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Selected Topics in Evolutionary Algorithms II

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Title: Selected Topics in Evolutionary Algorithms II


1
Selected Topics in Evolutionary Algorithms II
  • Pavel Petrovic
  • Department of Applied Informatics,
  • Faculty of Mathematics, Physics and Informatics
  • ppetrovic_at_acm.org
  • July 10th 2008

2
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3
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
4
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
5
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
6
Fitness landscape
  • Genotype space difficulty of the problem
    shape of fitness landscape, neighborhood function

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
7
Population diversity
  • Must be kept high for the evolution to advance

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
8
Premature convergence
  • important building blocks are lost early in the
    evolutionary run

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
9
Premature convergence
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
10
Genetic drift
  • Loosing the population distribution due to the
    sampling error

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
11
Exploration vs. Exploitation
  • Exploration phase localize promising areas
  • Exploitation phase fine-tune the solution

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
12
Selection methods
  • roulette wheel (fitness proportionate selection),
  • tournament selection
  • truncation selection
  • rank selection
  • elitist strategies

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
13
Selection pressure
  • Influenced by the problem
  • Relates to evolutionary operators

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
14
Direct vs. Indirect Representations
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
15
Fitness Space (Floreano)?
  • Functional vs. behavioral
  • Explicit vs. implicit
  • External vs. internal

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
16
Evolutionary Robotics
  • Solution Robots controller
  • Fitness how well the robot performs
  • Simulation or real robot

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
17
Fitness Influenced by
  • Environment difficulty
  • Task difficulty
  • Robots abilities (sensors, actuators)?

T
  • Controller abilities
  • Robot Morphology

Incremental change during evolution
Incremental Evolution
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
18
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
19
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
20
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
21
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
22
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 6
  • A 9 8 4 2 3 10 1 6 5 7
  • B 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
23
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
24
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
25
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
26
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
27
Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
28
Multiple-objective optimisation
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
29
Multiple-objective optimisation
Pcurrent(t)? Pknown(t)? Ptrue(t)?
Selected Topics in Evolutionary Algorithms II,
July 10th 2008
30
Multiple-objective optimisation
  • MOEA is an extension on an EA in which two
  • main 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.

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
31
Multiple-objective optimisation
  • 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

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
32
Multiple-objective optimisation
  • Maintaining diversity
  • Fitness sharing
  • Niching
  • Clustering
  • Geographically-based schemes to distribute
    solutions
  • Use of entropy

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
33
Multiple-objective EAs
  • Aggregating functions
  • combining objectives into single fitness
  • cannot generate non-convex portions
  • of the Pareto front regardless of the weight
    combination used

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
34
Multiple-objective EAs
  • Population-based approaches
  • concept of Pareto dominance is not directly
    incorporated into the selection process
  • population of an EA is used to diversify the
  • search
  • 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

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
35
Multiple-objective EAs
  • 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...

Selected Topics in Evolutionary Algorithms II,
July 10th 2008
36
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
37
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
38
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
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