Selected Topics in Evolutionary Algorithms II Pavel Petrovič Department of Applied Informatics,...
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Transcript of Selected Topics in Evolutionary Algorithms II Pavel Petrovič Department of Applied Informatics,...
Selected Topics in Evolutionary Algorithms II
Pavel PetrovičDepartment of Applied Informatics, Faculty of Mathematics, Physics and Informatics
[email protected] July 10th 2008
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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
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Solving problems with EA
Define and implement representation Define and implement objective function Design and implement initialization, mutation and
recombination operators Select appropriate algorithm and selection method Setup and tune evolutionary parameters:
Mutation rate Crossover rate Population size Selection parameters Termination criterion
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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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
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Genotype and Phenotype
Genotype – all genetic material of a particular individual (genes)
Phenotype – the real features of that individual
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Fitness landscape
Genotype space – difficulty of the problem – shape of fitness landscape, neighborhood function
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Population diversity
Must be kept high for the evolution to advance
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Premature convergence
important building blocks are lost early in the evolutionary run
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Genetic drift
Loosing the population distribution due to the sampling error
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Exploration vs. Exploitation
Exploration phase: localize promising areas Exploitation phase: fine-tune the solution
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Selection methods
roulette wheel (fitness proportionate selection),
tournament selection truncation selection rank selection elitist strategies
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Selection pressure
Influenced by the problem Relates to evolutionary operators
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Direct vs. Indirect Representations
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Fitness Space (Floreano)
Functional vs. behavioral Explicit vs. implicit External vs. internal
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Evolutionary Robotics Solution: Robot’s controller
Fitness: how well the robot performs Simulation or real robot
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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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
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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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
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Evolutionary algorithms
Genetic algorithm Genetic programming Evolutionary Strategies Evolutionary Programming
Classifier systems Ant-colony optimisation Memetic algorithms Artificial Immune Systems
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Example: Travelling Salesman Problem (TSP) Finding a closed path that visits all cities Difficult problem (NP-complete)
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Example: Travelling Salesman Problem (TSP)
Trivial representation:( 4, 1, 7, 2, 5, 3, 6 ) - list of cities visited
Representation is a permutation, however standard crossover results in descendants that are not permutations
Not suitable for standard recombination Need a different representation or recombination!
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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TSP Example: Partially matched crossover (PMX)
2 sites picked, intervening section specifies “cities” to interchange between parents:
A = 9 8 4 | 5 6 7 | 1 3 2 10
B = 8 7 1 | 2 3 10 | 9 5 4 6A’ = 9 8 4 | 2 3 10 | 1 6 5 7B’ = 8 10 1| 5 6 7 | 9 2 4 3
some ordering information from each parent is preserved, and no infeasible solutions are generat
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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TSP Example: Order Crossover (OX) 2 sites picked, intervening section specifies “cities”
to interchange between parents:A = 9 8 4 | 5 6 7 | 1 3 2 10
B = 8 7 1 | 2 3 10 | 9 5 4 6
B* = 8 H 1 | 2 3 10 | 9 H 4 H
B** = 2 3 10 | H H H | 9 4 8 1
B’ = 2 3 10 | 5 6 7 | 9 4 8 1
A’ = 5 6 7 | 2 3 10 | 1 9 8 4 Order crossover preserves more information about
RELATIVE ORDER than does PMX, but less about ABSOLUTE POSITION of each “city” (for TSP example)
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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TSP Example: Operator MPX
2 sites picked, intervening section specifies “cities” to interchange between parents:
A = 9 8 4 | 5 6 7 | 1 3 2 10
B = 8 7 1 | 2 3 10 | 9 5 4 6
C = 5 7 1 | 2 3 10 | 9 8 6 4
D = 6 4 1 | 2 3 10 | 9 5 7 8
C' = 5 | 5 6 7 | 7 1 | 2 3 10 | 9 8 6 4
D' = 6 4 1 | 2 3 10 | 9 5 | 5 6 7 | 7 8
C'' = * | 5 6 7 | * 1 | 2 3 10 | 9 8 * 4
C''' = 5 6 7 1 2 3 10 9 8 4
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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TSP Example: Cyclic Crossover CX Cycle crossover forces the city in each position to come
from that same position on one of the two parents:
A = 9 8 2 1 7 4 5 10 6 3
B = 1 2 3 4 5 6 7 8 9 10
A' = 9 - - - - - - - - -
9 - - 1 - - - - - -
9 - - 1 - 4 - - 6 -
9 2 - 1 - 4 - 8 6 10
A'' = 9 2 3 1 - 4 - 8 6 10
= 9 2 3 1 7 4 5 8 6 10
A''' = 9 2 3 1 5 4 7 8 6 10
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Multiple-objective optimisation
Several objectives to optimize Usually no single optimal solution Decision maker selects a solution from finite set
by making compromises First MOEAs in mid 80s, since then huge number
of papers on EMOO EAs are good for MOO:
• Inherently parallel• Less susceptible to the shape or continuity of
MO search space
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Pcurrent
(t)
Pknown
(t)
Ptrue
(t)
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Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II, July 10th 2008
MOEA is an extension on an EA in which twomain issues are considered:
• How to select individuals such that nondominated solutions are preferred over those which are dominated
• How to maintain diversity as to be able to maintain in the population as many elements of the Pareto optimal set as possible.
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Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Preference of nondominated solutions:
• All non-dominated individuals get the same probability to reproduce
• This probability is higher than the one corresponding to the individuals which are dominated
= PARETO RANKING
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Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Maintaining diversity:
• Fitness sharing
• Niching
• Clustering
• Geographically-based schemes to distribute solutions
• Use of entropy
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Multiple-objective EAs
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Aggregating functions
• combining objectives into single fitness:
• cannot generate non-convex portionsof the Pareto front regardless of the weight combination used
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Multiple-objective EAs
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Population-based approaches
• concept of Pareto dominance is not directly incorporated into the selection process
• population of an EA is used to diversify thesearch
VEGA = Vector Evaluated Genetic Algorithm
• At each generation, a number of sub-populations are generated by performing proportional selection according to each objective function in turn• Problem: selection scheme is opposed to the concept of Pareto dominance
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Multiple-objective EAs
Selected Topics in Evolutionary Algorithms II, July 10th 2008
Pareto-Based Approaches
• Goldberg's Pareto Ranking• Multi-Objective Genetic Algorithm (MOGA)• The Nondominated Sorting Genetic Algorithm
(NSGA)• NSGA II = NSGA + elitism & crowded comparison
operator (makes the search faster)• Niched Pareto Genetic Algorithm (NPGA) –
tournament• Strength Pareto Evolutionary Algorithm (SPEA) –
special clustering method to maintain diversity• SPEA2 – different clustering method (nearest
neighbor)• many other...
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Neuroevolution through augmenting topologies (NEAT) 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 II, July 10th 2008
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GECCO Contest
GECCO is the largest EA conference (European alternative: PPSN) Humies awards Contest tasks with prizes...
Selected Topics in Evolutionary Algorithms II, July 10th 2008
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Further information... Conferences: GECCO, PPSN, CEC (now part of
WCCI, EvoWorkshops, EA) Journals: Evolutionary Computation, Genetic
Programming and Evolvable Machines, IEEE Transactions on Evolutionary Computation
Scientific body: ACM SIGEVO, with newsletter Mailing list: ec-digest with archive: http://ec-digest.research.ucf.edu/
Recent publication about GP: Riccardo Poli, William B Langdon, Nicholas Freitag McPhee: A Field Guide to Genetic Programming http://www.lulu.com/content/2167025
Selected Topics in Evolutionary Algorithms II, July 10th 2008