Distributed Algorithms for Swarm Robotsigwoa/IGWOA_KM.pdf · Distributed Algorithms for Swarm...

DistributedAlgorithmsfor Swarm

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Examples ofsomeproblems

Arbitrarypatternformation

Leader election

Circle formation

Gathering

Fault tolerantgathering ofpoint robots

Gatheringunder unequalvisibility range

Conclusion

Distributed Algorithms for Swarm Robots

Krishnendu Mukopadhyaya

ACM UnitIndian Statistical Institute, Kolkata

Indo-German Workshop on Algorithms9-13 Feb 2015

1 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Outline

1 Introduction

2 Computational model

3 Examples of some problemsArbitrary pattern formationLeader electionCircle formationGathering

Fault tolerant gathering of point robotsGathering under unequal visibility range

4 Conclusion

2 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Swarm Robots

• Group of small, inexpensive, identical, autonomous, mobilerobots.

• Collaboratively executing work• moving large object, cleaning big surface.

• Geometric point of view: points moving on the 2Dplane.

• Tasks: Forming geometric patterns like point, circle etc.• Distributed in nature.

3 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

General characteristics of swarm robots

• Point/Unit Disc

• Autonomous

• Identical

• No message passing

• Sense surroundings

• Move on the 2D plane

• Limited computational power

4 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Execute wait-look-compute-move cycle.

In wait state robots do nothing.

5 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Rv (visibility range) can be limited or unlimited

6 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

Computer

• r computes its destination t

7 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• r moves to t• SYm: Rigid motion.• CORDA: Non-rigid motion.

Obliviousness

After executing a cycle the robots forget all data.

8 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Execute wait-look-compute-move cycle synchronously.

• All robots look at the same time

9 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Execute wait-look-compute-move cycle asynchronously.

r4r6 r7

• Different robots look, compute and move at differenttimes.

10 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Execute wait-look-compute-move cyclesemi-synchronously.

• An arbitrary set of robots look at the same time.

11 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Agreement on co-ordinate system.

• Robots having same Sense of Directions (SoD) and samechirality

12 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Robots having same SoD but different chirality

13 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Robots having different SoD but same chirality

14 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Robots having different SoD and different chirality

15 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Examples of some problems

Coordination: formation of pattern for executing some job,

• moving an object.

• covering/painting an area

• guarding a geographical area etc.

16 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• Arbitrary pattern formation [FPS2008]

17 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Arbitrary pattern formation

Solution approach

• A set of robots is selected for movement.

• While these robots are in motion this set of eligible robotsremains invariant.

• The set changes only after all the robots reach theirdestinations.

• In case of nonrigid motion, if a robot stops before reachingits destination, it is again selected for movement in itsnext cycle.

18 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Geometric characterization for pattern formation

Symmetric PatternsLine of Symmetry

Line of Symmetry

(a) (b) (c)

19 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Asymmetric Patterns

20 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Orderable set

• A set of points is called an orderable set, if there exists adeterministic algorithm, which produces a unique orderingof the points of the set, such that the ordering is sameirrespective of the choice of origin and coordinate system.

Theorem[GM2010]

• A symmetric pattern is not orderable.

• An asymmetric pattern is orderable.

21 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Results on pattern formation

Scheduling SoD Chirality ResultsAsync Yes No (i) Any pattern formable

with odd no. of robots(ii)Symmetric pattern is formable

for even no. of robots [FPSW1999].Async Yes Yes Arbitrary pattern is formable for

any no. of robots [FPSW2001].ASync No Yes Characterization of all patterns

formable from anyinitial configurations[FPS2008, YS2010].

Theorem [GM2010]

If a set of robots is orderable, then any asymmetric pattern canbe formed by them even without having common chirality andavoiding collisions.

22 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• Leader Election [DPV2010]

• The robots elect r1 as their leader.

23 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Results on leader election

SoD Chirality # of robots ResultsYes Yes Any Leader election possible [FPSW1999].Yes No Odd Leader election possible [FPSW2001].No Yes/No Any Leader election not possible [FPSW2001].No Yes Any characterization of all

geometric positions [DP2007].No No Odd characterization of all

geometric positions [DP2007].No No Any Characterization of all

geometric positions whereiterative leader election

(total ordering of robots) is possible.[GM2010]

24 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Results on leader election

Theorem [DP2010]

Leader election and pattern formation problems are equivalent.

Theorem [GM2010]

A set of robots is orderable if and only if leader election ispossible.

25 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Circle formation

Results on circle formation

Scheduling Visibility Agreement Resultsrange in co-ordinate

Sync Limited No Heuristic ofapproximate circle

formation[SS1990].

Ssync Unlimited No Circle formation[DK2002].

ASync Unlimited No Bi-angularCircle formation

[K2005].ASync Unlimited No Circle formation

[DS2008].Async Unlimited Agree in chirality Uniform Circle formation

by n 6= 4 robots[FGSV2014].

26 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Circle formation

Recent extension for fat robots [DDGM2012]

• Circle formation is possible for (i) transparent fat robots,(ii) with limited visibility, (iii) with agreement in SoD andChirality and (iv) without collision.

27 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Circle formation

Recent extension for transparent fat robots [DDGM2013]

• Circle formation is possible for (i) transparent fat robots,(ii) with unlimited visibility ,(iii) without agreement inSoD and Chirality and (iv) without collision.

28 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering (point robots)

• Gathering [P2007] or Convergence [CP2006]

29 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering (fat robots)

• Gathering Fat Robots [CGP2009].

30 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering

Solution approach

Find an point to gather, such that the point will not change till the robots gather.

• Centroid or center of gravity (CoG): Given a set of n points represented bytheir coordinate values as {(x1, y1), . . . , (xn, yn)}. COG of the points is

given by (xc, yc) where xc = x1+...+xnn

and yc = y1+...+ynn

• Weber point: Given a set of n points, Weber point is the point whichminimizes the sum of distances between itself and all the points. This isalso known as the Fermat or Torricelli point. Weber point does not changeif the points are moving towards it. Not computable for ≥ 5 points.

• Center of Minimum Enclosing Circle (MEC): It is an invariant point if thepoints defining the MEC do not move and no robot moves outside theMEC.

31 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering

Difficulties

• Asynchronous: The CoG Changes!

• Oblivious: Gathering two robots is not possible!

• No common direction or orientation: Gathering two robotsis not possible!

32 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Results on gathering

Gathering point robots

Scheduling Visibility Agreement Multiplicity Resultsrange in coordinate detection

Sync unlimited No No Solved [AOSY1999].ASync Any Yes No Solved [FPSW2001].ASync unlimited No Yes Not solvable for two

robots [P2007].ASync unlimited No Yes Solved for three and

four robots[CFPS2012].

Solved for more thanfour robots initially

(a)in bi-angularconfiguration.(b)not in anyregular n gon

ASync unlimited No No Not solvable[P2007,CRTU2015].

33 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Results on gathering

Gathering fat robots

Scheduling Agreement in Resultsco-ordinate

ASync No Solved for up tofour robots [CGP2009].

Async No Gathering any number oftransparent fat robots.

without collision [GM2010].Sync No Solved for any number

of robots [CDFHKKKKMHRSWWW2011].(randomized / considering.robots with identification

and communication power).Sync No Solved by simulation [BKF2012].

ASync Chirality Solved for anynumber of robots [AGM2012].

34 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Fault tolerant gathering of point robots

Earlier results

Scheduling Assumptions # of ResultsFaulty Robots

SSync Multiplicity 1 Solveddetection [AP2006].

ASync Strong Arbitrary SolvedMultiplicity for more thandetection 2 robots

and Chirality [BDT2012].

Recent extension

Scheduling Assumptions # of ResultsFaulty Robots

ASync One Arbitrary Solved foraxis any initial

agreement configurations [BGM2015].

35 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Fault tolerant gathering of point robots [BGM2015]

• A given robot configuration C on a 2-D plane.

36 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Outline of the algorithm

• Draw horizontal lines through each robots in C.

L1(C)L2(C)L3(C)L4(C)L5(C)

37 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Case-1: L1(C) contains one robot position.

38 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• Let ri be the robot position on L1(C).

39 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri does not move.

40 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri does not move.

• All other robots move towards ri along straight lines.

41 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Case-1: Correctness.

• L1(C) always contains one robot position.

42 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• L1(C) always contains one robot position.

• Wait free algorithm and hence can tolerate arbitrarynumber of faults.

43 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Case-2: L1(C) contains more than one robot positions.

44 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj be the two corner robot positions on L1(C).

45 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• Draw the equilateral triangle 4riTrj .

46 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj move towards T .

47 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj move towards T .

• All other robots move towards the nearest robot among riand rj .

48 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj move towards T synchronously.

L2(C′)

L3(C′)

L4(C′)

L5(C′)

L1(C′)

49 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj move towards T asynchronously.

L3(C′)

L4(C′)

L5(C′)

L6(C′)

L2(C′)

L1(C′)

50 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

• ri and rj move towards T asynchronously.

• Once ri reaches T , it becomes stationary.

L3(C′′)

L4(C′′)

L5(C′′)

L6(C′′)

L2(C′′)

L1(C′′)

51 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Future Scope

What happens if,

• the robots are not see through?

52 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering under unequal visibility range [CGM2015]

Computational model

• Unequal Visibility Rangea, agreement on both axes.

aNo result reported till now considering unequal visibility range.

• The robots can see finite unequal ranges (visibility ranges)around themselves.

• initially visibility is symmetric.

53 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Computational model

• Visibility graph is Strongly Edge Connected Graph (SECG)a

aA digraph G is SECG if (u, v) ∈ E → (v, u) ∈ E.

• The robots are treated as the nodes of the graph.

• If two robots are mutually visible they are connected bytwo arcs.

54 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

New result

The algorithm presented in ”P Flocchini, G. Prencipe, N.Santoro, and P. Widmayer. Gathering of asynchronous robotswith limited visibility. Theoretical Computer Science,337(1-3):147 - 168, 2005.” also works for limited nonuniformvisibility ranges with a slight modification.

55 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Features of the algorithm

• Let R = {r1 . . . , rn} be a finite set of robots.

• The robots do not know the total number of robots.

• Minimum visibility range ∆ > 0 known to all robots.

• initially G is SECG.

The algorithm assures

• G remains SECG throughout the algorithm.

• the robots gather in finite time.

56 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Move Down

• r sees robots only below on Vr(where Vr: vertical line throughr).

• r′ : is the robot nearest to r onVr.

• ∆̄ = Min(∆, Dist(r, r′))(whereMin(a, b): the minimumbetween a and b; Dist(a, b):thedistance between a and b.)

• Compute a point Tr on Vr suchthat Dist(r, Tr) = ∆̄

• r moves to Tr

57 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Move Right

Vr V ′r

• r sees robots only to its right

• r′ : the robot nearest to r andlies on the vertical line just nextto Vr.

• p : is the projection of r′ on Hr

(where Hr: horizontal line drawnthrough r).

• ∆̄ = Min(∆, Dist(r, p)).

• Compute a point Tr on Hr suchthat Dist(r, Tr) = ∆̄

• r moves to Tr

58 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Move Diagonal

r̄r′

V ′r

• When r sees robots both below on Vr andon its right

• r′ : the robot nearest to r on the verticalline just next to Vr

• B := Upper intersection point betweenV C(r) and Vr′(where V Cr: The circle centered at r)

• C := Lower intersection point betweenV C(r) and Vr′

• A := Point on Vr at distance vr below r

• 2β := Ar̂B

• If β < 60◦

• Rotate B around r such that β = 60◦

59 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Move Diagonal

r̄r′

V ′r

• Let B′ be the position of B afterrotation

• H :=The point on VB and onthe diagonal of the parallelogramwith sides rB and rA

• ∆̄ = Min(∆, Dist(r,H))

• Compute a point Tr along theray rH such thatDist(r, Tr) = ∆̄

• r moves to Tr

60 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Correctness of the algorithm

GR remainsconnected duringdown movementsof any robotr ∈ R.

Every internalchord of a trianglehas length less orequal to thelongest side of thetriangle.

GR remainsconnected duringright movementsof any robotr ∈ R.

Vr V ′r

61 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

r̄r′

V ′r

GR remainsconnected duringdiagonalmovements of anyrobot r ∈ R.

• r′ and r̄ cannot move.

• As r movesdiagonallyDist(r, r′)and Dist(r, r̄)reduce.

• Mutual connectivity between r,r′ and r, r̄ remainsintact.

Theorem

The graph GR remains connected during the executionof the algorithm.

62 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Theorem

The robots in R will gather in finite timeVl VR

Let VL be the left most vertical line,i.e., no robots lie to its left. Either (i)one of the robots on VL will leave, or(ii) all the robots on VL will begathered to the bottom-most roboton VL, in finite time.

Corollary

If there exists any robot at the right side of VL, then allrobots on VL will leave VL in finite time.

63 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Theorem

The robots in R will gather in finite time

The robots in R will not cross VR(right most vertical line).

Distance between VL and VR reducesby a finite amount in finite number ofmovements of the robots.

• Note: VL changes due to robots movement, but VR isfixed

64 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Theorem

The robots in R will gather in finite time

After a finite time there exists novertical line between VL and VR.

All the robots in R will reach VR infinite time.

If VL = VR, all the robots gather ondown most robot in finite time. 65 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Future Scope

• This algorithm is based on mutual visibility of the robotsand having agreement in the direction of X − Y .

• Is gathering possible if the robots are not mutually visible?

• Is gathering possible if the robots have agreement in oneaxis?

66 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Gathering is still an open problem!

• In presence of obstacles

• Near gathering

• In graph(discrete plane)

• ...

67 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Future Direction

• Obstructed Visibility [AFGSV2014, AFFSV2014].

• Unequal visibility range [CGM2015].

• Light model [DFPS2012, AFGSV2014]

• Flocking [CP2007]

• Designing Optimal/efficient Algorithms.

• ...

Motivation

What are the minimal requirements to solve a problem?

68 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

Swarm robots moving in graph

Robots moving on graph → discrete movements

• Gathering in graph [ASN2014]: ring, tree, grid.

• Exploring a graph: tree [FIPS2008]

• ...

69 / 70

Robots

KrishnenduMukopad-

Introduction

Computationalmodel

Leader election

Circle formation

Gathering

Conclusion

References

• ”Distributed Computing by Oblivious Mobile Robots”,Flocchini, P. and Prencipe, G. and Santoro, N., Morgan &Claypool Publishers, Synthesis Lectures on DistributedComputing Theory, 2012.

• Thesis by Prencipe, G (2002),http://sbrinz.di.unipi.it/peppe/Articoli/TesiDottorato.pdf

Thank You

70 / 70

Distributed Algorithms for Swarm Robotsigwoa/IGWOA_KM.pdf · Distributed Algorithms for Swarm...

Documents

Cyber Swarm Algorithms – Improving Particle Swarm ... · Cyber Swarm Algorithms – Improving Particle Swarm Optimization Using Adaptive Memory Strategies Peng-Yeng Yin1*, Fred

Data Clustering Using Swarm Intelligence Algorithms An Overview

MULTI-OBJECTIVE PARTICLE SWARM OPTIMIZATION: ALGORITHMS

Swarm Intelligence Approaches for Grid Load Balancingcs.ndsu.edu/~siludwig/Publish/papers/JGC2011.pdf · new distributed swarm intelligence inspired load balancing algorithms. One

Swarm Algorithms

Genetic Algorithms (cont.) Particle Swarm Optimization ... · Genetic Algorithms (cont.) Particle Swarm Optimization Tabu Search Optimization Algorithm Selection. Lecture 12 ... •

Swarm Intelligence Algorithms for Data Clustering · Swarm Intelligence Algorithms for Data ... textual document collection, im-age segmentation ... by insect colonies without any

Particle Swarm Optimization Algorithms Mohamed Tounsi 1

DISTRIBUTED ALGORITHMS AND BIOLOGICAL SYSTEMSsaketn/BDA2014/Material/... · • This has yielded interesting distributed algorithms results. • Q: But what can distributed algorithms

Particle Swarm Optimization Algorithms for Autonomous ...Particle Swarm Optimization Algorithms for Autonomous Robots with Leaders Using Hilbert Curves Doina Logofatu1, Gil Sobol2,

Swarm Intelligence Algorithms for Data Clustering

IOA: Distributed Algorithms Distributed Programs

Distributed Algorithms and Sublinear-Time Algorithms

Distributed Particle Swarm Optimizationcse.unl.edu/~lksoh/Classes/CSCE990AMAS_Spring13/Seminar08_Kahrobaee.pdf · •Applying Multi-Swarm Accelerating Particle Swarm Optimization

Distributed Algorithms

ANN Models Optimized using Swarm Intelligence Algorithms€¦ · · 2014-11-05ANN Models Optimized using Swarm Intelligence Algorithms . N. KAYARVIZHY1, S. KANMANI2, R.V. UTHARIARAJ3

Topic 7: Stigmergy, Swarm Intelligence and Ant Algorithms

November 2005Distributed systems: distributed algorithms 1 Distributed Systems: Distributed algorithms

Introduction to SWARM Software and Algorithms for Running ...multicore-swarm.sourceforge.net/Swarm_Documentation.pdf · 1 Introduction to SWARM Software and Algorithms for Running

1 Topic 7: Stigmergy, Swarm Intelligence and Ant Algorithms stigmergy swarm intelligence ant algorithms AntNet: routing AntSystem: TSP