Selected Topics in Evolutionary Algorithms I Pavel Petrovič Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics [email protected]

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

Selected Topics in Evolutionary Algorithms I, July 4th 2008

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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 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


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


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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


Documents

Selected Topics in Evolutionary Algorithms I Pavel Petrovič Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics [email protected]