Selected Topics in Evolutionary Algorithms II

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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

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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,
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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,
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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 Robots controller

• Fitness how well the robot performs
• Simulation or real robot

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Fitness Influenced by

• Environment difficulty

• Task difficulty

• Robots abilities (sensors, actuators)?

T

• Controller abilities

• Robot Morphology

Incremental change during evolution
Incremental Evolution
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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 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

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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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Multiple-objective optimisation
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Multiple-objective optimisation
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Multiple-objective optimisation
Pcurrent(t)? Pknown(t)? Ptrue(t)?
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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.

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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

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Multiple-objective optimisation

• 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 portions
• of the Pareto front regardless of the weight
  combination used

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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

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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,
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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,
July 10th 2008