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Evolutionary Algorithms General Concepts Prof. Thomas Bck Natural Computing Group Evolutionary Algorithms Optimization 1 Overview Taxonomy of EAs Key Features Literature etc. Prof. Thomas Bck Natural Computing Group

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  • Prof. Thomas Bäck

Optimization 1 Natural Computing Group Evolutionary Algorithms

Evolutionary Algorithms General Concepts

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Optimization 2 Natural Computing Group Evolutionary Algorithms

Overview

  • Taxonomy of EAs
  • Key Features
  • Literature etc.
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Optimization 3 Natural Computing Group Evolutionary Algorithms

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TAXONOMY

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Introduction

  • Modeling
  • Simulation
  • Optimization

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Input: Known (measured) Output: Known (measured) Interrelation: Unknown Input: Will be given Model: Already exists How is the result for the input? Objective: Will be given How (with which parameter settings) to achieve this objective?

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Evolutionary Algorithms Taxonomy

Evolutionary Algorithms

Genetic Algorithms (GA) Canoni cal GAs Messy GAs Real- coded GAs Order- based GAs Evolutionary Strategies (ES) (1+1) (1,l) (µ,l) Derand

  • mized

CMA Evolutio nary Progra mming (EP) Genetic Progra mming (GP)

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Key features

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Key Features ES vs GA

Evolutionary Strategies Genetic Algorithms Mixed-integer capabilities Discrete representations Emphasis on mutation Emphasis on crossover Self-adaptation No self-adaptation Small population sizes Larger population sizes Deterministic selection Probabilistic selection Developed in Europe Developed in US Theory focused on convergence speed Theory focused on schema processing

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Key Features of EAs (1)

  • Set of candidate solutions (individuals), forming a population.
  • Generating new solutions by:

− Reproduction: Copying an individual − Crossover (recombination):

2 (or more) parents à 1 (or more) offspring

− Mutation:

1 parent à 1 offspring

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Optimization 9 Natural Computing Group Evolutionary Algorithms

Key Features of EAs (2)

  • Quality measure of individuals: Fitness function, objective

function.

  • Survival-of-the-fittest principle
  • Mating-of-the-fittest principle
  • Algorithm cycles through iterations (generations)
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Main Components of EAs

1. Representation of individuals: Coding 2. Evaluation method for individuals: Fitness 3. Initialization procedure for 1st generation 4. Definition of variation operators (mutation, crossover) 5. Parent (mating) selection mechanism 6. Survivor (environmental) selection mechanism 7. Technical parameters

− mutation rates − population size − crossover rates

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Generalized EA

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Optimization 12 Natural Computing Group Evolutionary Algorithms

Generalized Evolutionary Algorithm

t := 0; initialize(P(t)); evaluate(P(t)); while not terminate do P‘(t) := mating_selection(P(t)); P‘‘(t) := variation(P‘(t)); evaluate(P‘‘(t)); P(t+1) := environmental_selection(P‘‘(t) È P(t)); t := t+1;

  • d

Variation summarizes mutation and recombination Environmental selection can take old parents into account!

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Advantages of EAs

1. Widely applicable, also in cases where no good solution techniques are available

− Multimodalities, discontinuities, constraints − Noisy objective functions − Multiple criteria decision making problems − Implicitly defined problems (simulation models)

2. No presumptions w.r.t. problem space 3. Low development costs, i.e., costs to adapt to new problem spaces 4. The solutions of EAs have straightforward interpretations 5. Can run interactively, always deliver solutions 6. Self-adaptation of strategy parameters

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Disadvantages of EAs

1. No guarantee for finding optimal solutions within a finite amount of time. This is true for all global optimization methods. 2. No complete theoretical basis (yet), but much progress is being made. 3. Parameter tuning is sometimes based on trial and error.

− Solution: Self-adaptation of strategy parameters

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Two Views on EAs

1. Global random search methods

− Probabilistic search with high “creativity” − Diversified search − Applying local search operators

2. Nature based search techniques

− Stochastic influence − Population based − Adaptive behavior − Recognizing/amplifying strong gene patterns Exploration Exploitation

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Numerical Function Optimization

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History, literature

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History (Incomplete)

  • Friedberg et al. 1958: Automatic programming, binary representations
  • Bremermann 1958: Binary/continuous variables, recombination and

mutation, estimation p*=1/l (optimal mutation rate).

  • Box 1957: Evolutionary operation, fractional design of experiments.
  • L.J. Fogel 1962 (San Diego, CA): Evolutionary Programming, finite state

machines, mutation only.

  • H.-P. Schwefel and I. Rechenberg 1965 (Berlin, Germany): Evolution

Strategies, experimental optimization, (1+1)-strategy, mutation only.

  • J. H. Holland 1962 (Ann Arbor, MI): Genetic Algorithms, binary variables,

mutation and recombination −

  • J. Koza 1989: Genetic Programming, S-expressions

− Holland et al., ca. 1985: Classifier Systems, classification and induction

  • rules. Pittsburgh vs. Michigan approach.
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Literature (Incomplete)

  • Th. Bäck: Evolutionary Algorithms in Theory and Practice, Oxford University

Press, NY, 1996.

  • Th. Bäck, D.B. Fogel, Z. Michalewicz: Handbook of Evolutionary Computation,
  • Vols. 1, 2, Institute of Physics Publishing, Bristol, UK, 2003.
  • A.E. Eiben, J. Smith: Introduction to Evolutionary Computing, Natural

Computing Series, Springer, Berlin, 2003.

  • D.B. Fogel: Evolutionary Computation: Toward a new philosophy of machine

intelligence, IEEE Press, 1995.

  • Z. Michalewicz: Genetic Algorithms + Data Structures = Evolution Programs,

Springer, 1996.

  • H.-P. Schwefel: Evolution and Optimum Seeking, Wiley, NY, 1995.