1. Selected Topics in Evolutionary Algorithms I Pavel Petrovič Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics ppetrovic@acm.org July 4 th 2008

2. 2 Riddle Theorem: 1$ = 10 cent Proof: We know that $1 = 100 cents, divide both sides by 100: $ 1/100 = 100/100 cents $ 1/100 = 1 cent Take square root both side: sqrt($1/100) = sqrt (1 cent) $ 1/10 = 1 cent Multiply both side by 10: $1 = 10 cent How many robots does it take to screw in a light bulb? Three – one to hold the bulb and two to turn the ladder.

3. 3 Robots in Everyday Life Rescue, Patrol, Safety, Security Assistance at Home and in Public Maintenance and Services Monitoring and Data Collection Production, Construction, Mining Transport, Shipping, Storehouses Education and Entertainment Space, Marine, Polar, Extreme Conditions Selected Topics in Evolutionary Algorithms I, July 4 th 2008

4. 4 Robotics: Multidisciplinary Efforts Robotics Biology Computer Science Psychology Physics Mechanical Engineering Material Science Electrical Engineering Communication Technology Selected Topics in Evolutionary Algorithms I, July 4 th 2008

5. 5 Robotics and Computer Science Signal and Data Processing and Analysis Prediction and Estimation Optimization, Scheduling, Planning, Search Image Processing and Pattern Recognition Machine Vision Simulation and Modelling Knowledge Representation and Machine Learning Human-Computer Interaction Selected Topics in Evolutionary Algorithms I, July 4 th 2008

6. 6 Robotics and Computer Science (2) ‏ Robotics = applied engineering field Computer Science = theoretical field Methods Algorithms Real-world tasks Commercial products Selected Topics in Evolutionary Algorithms I, July 4 th 2008

7. 7 Robotics Challenges Robotic applications in unpredictable, dynamic, non-deterministic environments Require real-time algorithms and reactive architectures that allow adaptation, learning, behavior plasticity Resulting systems exhibit features of ”intelligence” Selected Topics in Evolutionary Algorithms I, July 4 th 2008

8. 8 Long-term goal and efforts Building mobile robots capable of autonomous execution of complex tasks in realistic, dynamic, non-deterministic, unpredictable environments Require suitable sensors, actuators, morphologies and controllers: Important challenge: organization of controller architecture and its design, i.e. how a robot is ”trained” for the target task, how it can generate, revise and execute plans Selected Topics in Evolutionary Algorithms I, July 4 th 2008

9. 9 Industrial Robotics: Focused on working solutions, manufacturing robots, control theory, deterministic environments, repetitive operations Artificial Intelligence Intersection of Philosophy, and Psychology, spiced with Biology; parasiting on Computer Science: Set to answer questions of the fundamental principles of intelligence, knowledge acquisition, organization and representation; Dreams about discovering methods and algorithms that can be useful in applications Artificial Life Studies principles of generalized life mechanisms Needs/attempts for physical systems Approaches to Robotics Selected Topics in Evolutionary Algorithms I, July 4 th 2008

10. 10 Search Space of possible solutions Search criterion:  Determines what is the “best“ solution and which of any two solutions is “better“ Example:  4 people trying to cross the bridge at night  Max. two at the same time  Take different time: 1,2,5,10  Must use flashlight  What is the fastest strategy? Selected Topics in Evolutionary Algorithms I, July 4 th 2008

11. 11 Search Deterministic search:  Systematically exhausting: Depth-first search Breadth-first search Iterative deepening  Heuristic search Greedy search A* search – optimal Stochastic search Monte-carlo Simulated annealing Evolutionary algorithms TABU search Selected Topics in Evolutionary Algorithms I, July 4 th 2008

12. 12 Example: Search for shortest path Selected Topics in Evolutionary Algorithms I, July 4 th 2008

13. 13 Example: Search for shortest path Selected Topics in Evolutionary Algorithms I, July 4 th 2008

14. 14 Example: Search for shortest path Selected Topics in Evolutionary Algorithms I, July 4 th 2008

15. 15 Example: Search for shortest path Selected Topics in Evolutionary Algorithms I, July 4 th 2008

16. 16 Example of greedy search: Knight tour The knight is to visit every location exactly once Heuristic: visit the location with lowest # of DOF Selected Topics in Evolutionary Algorithms I, July 4 th 2008

17. 17 Example of heuristic search: Game15 Sliding numbered stones until target configuration is achieved: (about 10^13 possible states) Can you find the correct heuristic? Selected Topics in Evolutionary Algorithms I, July 4 th 2008

18. 18 Example of heuristic search: Game15 A* algorithm Admissible heuristic the number of misplaced tiles (admissible, because an out of place tile requires at least one move to get to the right place). the sum of the Manhattan distances of each tile from its proper place (admissible because each move can only move a tile one step closer). Comparison for the eight-puzzle (branching factor is around 3, sample runs at a depth of 12): Iterative-deepening expanded 3,644,035 nodes A* with the first heuristic expanded 227 nodes A* with the second heuristic expanded 73 nodes Selected Topics in Evolutionary Algorithms I, July 4 th 2008

19. 19 Problem solving: types of problems “Easy”: polynomial-time solution exists (class P)‏ Difficult: only non-deterministic polynomial-time solution exists (class NP), or not even that...  particular class NP-complete Difficult problems require exponential time a N – problems of realistic sizes cannot be solved using deterministic algorithms! Stochastic methods – find some good solution, instead of the best one: optimization Selected Topics in Evolutionary Algorithms I, July 4 th 2008

20. 20 Stochastic methods: Monte Carlo Determine the area of a particular shape: Selected Topics in Evolutionary Algorithms I, July 4 th 2008

21. 21 Stochastic methods: Simulated Annealing Navigating in the search space using local neighborhood: Selected Topics in Evolutionary Algorithms I, July 4 th 2008

22. 22 Principles of Natural Evolution Individuals have information encoded in genotypes that consist of genes, alleles The more successful individuals have higher chance of survival and therefore also higher chance of having descendants The overall population of individuals adapts to the changing conditions so that the more fit individuals prevail in the population Changes in the genotype are introduced through mutations and recombination Selected Topics in Evolutionary Algorithms I, July 4 th 2008

23. 23 Evolutionary Computation Search for solutions to a problem Solutions uniformly encoded Fitness: objective quantitative measure Population: set of randomly generated solutions Principles of natural evolution:  selection, recombination, mutation Run for many generations Selected Topics in Evolutionary Algorithms I, July 4 th 2008

24. 24 EA Concepts genotype and phenotype fitness landscape diversity, genetic drift premature convergence exploration vs. exploitation selection methods: roulette wheel (fit.prop.), tournament, truncation, rank, elitist selection pressure direct vs. indirect representations fitness space Selected Topics in Evolutionary Algorithms I, July 4 th 2008

25. 25 Genotype and Phenotype Genotype – all genetic material of a particular individual (genes)‏ Phenotype – the real features of that individual Selected Topics in Evolutionary Algorithms I, July 4 th 2008

26. 26 Fitness landscape Genotype space – difficulty of the problem – shape of fitness landscape, neighborhood function Selected Topics in Evolutionary Algorithms I, July 4 th 2008

27. 27 Population diversity Must be kept high for the evolution to advance Selected Topics in Evolutionary Algorithms I, July 4 th 2008

28. 28 Premature convergence important building blocks are lost early in the evolutionary run Selected Topics in Evolutionary Algorithms I, July 4 th 2008

29. 29 Premature convergence Selected Topics in Evolutionary Algorithms I, July 4 th 2008

30. 30 Genetic drift Loosing the population distribution due to the sampling error Selected Topics in Evolutionary Algorithms I, July 4 th 2008

31. 31 Exploration vs. Exploitation Exploration phase: localize promising areas Exploitation phase: fine-tune the solution Selected Topics in Evolutionary Algorithms I, July 4 th 2008

32. 32 Selection methods roulette wheel (fitness proportionate selection), tournament selection truncation selection rank selection elitist strategies Selected Topics in Evolutionary Algorithms I, July 4 th 2008

33. 33 Selection pressure Influenced by the problem Relates to evolutionary operators Selected Topics in Evolutionary Algorithms I, July 4 th 2008

34. 34 Direct vs. Indirect Representations Selected Topics in Evolutionary Algorithms I, July 4 th 2008

35. 35 Fitness Space (Floreano) ‏ Functional vs. behavioral Explicit vs. implicit External vs. internal Selected Topics in Evolutionary Algorithms I, July 4 th 2008

36. 36 Evolutionary Robotics Solution: Robot’s controller Fitness: how well the robot performs Simulation or real robot Selected Topics in Evolutionary Algorithms I, July 4 th 2008

37. 37 Fitness Influenced by Robot’s abilities (sensors, actuators)‏ Incremental change during evolution: Incremental Evolution Task difficulty Environment difficulty Controller abilities T Robot Morphology Selected Topics in Evolutionary Algorithms I, July 4 th 2008

38. 38 Evolvable Tasks Wall following Obstacle avoidance Docking and recharging Artificial ant following Box pushing Lawn mowing Legged walking T-maze navigation Foraging strategies Trash collection Vision discrimination and classification tasks Target tracking and navigation Pursuit-evasion behaviors Soccer playing Navigation tasks Selected Topics in Evolutionary Algorithms I, July 4 th 2008

39. 39 Neuroevolution through augmenting topologies The most successful method for evolution of artificial neural networks Sharing fitness Starting with simple solutions Global counter i.e. Topological crossover – very important for preserving evolved structures Selected Topics in Evolutionary Algorithms I, July 4 th 2008