas from bacterial foraging to solve this nongradient optimization problem.

First, say = position of a bacterium & J ()= combinedeffects of attractants and repellants from the environment,

for e.g., J () < 0 ; location in nutrient-rich, J () = 0 ; location in neutral, J () > 0 ; location in noxious environments.

[Basically, chemo taxis is a foraging behavior that implements a type of optimization where bacteria try toclimb up the nutrient concentration (find lower and lowervalues of J () ), avoid noxious substances, and search forways out of neutral media (avoid being at positions where J () 0). It implements a type of biased random

walk].



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Chemotaxis,Swarming ,

Reproduction,Elimination & Dispersal Lets define a chemo tactic step whether tumble followed

by a tumble or a tumble followed by a run. Let : j = index for chemo tactic step.

k= index for reproduction step.l= index of elimination-dispersal event.

P (j, k, l)={ i ( j, k, l) |i=1,2,,S } represents posi t i onof each member i n the populat i on of the S bacteri a at the j th chemo tact i c step, kth reproduct i on step, andlth eli mi nat i on-di spersal event.

Here, let J (i , j, k, l) denote the cost at the locat i on of the i th bacteri um i ( j, k, l) belong to Rp (somet i mes wedrop the i ndi ces and refer to the i th bacteri um posi t i onas i ).



1313

Contd«Contd«

Note: well interchangeably refer to J as being a cost

(from optimization theory) and as being a nutrient surface (in reference to the biological connections).

Let Nc = length of lifetime of bacteria as measured bythe number of chemo tactic steps they take during theirlife.

Let C(i)> 0,i=1,2,,S. denote a basic chemo tactic stepsize that we will use to define the lengths of steps duringruns.

To represent tumble, a unit length random direction,

say

( j), is generated; this will be used to define thedirection of movement after a tumble.

In particular, we let i (j+1,k,l)=i (j, k, l) + C(i )(j)

so that C(i ) i s the step si ze taken i n the random di rect i onspeci f i ed by the tumble.



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Contd«.Contd«.

If at i (j+1,k,l), the cost J (i , j+1,k,l) i s better (lower)

than at i ( j, k, l), then another step of si ze C(i ) i n thi ssame di rect i on will be taken.

Now, if that step resulted in a position with a better cost value than at the previous step, again another step istaken.

(this swim is continued to reduce the cost, but only up toa maximum number of steps, Ns). Hence, cell tends tomove heading in the direction of increasing favorableenvironments.

It was for the case where no cell-released attractants,used to signal other cells, that they should swarmtogether as in fig (a).

We also have cell-to-cell signaling via an attractant andwill represent that with J icc (, i ( j, k, l )),i=1,2,,S,

for the i th

bacteri um.



1515

Contd«Contd«

Fig (a): Nutrient landscape



1717

Contd«Contd«

J cc( , P (j, k, l)) = 7 J cc

i (, i( j, k, l ))

= 7[ d attract exp(-wattract 7( m- mi ) 2 )] +

7[h r epellant exp(-w r epellant 7 ( m- mi ) 2 )]

W h er e : 7is (i = 1 to S )

7 is (m = 1 to p ) Above equation denote the combined cell-to-cell

attraction and repelling effects,

Where =[1, ,p]T is a point on the

optimization domain m

i = m th com ponent of i th bacteri um posi t i on i

An eg for the case of S = 2 and the aboveparameter values is shown in Fig (b).



1818

Contd«Contd« Here, note that the two

sharp peaks represent the cell locations, & as wemove radially away fromthe cell, the functiondecreases and thenincreases (to model thefact that cells far awaywill tend not to beattracted, whereas cellsclose by will tend to try toclimb down the cell-to-cell nutrient gradient toward each other andhence try to swarm). Fig. (b) Cell-to-cell chemical attractant

model, S = 2.



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Contd«Contd«

After Nc chemo tactic steps, a reproduction step istaken.

Let Nre be the number of reproduction steps to betaken. Assuming that S is a positive even integer. Let Sr=s/2 be the number of population members whohave had sufficient nutrients so that they will reproduce(split in two) with no mutations

Hence Sr least healthy bacteria dies & other Srhealthiest bacteria split into two daughter cell

Let Ned be no. of elimination-dispersal with probabilityP ed.

Hence we assume that the frequency of chemo tacticstep>reproduction step>elimination-dispersal step.



2020

N utrient Hill Climbing N utrient Hill Climbing

choosing S = 50, Nc=100, Ns = 4, Nr e = 4,

Ned = 2, ped = 0.25,and the C(i)= 0.1,i=1,2,,S.

The bacter ia ar einitially spr ead r and omly over the

optimization d omain.(Referr ing to fig (a)).

Bacter ial motion t r ajector ies, on contour plots. (a) Gener ation 1, (b) gener ation 2,(c) gener ation 3,and (d ) gener ation 4.



2121

Contd«Contd«

B act erial motion traj ectori es, aft er an

elimination-disp ersal event . (a) Gen1, ( b ) gen eration 2, (c) gen eration 3, and (d) gen eration 4.

Swarm beh avior of E . coli on a t est

function . (a) Gen 1, ( b ) Gen 2, (c) gen eration 3, and (d) gen eration 4.



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Bacterial Foraging Algorithm Bacterial Foraging Algorithm This algorithm models bacterial population chemo taxis,

swarming, reproduction, elimination, and dispersal whichis given here (initially j=k=l=0). Specifying iterations as:

1) Elimination-dispersal loop: l =l +12) Reproduction loop: k = k + 1

3) Chemo taxis loop: j = j +1a) For i =1,2,,S, tak e a chemo tactic step for

bacterium i as follows.b) Compute J (i, j , k , l). Let J (i, j , k , l)= J (i, j , k , l) +

J cc ( i(j, k, l), P (j, k, l)) (i.e., add on the cell-to-cell attractant effect tothe nutrient conc.)

c) Let J last = J(i, j, k, l) to save this value since wemay find a better cost via a run.



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Contd«Contd«(d) Tumble: Generate a random vector, (i )

belongs to Rp, wi th each element m(i ), m=1,2,.., p , a random number on[1,1].

(e) Move : let (e) Move : let

i (j+1, k, l)= i (j, k, l) + C(i )

Thi s results i n a step of si ze C(i ) i n the

di rect i on of the tumble for bacteri um i .(f) Compute J(i , j+1, k, l), & then let J(i , j+1, k,

l) = J(i , j+1, k, l) + J cc ( i (j+1, k, l), P(j+1,

k, l)).

(i ) T(i ) (i )



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Contd«Contd« Swim:Swim:

i) Let m = 0 (counter for swim length).ii) While m Ns < (if have not climbed down too long)

Let m=m+1.

I f J(i, j +1, k , l)<J last (if doing better), let

J last =(i, j +1, k , l) and let

i(j+1, k, l)= i(j+1, k, l) + C(i)

& use this i(j+1, k, l) to compute the new

J(i, j+1, k, l) as we did in (f). Else, let m = Ns . This is theend of the while statement .

(i )

T(i ) (i )



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Contd«Contd«Sort bacteria and chemo tactic parameters C(i )

in order of ascending cost J health (higher cost means lower health ) .

b ) The Sr bacteria with the highest J health values

die and the other Sr bacteria with the best

values split (and the copies that are made are

placed at the same location as their parent ) .

6 ) If k< N6 ) If k< Nrere, go to step 2. In this case, we, go to step 2. In this case, we

have not reached the no. of specifiedhave not reached the no. of specifiedreproductions steps, so we start the next reproductions steps, so we start the next

generation in the chemo tactic loopgeneration in the chemo tactic loop



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Contd«Contd«

7) Elimination-dispersal: For i = 1,2,,S, with

probability ped , eliminate and disperse each

bacterium (this keeps the number of bacteria inthe population constant).

8) If l < Ned , then go to step 1; otherwise

end.



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Foraging for adaptive control Foraging for adaptive control

S warm foraging in adaptiv e control (r(t): r ef er enc e or d esir ed plant output) .



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Autonomous Vehicle Guidance Autonomous Vehicle Guidance

What Can Nature Teach Us?

The artificial potential field method in autonomousvehicle guidance bears some similarities to bacterialforaging algorithms.

Clear analogies between foraging and cooperative

control of groups of uninhabited autonomous vehicles(UAVs) are used in military (or commercial) applicationsare:

i) Animals, organisms = UAVs,

ii) social foragers = group of cooperating UAVs

that can communicate with each other,iii) prey, nutrients = targets,

iv) predators, noxious substances = threats, and

v) environment = battlefield.



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ConclusionConclusion

Thus Bacterial Foraging algorithm, explains SocialThus Bacterial Foraging algorithm, explains SocialForaging, Genetic Algorithm, Swarm Optimization.. whichForaging, Genetic Algorithm, Swarm Optimization.. whichthus makes it imperative to analyses strategies requiredthus makes it imperative to analyses strategies requiredfor Global Optimization.for Global Optimization.

Optimal Foraging theory uses computational or analyticalOptimal Foraging theory uses computational or analyticalmethods to provide an optimal foraging policy that methods to provide an optimal foraging policy that specifies how foraging decisions are made.specifies how foraging decisions are made.

Hence the potential uses of Biomimcry of BacterialHence the potential uses of Biomimcry of BacterialForaging optimization techniques is to develop adaptiveForaging optimization techniques is to develop adaptive

controllers & cocontrollers & co--operative control strategies foroperative control strategies forautonomous vehicles.autonomous vehicles.



Thank You!Thank You!

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