Computational Intelligence Winter Term 2011/12

1. ComputationalIntelligence Winter Term 2011/12 Prof. Dr. Günter Rudolph Lehrstuhl für Algorithm Engineering (LS 11) Fakultät für Informatik TU Dortmund

2. Swarm Intelligence Contents • Ant algorithms (combinatorial optimization) • Particle swarm algorithms (optimization in Rn) G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 2

3. concepts: ● evaluation of own current situation ● comparison with other conspecific ● imitation of behavior of successful conspecifics Swarm Intelligence metaphor swarms of bird or fish seeking for food ants or termites seeking for food concepts: ● communication / coordination by means of „stigmergy“ ● reinforcement learning → positive feedback  audio-visual communication  olfactoric communication G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 3

4. Swarm Intelligence ant algorithms (ACO: Ant Colony Optimization) paradigm for design of metaheuristics for combinatorial optimization stigmergy = indirect communication through modification of environment »1991 Colorni / Dorigo / Maniezzo: Ant System (also: 1. ECAL, Paris 1991) Dorigo (1992): collectivebehavorofsocialinsects (PhD) somefacts: • about 2% of all insectsaresocial • about 50% of all socialinsectsareants • total weightof all ants = total weightof all humans • antspopulateearthsince 100 millionsyears • humanspopulateearthsince 50.000 years G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 4

5. nest food nest food Swarm Intelligence double bridgeexperiment (Deneubourg et al. 1990, Goss et al. 1989) initially:both bridges used equally often finally:all ants run over single bridge only! finally:all ants use the shorter bridge! G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 5

6. positive feedbackloop Swarm Intelligence • Howdoesitwork? • antsplacepheromons on theirway • routingdepends on concentrationofpheromons moredetailed: antsthatuseshorterbridgereturnfaster )pheromoneconcentrationhigher on shorterbridge )antschooseshorterbridgemorefrequentlythanlongerbridge )pheromonconcentration on shorterbridgeevenhigher )evenmoreantschooseshorterbridge )a.s.f. G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 6

7. Swarm Intelligence • Ant System (AS) 1991 combinatorial problem: • components C = { c1, c2, ..., cn } • feasible set F µ 2C • objective function f: 2C→R ants = set of concurrent (or parallel) asynchronous agents move through state of problems partial solutions of problems )caused by movement of ants the final solution is compiled incrementally G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 7

8. ‘trails‘ paths ‘attractiveness‘ excitement, stimulus feedback Swarm Intelligence movement: stochastic local decision (2 parameters) • while constructing the solution (if possible), otherwise at the end: • evaluation of solutions • modification of ‘trail value‘ of components on the path G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 8

9. Swarm Intelligence • ant k in state i • determine all possible continuations of current state i • choice of continuation according to probability distribution pij pij = q( attractivity, amount of pheromone ) heuristic is based on a priori desirability of the move a posteriori desirability of the move„how rewarding was the move in the past?“ • update of pheromone amount on the paths: as soon as all ants have compiled their solutions good solution % increase amount of pheromone, otherwise decrease & G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 9

10. Swarm Intelligence Combinatorial Problems (Example TSP) • TSP: • ant starts in arbitrary city i • pheromone on edges (i, j): ij • probability to move from i to j: • ij = 1/dij ; dij = distance between city i and j •  = 1 and 2 [2, 5] (empirical), 2 (0,1) “evaporation rate“ • Ni(t) = neighborhood of i at time step t (without cities already visited) • update of pheromone after  journeys of ants: • ij(k) = 1 / (tour length of ant k), if (i,j) belongs to tour G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 10

11. Swarm Intelligence • two additional mechanisms: • trail evaporation • demon actions (for centralized actions; not executable in general) Ant System (AS) is prototype tested on TSP-Benchmark → not competitive )but: works in principle! • subsequent: 2 targets • increase efficiency (→ competitiveness with state-of-the-art method) • better explanation of behavior 1995 ANT-Q (Gambardella & Dorigo), simplified: 1996 ACS ant colony system G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 11

12. Swarm Intelligence Particle Swarm Optimization (PSO) abstraction from fish / bird / bee swarm paradigm for design of metaheuristics for continuous optimization developedby Russel Eberhard & James Kennedy (~1995) • concepts: • particle (x, v) consists of position x 2Rn and “velocity” (i.e. direction) v 2Rn • PSO maintains multiple potential solutions at one time • • during each iteration, each solution/position is evaluated by an objective function • • particles “fly” or “swarm” through the search space to find position of an extremal value returned by the objective function G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 12

13. Swarm Intelligence PSOupdate ofparticle (xi, vi) atiteration t 1st step: const. const. const. random variable random variable bestsolutionamong all solutionsuptoiteration t ≥ 0 bestsolutionamong all solutionsofiteration t ≥ 0 G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 13

14. Swarm Intelligence PSOupdate ofparticle (xi, vi) atiteration t 1st step: newdirection olddirection directionfrom to directionfrom to G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 14

15. Swarm Intelligence PSOupdate ofparticle (xi, vi) atiteration t 2nd step: Note thesimilaritytotheconceptofmutativestepsizecontrol in EAs: firstchangethestepsize (direction), thenusechangedstepsize (direction) forchangingposition. newposition newdirection oldposition G. Rudolph: ComputationalIntelligence▪ Winter Term 2011/12 15