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

2 Some natural Swarm Intelligence systems Ants  find the shortest path to food  go on raiding parties to gather it  carry it cooperatively  make cemeteries  sort their brood by size  etc. Termites  build nests with complex features like fortified chambers spiral air vents fungus gardens etc. Bees  gather pollen with high efficiency, exploiting the nearest richest food source first. Geese  coordinate takeoff and landing  flight patterns  etc. Fish / Birds /…  swarms Human societies  economies ?

3 Swarm Intelligence “Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) agents interacting locally with their environment cause coherent functional global patterns to emerge.” characteristics of a swarm:  distributed, no central control or data source  no (explicit) model of the environment  perception of environment, i.e. sensing  ability to change environment  problem solving is emergent behaviour

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6 How Do Social Insects Coordinate Their Behaviour? communication is necessary two types of communication  direct antennation, trophallaxis (food or liquid exchange), mandibular contact, visual contact, chemical contact, etc.  indirect two individuals interact indirectly when one of them modifies the environment and the other responds to the new environment at a later time called stigmergy

7 Stigmergy “La coordination des taches, la regulation des constructions ne dependent pas directement des oeuvriers, mais des constructions elles-memes. L’ouvrier ne dirige pas son travail, il est guidé par lui. C’est à cette stimulation d’un type particulier que nous donnons le nom du STIGMERGIE (stigma, piqure; ergon, travail, oeuvre = oeuvre stimulante).” Grassé P. P., 1959 [“The coordination of tasks and the regulation of constructions does not depend directly on the workers, but on the constructions themselves. The worker does not direct his work, but is guided by it. It is to this special form of stimulation that we give the name STIGMERGY (stigma, sting; ergon, work, product of labour = stimulating product of labour).”]

8 Example of Stigmergy: Trail Following and Ants Foraging Behaviour while walking, ants and termites  may deposit a pheromone on the ground  follow with high probability pheromone trails they sense on the ground Nest Food

9 Example of Stigmergy: Ant cemeteries in nature simple behaviour rules for ants  wander around  if you find a dead ant pick it up with probability inversely proportional to the number of other dead ants nearby  if you are carrying a dead ant put it downwith probability directly proportional to the number of other dead ants nearby

10 Stigmergy Stimulation of workers by the performance they have achieved Grassé P. P., 1959

11 Stigmergy Communication through marks in the environment …  Marks serve as a shared memory for the agents  Promotes loose coupling  Robust Stigmergy ~ action + sign:  Agents put marks in the environment (inform other agents about issues of interest)  other agents perceive these marks (influence their behavior)  manipulate marks  other agents perceive the marks  ….etc. Marks can be  static (environment does not manipulate marks over time) e.g., flags  dynamic (environment manipulates marks over time) e.g., pheromones, gradient fields

12 Ants Foraging Behaviour Example: The Double Bridge Experiment 15 cm NestFood A B Simple bridge % of ant passages on the two branches Goss et al., 1989, Deneubourg et al., 1990

13 Food foraging in nature

14 Asymmetric Binary Bridge Experiment

15 Some Results r is the length ratio among the two bridges r = 1 r = 2 Short branch added later

16 “Artificial” Stigmergy Indirect communication mediated by modifications of environmental states which are only locally accessible by the communicating agents Dorigo & Di Caro, 1999 Characteristics of artificial stigmergy:  Indirect communication  Local accessibility

17 What Are Ant Algorithms? Ant algorithms are multi-agent systems that exploit artificial stigmergy as a means for coordinating artificial ants for the solution of computational problems examples 1. AntNet: network routing 2. AntSystem: TSP

18 AntNet: An Ant Algorithm for Routing in Packet-Switched Networks (e.g. Internet) the routing problem build routing table at each node costs are dynamic adaptive routing is hard

19 AntNet data structure routing table  probabilities of choosing each neighbor nodes for each possible final destination trips vector  contains statistics about ants’ trip times from current node k to each destination node d (means and variances) P(k,n,d)

20 Artificial Ants in a Network ? Probabilistic rule to choose the path Pheromone trail depositing Source Destination Memory

21 Simple AntNet Algorithm ants are launched regularly from each node to randomly chosen destination ants build their paths probabilistically with probability function of  artificial pheromone values  heuristic values ants memorize visited nodes and incurred costs once destination is reached, ants deterministically retrace their path backwards, updating pheromone trails that is a function of the quality of the solution they generated  refresh + evaporation !!

22 AntNet Routing - Agents Two kinds of Agents  Forward Ant explores the network and collects information when reaches the destination, changes into backward ant  Backward Ant goes back in the same path as forward ant update routing tables for all the nodes in the path

23 AntNet: F-Ants and B-Ants F-ants  collect implicit and explicit information on paths and traffic load implicit through arrival rate at destination explicit by storing experienced trip times  share queues with data packets B-ants  backpropagate fast  use higher priority queues Backward Ant Forward Ant (N1,T1) (N2,T2) (N1,T1) Forward Ant (N1,T1) (N2,T2) (N3,T3) Forward Ant (N1,T1) (N2,T2) (N3,T3) (N4, T4) Forward Ant Backward Ant

24 Using Pheromone and Memory to Choose the Next Node Memory of visited nodes i  ijd  ird j k  ikd r

25 Ants’ Probabilistic Transition Rule  ijd is the amount of pheromone trail on edge (i,j,d) J i k is the set of feasible nodes ant k positioned on node i can move to

26 Using Pheromone and Heuristic to Choose the Next Node Memory of visited nodes i j k r  ikd ;  ikd  ijd ;  ijd  ird ;  ird stored in pheromone table a heuristic evaluation of link (i,j,d) which introduces problem specific information

27 Using Pheromone and Heuristic to Choose the Next Node Memory of visited nodes i j k r  ikd ;  ikd  ijd ;  ijd  ird ;  ird stored in pheromone table a heuristic evaluation of link (i,j,d) which introduces problem specific information: for AntNet: proportional to the inverse of link (i,j) queue length

28 B-ants update routing tables:  if B-ant has source node d and goes from node n to k  Increase the probability of the channel that backward ant comes from P(k,n,d) = P(k,n,d) + R.(1 – P(k,n,d))  Decrease the probability of the other channels P(k,i,d) = P(k,i,d) - R.(1 – P(k,i,d))for all i != n R (0 < R <= 1), function of - T: time experienced by F-ant - m: avg time for same destination memorized in trips table - sigma: std. deviation for same destination memorized in trips table P(k,n,d)

29 AntNet evaluation extensive tests and experiments  American NSF net  Japanese NTT net  artificial networks simple graphs grid networks in short: good results  similar throughput compared to other routing algorithms  remarkably smaller avg. packet delay

30 Ant Colony Optimization (ACO) TSP has been a popular problem for the ACO models. - several reasons why TSP is chosen … Key concepts:  Positive feedback build a solution using local solutions, by keeping good solutions in memory.  Negative feedback want to avoid premature convergence, evaporate the pheromone.  Time scale number of runs are also critical.

31 Traveling Salesman Problem (TSP)

32 Ant Optimization of TSP 1. seed all paths with initial pheromone 2. ants make a tour of all cities  ant probabilistically selects next city to visit considering distance and pheromone strength on each path 3. ants deposit pheromone on their path with an intensity inversely proportional to the length of their tour 4. pheromone decays with each time step 5. repeat steps until some threshold is met

33 A simple TSP example A E D C B 1 [] d AB =100;d BC = 60…;d DE =150

34 Iteration 1 A E D C B 1 [A] 5 [E] 3 [C] 2 [B] 4 [D]

35 How to build next sub-solution? A E D C B 1 [A] [A,D]

36 Iteration 2 A E D C B 3 [C,B] 5 [E,A] 1 [A,D] 2 [B,C] 4 [D,E]

37 Iteration 3 A E D C B 4 [D,E,A] 5 [E,A,B] 3 [C,B,E] 2 [B,C,D] 1 [A,D,C]

38 Iteration 4 A E D C B 4 [D,E,A,B] 2 [B,C,D,A] 5 [E,A,B,C] 1 [A,D,C,E] 3 [C,B,E,D]

39 Iteration 5 A E D C B 1 [A,D,C,E,B] 3 [C,B,E,D,A] 4 [D,E,A,B,C] 2 [B,C,D,A,E] 5 [E,A,B,C,D]

40 Path and Pheromone Evaluation 1 [A,D,C,E,B] 5 [E,A,B,C,D] L 1 =300 L 2 =450 L 3 =260 L 4 =280 L 5 =420 2 [B,C,D,A,E] 3 [C,B,E,D,A] 4 [D,E,A,B,C]

41 End of First Run All ants die New ants are born Save Best Tour (Sequence and length) stopping criteria stagnation max.runs

42 Ant cycle for TSP 1. tabu list 2. random walk 3. priorities 4. backtracing and considering edge length

43 Tabu List n : number of cities = one city tour m : number of ants k : ant index s : member in tabu list (current city) for each iteration in the ant algorithm cycle: insert town in „visited node list“ for (int k = 1 ; k <= m ; k++) { insert town of ant k in Tabu k (s) }

44 Random Walk & Priorities i,j : edge between nodes i,j n ij : 1/distance(i,j)  : weight for marking  : weight for node „neighbourhoodness“ probability of ant k for going from city i to city j from ant routing table: allowed k : unvisited cities for ant k

45 Backtracing i,j : edge between nodes i,j  ij (t): marking at time t  : evaporation rate (t,t+n) marking after tour = evaporation_rate * marking_old + marking_delta marking_delta = sum of markings of all ants k who passed (i,j) Q/L k : const/tour-length of ant k With Tabu List, ant routing table:

46 Ant System (Ant Cycle) Dorigo [1] 1991 t = 0; NC = 0; τ ij (t)=c for ∆τ ij =0 Place the m ants on the n nodes Update tabu k (s) Compute the length L k of every ant Update the shortest tour found = For every edge (i,j) Compute For k:=1 to m do Initialize Choose the city j to move to. Use probability Tabu list management Move k-th ant to town j. Insert town j in tabu k (s) Set t = t + n; NC=NC+1; ∆τ ij =0 NC<NC max && not stagn. Yes End No Yes

47 10-Cities-Problem CCA0 AntSystem marking distribution at beginning and after 100 cycles

48 Oliver30 Problem cycles: 342 length : 420  = 1  = 5  = 0.5

49 Advantages: positive feedback accounts for rapid discovery of good solutions distributed computation avoids premature convergence the greedy heuristic helps find acceptable solution in the early solution in the early stages of the search process the collective interaction of a population of agents Disadvantages: slower convergence than other heuristics performed poorly for TSP problems larger than 75 cities

50 Improvements to AS: Ant Colony System (ACS) ACS (pheromone update)  update pheromone trail while building the solution  ants eat pheromone on the trail  local search added before pheromone update

51 Research Summary Ant System (AS) [Dorigo, Maniezzo & Colorni]  Original implementation of ant-inspired optimization Ant Colony System (ACS) [Dorigo & Gambardella]  Ants probabilistically choose exploitation or biased exploration Max-Min Ant System (MMAS) [Stutzle & Hoos]  Only ant with best tour deposits pheromone  Range of pheromone limited to given interval  Pheromone levels initialized to max levels

52 Research Summary refinements  Pheromone Trail Smoothing (PTS)  increases pheromone on all segments in proportion to the difference from the max value  Ranked Ants  n ants with best paths deposit pheromone based on rank  Elite Ants  best path per cycle receives additional pheromone  Modified 3-Opt  iteratively swap order of three-city sub-paths such that total path length decreases

53 Result Comparison PTS = Pheromone Trail Smoothing MMAS = MaxMin AntSystem ACS = Ant Colony System AS = Ant System 10,000 cycles per run [Stutzle & Hoos, 1999]

54 General ACO a stochastic construction procedure probabilistically build a solution iteratively adding solution components to partial solutions  heuristic information  pheromone trail reinforcement modify the problem representation at each iteration ants work concurrently and independently collective interaction via indirect communication leads to good solutions

55 Conclusion general ACO work well on static problems like TSP, but hard to beat specialist algorithms but most of all … ants are “dynamic” optimizers inherently capable of dealing with dynamism Other Application Domains for Ants manufacturing control peer-2-peer active networking …  similar principles artificial stigmergy / feedback through pheromones information decay (pheromone evaporation) probabilistic choice in path following …