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Genetic Algorithms and Ant Colony Optimisation (lecture slides)

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Genetic Algorithms and Ant Colony Optimisation (lecture slides)

  1. 1. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Genetic Algorithms and Ant Colony Optimisation - An Introduction - Prof. Dr. Dagmar Monett Díaz Computer Science Dept. Faculty of Cooperative Studies Berlin School of Economics and Law dagmar@monettdiaz.com Europe Week, 3rd – 7th March 2014
  2. 2. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 2 Can you guess what it is?
  3. 3. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  4. 4. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  5. 5. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  6. 6. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  7. 7. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  8. 8. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield
  9. 9. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield By Roger Alsing At http://rogeralsing.com/2008/12/07/genetic-programming-evolution-of-mona-lisa/ After 904 314 iterations, the evolution of only 50 semi- transparent polygons is almost perfect to Mona Lisa!! Evolution of Mona Lisa
  10. 10. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 10 Agenda
  11. 11. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 11 Agenda  Where does the major content come from?  What are metaheuristics?  What is to be optimised?  Examples of metaheuristics  What do GA and ACO have in common?  Genetic Algorithms  Ant Colony Systems  Metaheuristics: current trends  Further reading, sources of inspiration, and more…
  12. 12. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 12 ©
  13. 13. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Genetic Algorithms in Search, Optimization, and Machine Learning David E. Goldberg 432 pp. Addison-Wesley, 1989 ISBN-13: 978-0201157673 What I also use in my lectures at the HWR… 13
  14. 14. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Genetic Algorithms + Data Structures = Evolution Programs Zbigniew Michalewicz 3rd, revised and extended Edition Springer-Verlag, 1999 ISBN-13: 978-3540606765 What I also use in my lectures at the HWR… 14
  15. 15. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Ant Colony Optimization Marco Dorigo and Thomas Stützle MIT Press, Cambridge, MA, 2004 ISBN-13: 978-3540606765 15 Further reading
  16. 16. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Further reading  M. Dorigo, M. Birattari and T. Stützle (2006): “Ant Colony Optimization: Artificial Ants as a Computational Intelligence Technique”. Available at http://iridia.ulb.ac.be/IridiaTrSeries/rev/IridiaTr2006- 023r001.pdf  M. Dorigo and K. Socha (2007): “An Introduction to Ant Colony Optimization”. Available at http://iridia.ulb.ac.be/IridiaTrSeries/rev/IridiaTr2006- 010r003.pdf 16
  17. 17. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 17 What are metaheuristics?
  18. 18. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield A metaheuristic is… „[…] a master strategy that guides and modifies other heuristics (like local search procedures) to produce solutions beyond those that are normally generated in a quest for local optimality.“ 18 According to Laguna (2002)
  19. 19. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 19 What is to be optimised?
  20. 20. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Bowled function 20 Z = X.^2 + Y.^2
  21. 21. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Mexican hat 21 Z = sin(sqrt(X.^2+Y.^2)) ./ sqrt(X.^2+Y.^2)
  22. 22. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield The peaks surface 22 [X,Y,Z] = peaks(30); surfc(X,Y,Z) colormap hsv Image © http://www.mathworks.de/de/help/matlab/ref/surfc.html
  23. 23. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 1 23 By Dantzig, Fulkerson, and Johnson (1954) Solved instance: 42 cities in USA Image © http://www.tsp.gatech.edu
  24. 24. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 2 24 By Groetschel and Holland (1987) Solved instance: 666 interesting places in the world Image © http://www.tsp.gatech.edu
  25. 25. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP example nr. 3 25 By Applegate, Bixby, Chvatal, and Cook (2001) Solved instance: 15,112 German cities Image © http://www.tsp.gatech.edu
  26. 26. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 26 By Applegate, Bixby, Chvatal, Cook, and Helsgaun (2004) Solved instance: 24,978 cities in Sweden Image © http://www.tsp.gatech.edu TSP ex. nr. 4
  27. 27. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 27 By Nagata (2009) Solved instance: 100,000 cities (Mona Lisa TSP) Image © http://www.tsp.gatech.edu TSP ex. nr. 5
  28. 28. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield TSP ex. nr. 6 28 By Helsgaun (2009) Solved instance: 1,904,711 cities (World TSP) Image © http://www.tsp.gatech.edu
  29. 29. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Other domains 29  Quadratic assignment problems  Scheduling problems  Vehicle routing  Routing in communication networks  Graph colouring  Design problems in engineering  And many, many more!
  30. 30. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 30 Examples of metaheuristics
  31. 31. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 31  Traditional approaches:
  32. 32. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 32  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.
  33. 33. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 33  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.  SA (Simulated Annealing), TS (Tabu Search), ANN (Artificial Neural Networks), EDA (Estimation of Distribution Algorithms), ACO (Ant Colony Optimization), etc.
  34. 34. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Metaheuristics 34  Traditional approaches:  EC (Evolutionary Computation) • GA (Genetic Algorithms), ES (Evolution Strategies), GP (Genetic Programming), etc.  SA (Simulated Annealing), TS (Tabu Search), ANN (Artificial Neural Networks), EDA (Estimation of Distribution Algorithms), ACO (Ant Colony Optimization), etc.  Hybrid metaheuristics  recent approaches!
  35. 35. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 35 What do GA and ACO have in common?
  36. 36. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 36
  37. 37. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 37  Nature-inspired algorithms  GA (Holland, 1975): simulates the process of natural selection (i.e. Darwin’s theory of evolution)  ACO (Dorigo, 1991): simulates behaviour of ant colonies
  38. 38. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 38  Nature-inspired algorithms  GA (Holland, 1975): simulates the process of natural selection (i.e. Darwin’s theory of evolution)  ACO (Dorigo, 1991): simulates behaviour of ant colonies  Population-based algorithms
  39. 39. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 39  Nature-inspired algorithms  GA (Holland, 1975): simulates the process of natural selection (i.e. Darwin’s theory of evolution)  ACO (Dorigo, 1991): simulates behaviour of ant colonies  Population-based algorithms  Stochastic search methods (probabilities are used)
  40. 40. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 40  Nature-inspired algorithms  GA (Holland, 1975): simulates the process of natural selection (i.e. Darwin’s theory of evolution)  ACO (Dorigo, 1991): simulates behaviour of ant colonies  Population-based algorithms  Stochastic search methods (probabilities are used)  Near-optimal solutions are to be found (global convergence is not guaranteed)
  41. 41. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA and ACO 41  Nature-inspired algorithms  GA (Holland, 1975): simulates the process of natural selection (i.e. Darwin’s theory of evolution)  ACO (Dorigo, 1991): simulates behaviour of ant colonies  Population-based algorithms  Stochastic search methods (probabilities are used)  Near-optimal solutions are to be found (global convergence is not guaranteed)  Parameter tuning plays an important role
  42. 42. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 42 Genetic Algorithms – Pseudo code –
  43. 43. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 43 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA;
  44. 44. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 44 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Initialize a usually random population of individuals
  45. 45. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 45 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Evaluate the fitness of all individuals
  46. 46. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 46 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Compute statistics, keep the best individual so far, etc.
  47. 47. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 47 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Test for termination criteria
  48. 48. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 48 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Select a sub-population for offspring production
  49. 49. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 49 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Stochastically perturb genes of selected parents (apply mutation operators) and recombine them (apply crossover operators)
  50. 50. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 50 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Evaluate the new fitness of all individuals
  51. 51. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 51 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ); statistics P( t ); } end GA; Select the survivors for next generations. Should you apply elitism?
  52. 52. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield GA pseudo code 52 begin GA; t = 0; random P( t ); evaluate P( t ); statistics P( t ); while not done { t = t+1; P' = select P( t ); recombine P'( t ); evaluate P'( t ); P = survive P( t ), P'( t ) statistics P( t ); } end GA; Compute new statistics
  53. 53. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 53 What are the basic components in a GA? What should be defined? Image © renjith krishnan at http://www.freedigitalphotos.net/
  54. 54. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 54 Genetic Algorithms – Basic components –
  55. 55. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 55
  56. 56. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 56  A genetic representation of solutions to the problem,
  57. 57. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 57  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,
  58. 58. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 58  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’
  59. 59. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 59  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’  ‘genetic’ operators that alter the genetic composition of children during reproduction, and
  60. 60. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Basic components 60  A genetic representation of solutions to the problem,  a way to create an initial population of solutions,  an evaluation function (i.e., the environment), rating solutions in terms of their ‘fitness’  ‘genetic’ operators that alter the genetic composition of children during reproduction, and  values for the parameters (population size, probabilities of applying genetic operators, etc.)
  61. 61. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 61 Genetic Algorithms – Genetic operators –
  62. 62. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Example of crossover operator 62 Single point crossover (Also “Simple crossover”) Parents: Offspring: Crossover point: kth position . . . . . . 1 k k+1 q P1=(x1, …, xq) P2=(y1, …, yq) O1=(x1, …, xk, yk+1, …, yq) O2=(y1, …, yk, xk+1, …, xq)
  63. 63. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Example of mutation operator 63 Boundary mutation When using floating point representation: assign the new allele the value of one of the boundaries: if r < 0.5 then NewAllele := LowerBound; else NewAllele := UpperBound; with r generated at random in [0, 1] LowerBound UpperBound NewAllele = or OldAllele
  64. 64. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 64 Genetic Algorithms – Other issues –
  65. 65. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Other issues 65  Representation of individuals  Selection mechanisms  Parallel implementations  Adaptive Genetic Algorithms  Other evolutionary algorithms  Application domains
  66. 66. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 66 Ant Colony Optimization
  67. 67. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO 67  Strategies of real ants (e.g. to find food) are used to solve optimisation problems  The behaviour of the system (swarm) emerges as a result of the indirect communication of individuals through the environment (‘stigmergy’)  Ants lay and follow pheromone trails  Deposited pheromone on a path depends on the quality of that solution. It evaporates with time.  Ants collectively search the solution space
  68. 68. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 68 Ant Colony Optimization – Pseudo code –
  69. 69. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 69 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
  70. 70. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 70 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf
  71. 71. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 71 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf Ant lifecycle
  72. 72. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 72 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf The pheromone trail intensity automatically decreases over time
  73. 73. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (i) 73 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/I501F13/readings/dorigo99ant.pdf E.g., activation of a local optimisation procedure
  74. 74. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 74 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf
  75. 75. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 75 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Where to go next? E.g., go to nearest node or follow more intense pheromone trail?
  76. 76. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 76 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Update pheromone trail locally
  77. 77. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 77 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Update pheromone trail after constructing a complete solution
  78. 78. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield ACO pseudo code (ii) 78 © Dorigo & Di Caro at http://informatics.indiana.edu/jbollen/ I501F13/readings/dorigo99ant.pdf Free allocated resources
  79. 79. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 79 Metaheuristics: current trends
  80. 80. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Current trends  Combination of aspects from different metaheuristics, Artificial Intelligence, Operations Research techniques, etc.  Parallel algorithms to distribute the computational effort.  Optimization of parameters (i.e. configuration process) is a relevant issue  Application to other domains
  81. 81. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Configuration of algorithms (or “fine-tuning” of algorithms) Not all metaheuristic algorithms are auto-adaptive (in particular the hybrid approaches) Usually, control parameters are set by hand or in the spirit of brute-force mechanisms; time-consuming task Few published research works; not yet an established research area Distributed, remote or parallel execution of configuration algorithms: not existing (?) Shortcomings: Special topic in most recent conferences and workshops; current open question!!
  82. 82. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 82 Homework: “Search for implementations of GA and ACO that simulate their functioning and evaluate them!” Image © renjith krishnan at http://www.freedigitalphotos.net/
  83. 83. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 83 Assessment Image © renjith krishnan at http://www.freedigitalphotos.net/
  84. 84. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Questions 84 Mention and comment three similarities between Genetic Algorithms and Ant Colony Optimisation! Mention and comment three differences! PLEASE ANSWER AT: https://docs.google.com/forms/d/1Mog_vgm1hFV4CLnM1XjYUYVmPlepH6iu9OTeivKONQA/viewform
  85. 85. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 85 References
  86. 86. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Others… 86
  87. 87. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Further reading and sites…  Metaheuristics Network, at http://www.metaheuristics.net/  Ant Colony Optimization, official Web site of the ant colony metaheuristic, at http://www.aco- metaheuristic.org/ 87
  88. 88. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 88 Can you guess what it is?
  89. 89. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 516 – 7
  90. 90. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 1 013 – 9
  91. 91. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 2 520 – 15
  92. 92. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 3 519 – 16
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  94. 94. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 7 015 – 21
  95. 95. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 10 016 – 24
  96. 96. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 15 017 – 25
  97. 97. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 20 039 – 27
  98. 98. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 35 008 – 38
  99. 99. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 51 479 – 52
  100. 100. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 160 768 – 86
  101. 101. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 356 051 – 103
  102. 102. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 1 008 736 – 140
  103. 103. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 103 ?
  104. 104. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield Timmy
  105. 105. D. Monett – Europe Week 2014, University of Hertfordshire, Hatfield 105 Slides of the talk per request: dagmar@monettdiaz.com Prof. Dr. Dagmar Monett Díaz monettdiaz @dmonett http://monettdiaz.com

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