Introduction • What is swarm intelligence ? “Swarm Intelligence (SI) is the property of a system whereby Swarm Intelligence: From Natural to the collective behaviors of (unsophisticated) agents interacting Artificial Systems locally with their environment cause coherent functional global patterns to emerge.” Eric Bonabeau, Marco Dorigo, and Guy Theraulaz • “SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model.” (http://dsp.jpl.nasa.gov/members/payman/swarm/) 2/25/2003 CS 851: Bio-Inspired Computing 1 2/25/2003 CS 851: Bio-Inspired Computing 2 Chapter 2: Ant Foraging Behavior, Combinatorial Optimization, Foraging Strategies in Ants and Routing in Communications Network • http://uk.geocities.com/markcsinclair/aco.html • The Binary Bridge Experiment (Page 27) The ants choose one branch over the other due to some random • http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html fluctuations. • http://www.iwr.uni- heidelberg.de/groups/comopt/software/TSPLIB95/index.html • Probability of choosing one branch over the other ~ k + A n ( ) = = − P i P 1 A B k + A n + k + B n ( ) ( ) i i • The values of k and n determined through experiments. k = degree of attraction of an unmarked branch n = choice function 2/25/2003 CS 851: Bio-Inspired Computing 3 2/25/2003 CS 851: Bio-Inspired Computing 4 Foraging Strategies in Ants Foraging Strategies in Ants • Ants deposit pheromone on the paths that they cover and this • Inter-nest Traffic studied – a case of natural optimization results in the building of a solution (optimal path). • Similarity with MST shown by Aron et al. • Other experiments done – effect of light vs dark, chemical vs • In SI and optimization, concept of pheromone evaporation is visual cues. used. • Helps in avoiding suboptimal solutions – local optima. • Conclusion here: some colonies have networks of nests several • May differ from how it takes places in the real world. hundreds of meters in span – it is possible this is close to a MST. 2/25/2003 CS 851: Bio-Inspired Computing 5 2/25/2003 CS 851: Bio-Inspired Computing 6 1
� ✁ Raid Patterns of Army Ants Raid Patterns of Army Ants • An example of powerful, totally • 3 species of ants have a common ancestor. decentralized control. • Can the foraging behavior be explained through a different environment in each case? • Example : Eciton burchelli can • Deneubourg et al. modeled the behavior of these ants. consist of as many as 200,000 workers. • Used a 2-D grid • Had several rules like: • These individuals are blind, • 1 ant deposits 1 unit of pheromone per each visited site while communication via pheromone. returning to its nest. • Maximum number of ants per site 2/25/2003 CS 851: Bio-Inspired Computing 7 2/25/2003 CS 851: Bio-Inspired Computing 8 Raid Patterns of Army Ants Ant Colony Optimization (ACO) • Pheromone disappearance rate at • We now come to more rigorous mathematical models. each site • TSP has been a popular problem for the ACO models. • Movement of an ant from one site - several reasons why TSP is chosen….. to the other based on a probabilistic mechanism shown earlier. • Key concepts: • Particular food distribution in the • Positive feedback – build a solution using local solutions, by network keeping good solutions in memory. • A well-defined raid pattern is observed. • Negative feedback – want to avoid premature convergence, • Some similarity with the actual evaporate the pheromone. observations. • Time scale – number of runs are also critical. 2/25/2003 CS 851: Bio-Inspired Computing 9 2/25/2003 CS 851: Bio-Inspired Computing 10 Ant System (AS) Ant System (AS) • Transition Rule • Used to solve TSP • Probability of ant k going from city i to j: • Transition from city i to j depends on: [ ] [ ] 1. Tabu list – list of cities not visited α β τ η t ( ) . 2. Visibility = 1/d ij ; represents local information – heuristic k = ij ij p t ( ) [ ] [ ] ij α β desirability to visit city j when in city i. τ η t ( ) . il il 3. Pheromone trail T ij (t) for each edge – represents the learned k ∈ J i desirability to visit city j when in city i. • Alpha and beta are adjustable parameters. • Generally, have several ants searching the solution space. m = n 2/25/2003 CS 851: Bio-Inspired Computing 11 2/25/2003 CS 851: Bio-Inspired Computing 12 2
✂ ✄ Ant System (AS) Ant System (AS) [ ] [ ] α β τ t η • Pheromone update : ( ) . ij ij p k t = ( ) [ ] [ ] ∆ τ k = k ∈ k Q L t if i j T t else ij α β τ t η / ( ) ( , ) ( ) 0 . ( ) . ij il il k ∈ J i • T is the tour done at time t by ant • Alpha = 0 : represents a greedy approach k, L is the length, Q is a heuristic parameter. • Beta = 0 : represents rapid selection of tours that may not be • Pheromone decay: optimal. τ t = − ρ τ t + ∆ τ t ( ) ( 1 ). ( ) ( ) • Thus, a tradeoff is necessary. ij ij ij 2/25/2003 CS 851: Bio-Inspired Computing 13 2/25/2003 CS 851: Bio-Inspired Computing 14 Ant System (AS) Ant System (AS) • Modifications to the algorithm: • Does not converge to a single solution – is that a good criteria? • Elitist scheme borrowed from GA • Use the elitist to update its own tour (T+) edges for pheromone deposition. • However, they conclude that the “nonconvergence” property is interesting – • Could extend the same concept to “e” elitists ants. 1. It tends to avoid trappings in local optima. 2. Could be used for dynamic problems. • Results …..? • Does not perform as well as other methods – the ones mentioned are TS (Tabu Search) and SA. • So next …..ACS 2/25/2003 CS 851: Bio-Inspired Computing 15 2/25/2003 CS 851: Bio-Inspired Computing 16 Ant Colony System (ACS) Ant Colony System (ACS) τ = − ρ τ + ρ ∆ τ t t t ( ) ( 1 ). ( ) . ( ) ij ij ij [ ] [ ] β j = τ t η if q ≤ q j = J arg max { ( ) . } u ∈ J i ij iu o k • Pheromone update rule (new): • Modifications to AS. • However, only applied to the best ant. • New transition rule: • The change in the pheromone concentration = 1/L+. q o is a parameter that can be tweaked • It is similar to tuning temperature in SA. • Local updates done as follows: • J is a city randomly selected according to the probability calculated previously. • This helps ACS to improvise on the best solutions. τ t = − ρ τ t + ρτ ( ) ( 1 ). ( ) ij ij 0 2/25/2003 CS 851: Bio-Inspired Computing 17 2/25/2003 CS 851: Bio-Inspired Computing 18 3
✆ ☎ ✝ Ant Colony System (ACS) Ant Colony System (ACS) • To improves its search methodology, uses a candidate list of cl • Use a local search method in conjunction with ACS-TSP. closest cities, considers these first, considers other cities only • Called as 2-opt, 3-opt – refers to the number of edges when the list is exhausted. exchanged iteratively to obtain a local optima. • Example cl = 15 on Page 51. • Has been shown to be comparable to the best techniques • ACS-TSP has been applied on problems of various sizes. available (GA). • ACS-TSP has been shown to be superior over other methods like GA, SA, EP for problems of size 50 – 100 cities. • Other methods for improvement- • For larger size problems……… • Elitism, worst tours (pheromone removed), local search enhancement. 2/25/2003 CS 851: Bio-Inspired Computing 19 2/25/2003 CS 851: Bio-Inspired Computing 20 The Quadratic Assignment Problem (QAP) The Quadratic Assignment Problem • Find pi such that the following is minimized: • Associate the minimum total flow at a node with the maximum total potential and so on : min-max coupling rule. n • This is a good heuristic, but does not give the optimal results. π = C d ij f ( ) π π i j ( ) ( ) i j = , 1 • Hence AS-QAP proposed. • The transition rule – the probability that the kth ant chooses activity j as • QAP has shown to be NP-hard. the activity to assign to location i is: • d’s are the distance between the nodes and f’s are the flows between nodes. [ ] [ ] τ α η β • The problem is similar to TSP. t ( ) . k = ij ij p t ( ) • distance potentials and flow potentials. [ ] [ ] ij α β τ t η ( ) . il il k ∈ J i 2/25/2003 CS 851: Bio-Inspired Computing 21 2/25/2003 CS 851: Bio-Inspired Computing 22 The Quadratic Assignment Problem Hybrid Ant System (HAS) τ = − ρ τ + ∆ τ t t t ( ) ( 1 ). ( ) ( ) • Departs radically from previously described ACO algorithms. ij ij ij • Three procedures: • Same pheromone update rule as AS-TSP. 1. Pheromone-trail-based modification Here the change is equal to Q/C k (t) though – hence low coupling (C) • 2. Local search value means a stronger pheromone trail. 3. Pheromone trail updating • Results : …..kind of the same idea as ACS. • GA, ES < AS-QAP < TS, SA • Improvements….. 2/25/2003 CS 851: Bio-Inspired Computing 23 2/25/2003 CS 851: Bio-Inspired Computing 24 4
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