selected topics in evolutionary algorithms i pavel petrovič department of applied informatics,...
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Selected Topics in Evolutionary Algorithms I
Pavel PetrovičDepartment of Applied Informatics, Faculty of Mathematics, Physics and Informatics
[email protected] July 4th 2008
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RiddleTheorem: 1$ = 10 centProof: 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 centMultiply 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.
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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
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Robotics: Multidisciplinary Efforts
Robotics
BiologyComputer Science
Psychology
Physics Mechanical
Engineering
Material Science
Electrical Engineering
Communication Technology
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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
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Robotics and Computer Science (2)Robotics = applied
engineering field
Computer Science
= theoretical field
Methods Algorithms
Real-world tasks Commercial products
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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”
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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
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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
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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?
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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
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Example: Search for shortest path
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Example: Search for shortest path
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Example: Search for shortest path
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Example: Search for shortest path
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Example of greedy search: Knight tour
The knight is to visit every location exactly once Heuristic: visit the location with lowest # of DOFSelected Topics in Evolutionary Algorithms I, July 4th 2008
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Example of heuristic search: Game15 Sliding numbered stones until target configuration is
achieved: (about 10^13 possible states) Can you find the correct heuristic?
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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
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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 aN – problems of realistic sizes cannot be solved using deterministic algorithms!
Stochastic methods – find some good solution, instead of the best one: optimization
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Stochastic methods: Monte Carlo Determine the area of a particular shape:
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Stochastic methods: Simulated Annealing
Navigating in the search space using local neighborhood:
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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
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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
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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
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Genotype and Phenotype
Genotype – all genetic material of a particular individual (genes)
Phenotype – the real features of that individual
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Fitness landscape
Genotype space – difficulty of the problem – shape of fitness landscape, neighborhood function
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Population diversity
Must be kept high for the evolution to advance
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Premature convergence
important building blocks are lost early in the evolutionary run
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Premature convergence
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Genetic drift
Loosing the population distribution due to the sampling error
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Exploration vs. Exploitation
Exploration phase: localize promising areas Exploitation phase: fine-tune the solution
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Selection methods
roulette wheel (fitness proportionate selection),
tournament selection truncation selection rank selection elitist strategies
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Selection pressure
Influenced by the problem Relates to evolutionary operators
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Direct vs. Indirect Representations
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Fitness Space (Floreano)
Functional vs. behavioral Explicit vs. implicit External vs. internal
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Evolutionary Robotics Solution: Robot’s controller
Fitness: how well the robot performs Simulation or real robot
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Fitness Influenced by
Robot’s abilities (sensors, actuators)
Incremental change during evolution:
Incremental Evolution
Task difficulty
Environment difficulty
Controller abilities
T Robot Morphology
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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
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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
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