![Page 1: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/1.jpg)
Swarm Intelligence: Distributed Problem Solving Inspired by Collective Behavior of Insects and other Natural Multi-Agent Systems
Dr. Vincent CicirelloStockton College of NJ
![Page 2: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/2.jpg)
Outline
What is Swarm Intelligence?Self-organization and Social Insects
Self-synchronizationCollective buildingForaging ants
Inspiration for problem solving toolsAnt Colony OptimizationWasp-inspired Task Allocation
Conclusion
![Page 3: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/3.jpg)
What is Swarm Intelligence?
Branch of artificial intelligence that takes problem solving inspiration from natural multi-agent systemsLargely inspired by mathematical models of the behavior of social insectsKey Ideas:
Very simple computational agentsIndividually “dumb”Indirect communication via changes in environmentPositive reinforcementMeans of “forgetting”“Intelligence” through collective behavior
![Page 4: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/4.jpg)
Social InsectsDefining properties of eusociality:
Reproductive division of laborOverlapping generationsSterile castesE.g., reproductive queens and sterile workers
Social Insects AntsTermitesBees1
Wasps1
Individuals possess little intelligenceSimplicity of individual behaviorCollective behavior of colony complexHow is it governed? By whom?
1. Not all species of wasps and bees are social, some are solitary insects.
![Page 5: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/5.jpg)
Self-Organization Governed by Stigmergy
Stigmergy (term introduced by Grassé): From the Greek stigma (sting) and ergon (work)An environmental stimuli induces a behavioral response
Term typically used to refer to indirect communication via changes in the environmentExamples:
Ants leave pheromone (chemical) trails… other ants follow these trailsAnts carrying dead ants more likely to drop them next to other dead ants (forming cemeteries)
![Page 6: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/6.jpg)
Simulating the Biological ProcessesMathematics involved usually includes:
Probability and StatisticsCalculusDiscrete mathDifferential equations and difference equations
Time typically simulated in discrete intervals Grid world used to represent the physical world
Grid cells have properties:Number of insects that can be located thereQuantity of food located thereQuantity and type of pheromone (chemical left by insects) located there
![Page 7: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/7.jpg)
Outline
What is Swarm Intelligence?Self-organization and Social Insects
Self-synchronizationCollective buildingForaging ants
Inspiration for problem solving toolsAnt Colony OptimizationWasp-inspired Task Allocation
Conclusion
![Page 8: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/8.jpg)
Self-Synchronizing Systems
Cricket chirpingHorses gallopingPeople clappingTwo pendulum clocks suspended from the same frame
Swing at same frequency180° out of phase According to the Dutch physicist Christiaan Huygens (1665) the inventor of the pendulum clock
![Page 9: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/9.jpg)
Firefly Synchronization
Pteroptyx Cribellata, from Philippines and New GuineaAggregate in large numbers and flash in unisonIndividually each follows its own rhythmFlashes by others stimulateindividuals to flash soonerEffect is cumulative
![Page 10: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/10.jpg)
Fire Flies Simulation
![Page 11: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/11.jpg)
Collective Building by Insects
![Page 12: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/12.jpg)
Termite Nest Building(Kugler et al. 1990)
Termites construct hills (> 5m high, >10 tons) Multiple floors Intricate networks of passageways Dedicated “climate controlled” chambers to:
store food, raise the brood, house the population
...and there’s not a supervisor among them!
![Page 13: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/13.jpg)
Basic Idea
Completed work is a guide for future work
If all builders removed from the site And new population introducedThey will continue exactly as original team would
![Page 14: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/14.jpg)
The Queen and Pheromone DiffusionThe queen emits a pheromone that diffusesA worker deposits a soil pellet if the concentration of the pheromone is just rightWax dummy queen does not stimulate construction
![Page 15: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/15.jpg)
Termite Pillar Construction
Early deposits attract later ones, yielding concentrationsNewest (strongest) Pheromones on top lead to columnsCompetition among columns promotes even spacingNearby columns lean toward one another, building archesMultiple arches contact to form floors
![Page 16: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/16.jpg)
As a ResultTermite moundsUp to 20' tallUp to 6' diameter at baseUp to 120' below groundExceeds any human structure if measured in body length or weight
![Page 17: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/17.jpg)
Foraging in Army AntsTwo parts:
Pheromone layingWhile returning with food
Pheromone followingAlways attempt to follow the trail
PheromoneEvaporatesDiffusesPheromone deposits on trail sumSome lab measurements suggest half-life of 45 minBut can persist for months
![Page 18: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/18.jpg)
The Double Bridge Experiment
Initially no pheromoneChoice of branch is randomPheromone left by ants returning from food sourceOne branch is eventually chosen by a few more antsIt becomes more attractiveAnts increasingly drawn to itColony converges on itAll (most) ants use that path
![Page 19: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/19.jpg)
Double Bridge Experiment: Unequal Paths
Ants will return faster over the shorter edgeOther ants are then more likely to follow shorter edgeWhat if that edge is introduced later?
![Page 20: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/20.jpg)
Food Selection
Chemical trail following is not preciseIs it a problem?
![Page 21: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/21.jpg)
Food Selection
Chemical trail following is not preciseSome ants will lose trail and wanderThey may discover new food sourcesRecruit others via pheromone trail Richer food source = more pheromoneNearby, rich sourcecan make colony switch
![Page 22: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/22.jpg)
Behavioral ModelProbabilistic trail following outPheromone laid in both directionsEvaporationMove left with prob.
CongestionMove to neighboring cell Wait until space is free, if all cells are congested
22
2
)5()5()5(
rl
lpρρ
ρ+++
+=
![Page 23: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/23.jpg)
Foraging Ants Movie
![Page 24: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/24.jpg)
Outline
What is Swarm Intelligence?Self-organization and Social Insects
Self-synchronizationCollective buildingForaging ants
Inspiration for problem solving toolsAnt Colony OptimizationWasp-inspired Task Allocation
Conclusion
![Page 25: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/25.jpg)
Ant Colony Optimization (ACO)
First introduced for shortest route problemsE.g., the traveling salesperson problem (TSP)
Key concepts:Population of artificial ants Probabilistically build a solution following artificial pheromone Reinforce pheromone trail according to quality of found solution (positive feedback)Evaporate the pheromone to avoid search stagnation (negative feedback) Time scale – number of runs is also critical.
![Page 26: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/26.jpg)
ACO Example: Traveling Sales Ants
![Page 27: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/27.jpg)
Ant System (AS): The first ACO algorithm
Transition from city i to j depends on: “Tabu list” – list of visited citiesHeuristic, ηij, local desirability to visit city jwhen at city i is (for TSP ηij = 1/dij)Artificial pheromone trail τij(t)– represents the learned, desirability of visiting city jfrom city i
Generally, have several “ants” searching the solution space.
![Page 28: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/28.jpg)
Ant System (AS)
Transition rule is a combination of heuristic and pheromone trailProbability of ant k going from city i to j:
Alpha and beta are adjustable parametersα= 0 : represents a greedy approachβ= 0 : represents rapid selection of tours that may not be optimal.
[ ] [ ][ ] [ ]∑
∈
=
kiJ
ilil
ijijkij t
ttp
l
βα
βα
ητητ.)(
.)()(
![Page 29: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/29.jpg)
Ant System (AS)
Pheromone update :
T is the tour made at time t by ant k, L is the length, Q is a parameter.Pheromone decay:
⎩⎨⎧ ∈
=Δotherwise0
)(),(if)(/ tTjitLQ kkkijτ
)()().1()1( ttt ijijij ττρτ Δ+−=+
![Page 30: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/30.jpg)
Dynamic ACO Movie
![Page 31: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/31.jpg)
Wasp Task Differentiation (Theraulaz et al. 1991)
Wasps in a nest divide into:
Foragers who hunt for food, Nurses who care for the brood.
The relative proportion of Foragers and Nurses varies with the demand...but no wasp explicitly computes the demand.
![Page 32: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/32.jpg)
Division of Labor
MorphologicalInherent physical properties of individuals
TemporalThe time of day,year, age
BehavioralSpecialize/adapt to allocated tasks
![Page 33: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/33.jpg)
Fixed Threshold model
Each task produces a stimulusEach ant has a “response” thresholdIf it is exceeded, theant starts performing the taskJust like a dirty coffee pot in the officeCan be tied to antmorphology
![Page 34: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/34.jpg)
Time Based Thresholds
Older bees/ants forage moreThresholds can change
Age of beeTime of dayTime of year
4
![Page 35: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/35.jpg)
Adjustable Thresholds
Polist Wasps Small coloniesNo differencesCapable of performing any task
As wasp works on a task:
Associated threshold is loweredAll others are raised
Promotes specialization but keeps it flexible
![Page 36: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/36.jpg)
response thresholds
Wasp Task Allocation for Vehicle Paint Booth Scheduling
Machine 1
Machine 2
Machine N
A
A
B
B
C
C
,..., BA θθ
stimulusBS
22
2
),|(TT
TTT S
SSbidPθ
θ+
=B B
B
A
C
C
CA
Truck fresh from assembly line
Trucks arrivingfrom assemblyline
![Page 37: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/37.jpg)
Response Threshold Updates
While painting (or switching to) color j
While painting (or switching to) color other than j
While idle for all colors j2,, δθθ += jwjw
1,, δθθ −= jwjw
3,, δθθ −= jwjw
![Page 38: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/38.jpg)
Outline
What is Swarm Intelligence?Self-organization and Social Insects
Self-synchronizationCollective buildingForaging ants
Inspiration for problem solving toolsAnt Colony OptimizationWasp-inspired Task Allocation
Conclusion
![Page 39: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/39.jpg)
Much to learn from the natural world
Social insects coordinate to solve complex problems with very simple coordination methods and minimal communication.What can we learn from nature?Biologists in their studies have produced mathematical models:
To simulate the biological systemsTo test their hypotheses about the biology
![Page 40: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/40.jpg)
Much to learn from the natural world
Biotracking ProjectGroup at Georgia TechLead: Tucker BalchFocusing on:
Automatically tracking biological entities in videoAutomatically identifying behavioral patternsWhat can we learn that can be applied to robotic systems?
![Page 41: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/41.jpg)
Much to learn from the natural world
Computer scientists have taken inspiration in developing problem solving systemsAnt Colony Optimization has been applied to:
TSPSchedulingNetwork routingGraph coloringMany many other combinatorial optimization problems
Many other swarm-inspired tools:Particle Swarm OptimizationResource allocation inspired by waspsMulti-robot coordination inspired by ants, wasps, bees, etcMany many others
![Page 42: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/42.jpg)
EXTRA SLIDES FOLLOW
![Page 43: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/43.jpg)
Ant Colony System (ACS)
Modifications toAS with new transition rule:
j’ is a city randomly selected according to the probabilistic rule of the Ant Systemqo is a parameter between 0 and 1This helps ACS to improvise on the best solutions
[ ]{ }max ( ) . ,
,
ik
ij iu ou J
ik o
t if q qj
j J if q q
βτ η∈
⎧ ⎡ ⎤ ≤⎪ ⎣ ⎦=⎨′∈ >⎪⎩
![Page 44: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/44.jpg)
Ant Colony System (ACS)
Pheromone update rule (new):
Only applied to the best ant. The change in the pheromone:
(i,j) edges of the best tourρ parameter governs pheromone decayL length of the best tour
Local update ruleLnn length of the nearest neighbor tour
( ) (1 ) ( ) ( )ij ij ijt t tτ ρ τ ρ τ= − ⋅ + ⋅Δ
1ij LτΔ =
( ) (1 ) ( )nnij ij n Lt t ρτ ρ τ ⋅= − ⋅ +
![Page 45: Dr. Vincent Cicirello Stockton College of NJcourseware.deadcodersociety.org/csis4469-artificial...Stockton College of NJ. Outline {What is Swarm Intelligence? {Self-organization and](https://reader033.vdocument.in/reader033/viewer/2022050406/5f8343d3962cd67c8d153c0e/html5/thumbnails/45.jpg)
Ant Colony System (ACS)
Other methods for improvementUse a local search method in conjunction with ACS-TSP.Elitism, worst tours (pheromone removed), local search enhancement.
Has been shown to be comparable to the best techniques available