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

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


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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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Evolutionary algorithms

Genetic algorithm Genetic programming Evolutionary Strategies Evolutionary Programming

Classifier systems Ant-colony optimisation Memetic algorithms Artificial Immune Systems


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Example: Travelling Salesman Problem (TSP) Finding a closed path that visits all cities Difficult problem (NP-complete)


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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!


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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


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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)


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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


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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


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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


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Pcurrent

(t)

Pknown

(t)

Ptrue

(t)

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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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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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Maintaining diversity:

• Fitness sharing

• Niching

• Clustering

• Geographically-based schemes to distribute solutions

• Use of entropy

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Multiple-objective EAs


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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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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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


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GECCO Contest

GECCO is the largest EA conference (European alternative: PPSN) Humies awards Contest tasks with prizes...


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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 Pavel Petrovič Department of Applied Informatics, Faculty of Mathematics, Physics and Informatics [email protected].

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