Ant Colony Optimization with Castes

Transkript

1 Ant Colony Optimization with Castes Oleg Kovářík Computational Intelligence Group Department of Computer Science and Engineering Faculty of Electrical Engineering Czech Technical University in Prague

2 Content 1) Ant Algorithms 2) ACO & Applications 3) ACO with Subsolutions 4) ACO with Castes 5) Continuous ACO

3 1) ANT ALGORITHMS Clustering (ACA, ATTA, ACLUSTER, DataBots, Cellular Ants,...) Combinatorial Optimization (ACO, MMAS, AS,...) Continuous and mixed-variable optimization AACA, BACA,...) (ACO*, DACO, Classification Rules Extraction (Ant-Miner) Feature Extraction Robotics

4 Clustering Real and simulated ant clustering Cellular ants Color and shape negotiations automatic number of classes, similarity Moere et al. (2006)

5 Combinatorial Optimization Bruce G. Marcot TSP, VRP, Quadratic assignment, Job-shop sheduling, Sequential ordering, Graph coloring, Bin packing, Shortest common subsequence,... + dynamic problems like Network Routing or Network Flows

6 2) ANT COLONY OPTIMIZATION

7 ACO (Dorigo) Ant Colony Optimization metaheuristic parallel stochastic search probability updated guided by pheromone by feedback and evaporation?

8 TSP Travelling Salesman Problem the shortest closed simple path through given cities NP-complete

9 ACO - path construction Pheromone map Which next? Nearest? Used in best solutions? radnom starting city

10 Max-Min Ant System (MMAS) Probability of choosing path from city i to city j pheromone level memory distance-1 heuristic Update by best solution & evaporation depends on inclusion in best tour

11 Logistics, Circuit Boards Travelling Salesman, Vehicle Routing,... Circuit Boards Drilling (Laser)

12 Phylogenetic trees DNA Similarity matrix ACTCGTATCGTGTATGTGCTA... CACGACAGGTCTTGCTACATT... GGGCTCGCATACATTACTATA... ACO on TSP Phylogenetic tree

13 3) ACO WITH SUBSOLUTIONS

14 Parallelization on Cell Cell Broadband Engine Processor 1 x PPE 8 x SPE

15 Step 1: Select Subsets of Cities solve on separate units using ACO

16 Step 2: Solve & Return Pheromone merge pheromone matrices

17 Pheromone Map for 1000 Cities with one solution:

18 Results

19 4) ACO WITH CASTES

20 Problem with Optimal Parameters Probability of choosing path from city i to city j pheromone level distance-1 We can search for optimal parameters (problem dependent) Adapt parameters OR

21 ACO+C: Ant Castes Specialization of ants -> castes different behaviour (workers, explorers,...) several kinds of pheromone (attractive vs. repulsive)

22 Example: MMAS+C Castes with different parameters αl, βl Probability of choosing city for l-th caste Different beaviour for each caste

23 Data 8 TSP, 3 Assymetric TSP from TSPLIB Real cities, drilling problems: lin105.tsp eil101.tsp pr107.tsp

24 MMAS vs. MMAS+C MMAS MMAS+C (10 castes) Averages from 30 runs, lower = better:

25 Adaptive castes Dynamic number of ants in castes Depends on number of improvements max number of ants caste 1 caste 2 0, 0 iteration imax Improvement not significant (larger problems?)

26 Dynamics pheromone based local search -> tour length <- strong nearest distance heuristric tour lengths for all ants castes (color = caste) best solution found iterations

27 GA castes design Genetic algorithm improving "queens" worker explorer Improvement not significant Algorithm is robust or Results too close to optimum -> larger problems?

28 Demo: Configuration # castes: #id weight greedyprob # pheromones # id evaporation NN beta attractpheromone[] repulsepheromone[] laypheromone[] caste 2 is attracted to the pheromone 1 by exponent 2.0 and lays most substance to the pheromone 2

29 Demo: Visualization 3 standard pheromones solutions for all pheromones (thicker lines = best solution) static "greedy" pheromone... demonstration

30 Improvemets Limited neighborhood Restarts (pheromone reinitialization) Hybridization (k-opt, Lin-Kernighan) but random + restarts + LK = are the ants necessary? experiments needed

31 Comparison with other methods Reported to perform better than GA and SA on TSP, but results depend strongly on parameters, lot of experiments only on e.g. 3 small datasets Comparison with standard methods e.g. Concorde ( comparison not available results of Concorde seems to be unreachable biggest problem: celestial objects found path that is proved to be within 0.796% of the cost of an optimal tour (using decomposition)

32 5) CONTINUOUS ACO

33 Direct Application of ACO DACO (Min Kong, Peng Tian 2006) n variables xi with normal distribution N (μi, σi ), i {1,, n} x2 Updates by global best solution x: x1 μ(t) = (1 ρ) μ (t 1) + ρx σ(t) = (1 ρ) σ (t 1) + ρ x μ(t 1)

34 Extended ACO ACO* (Socha 2004) complex pheromone distribution x1 Gaussian kernel PDF

35 Ants & Neural Networks Ant Colony Optimization for combinatorial optimization (TSP) can be extended for continuous optimization......can optimize NN weights (Blum, Socha 2005)

36 GAME (Kordík) Select: transfer function, parameters, optimization method for each unit Niching Genetic Algorithm

37 GAME Niching Genetic Algorithm

38 GAME

39 Two spirals dataset Classification 2 classes

40 Training and testing set

41 Results on testing dataset

42 Thank you