Upload
jatinmec
View
220
Download
0
Embed Size (px)
Citation preview
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 1/33
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
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 2/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 3/33
11
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..
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 4/33
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 5/33
33
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..
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 6/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 7/33
55
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 8/33
66
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
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 9/33
77
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 10/33
88
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 11/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 12/33
1010
Swimming & Tumbling of bacteria Swimming & Tumbling of bacteria
Swimming, Tumbling & Chemo tactic behavior of E. Coli
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 13/33
1111
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].
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 14/33
1212
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 ).
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 15/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 16/33
1414
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 17/33
1515
Contd«Contd«
Fig (a): Nutrient landscape
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 18/33
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 19/33
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).
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 20/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 21/33
1919
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 22/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 23/33
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 24/33
2222
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 25/33
2323
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 )
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 26/33
2424
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 )
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 27/33
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 28/33
2626
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
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 29/33
2727
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 30/33
2828
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) .
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 31/33
2929
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.
8/8/2019 Biomimcry of Bacterial Foraging-For Distributed ion
http://slidepdf.com/reader/full/biomimcry-of-bacterial-foraging-for-distributed-ion 32/33
3030
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.