Evolutionary Algorithms

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Evolutionary Algorithms
An Introduction
"Genetic algorithms are based on a biological
metaphor They view learning as a competition
among a population of evolving candidate problem
solutions. A 'fitness' function evaluates each
solution to decide whether it will contribute to
the next generation of solutions. Then, through
operations analogous to gene transfer in sexual
reproduction, the algorithm creates a new
population of candidate solutions."
Matthias Trapp, Diploma Student - Computer
Science, Theoretical Ecology Group - University
of Potsdam, Stanislaw Lem Workshop on Evolution
10.-14. October - Lviv 2005, trapp.matthias_at_freene
t.de
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Agenda

• Introduction
• Structure of an EA
• Genetic Operators
• Classification
• Implementation
• Discussion

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Introduction
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Motivation - The Problem(s)

• Global optimization problem
• Function has many local optima
• Function is changing over time
• Function have many parameters
• ? very large search space
• Combinatorial problems / Data Mining
• Classical NP-hard problems
• TSP
• SAT

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Overview Application Domains
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Evolution and Problem Solving

• Algorithm Automated Problem Solver
• Broad Scope Natural Computing
• Family of algorithms which mimickingnatural
  processes
• Neural Networks
• Simulated Annealing
• DNA Computing
• Evolutionary Algorithms

Evolution vs. Problem Solving
Environment ?? Problem
Individual ?? Candidate Solution
Fitness ?? Quality
Approximation ?? Optimization
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Evolutionary Algorithms

• EAs are adaptive heuristic search algorithms
• Metaphor trail and error (a.k.a generate and
  test)
• EAs are inspired by Darwin's theory of evolution
• problems are solved by an evolutionary
  process resulting in a best (fittest) solution
  (survivor) from a population of solution
  candidates
• EAs has been successfully applied to a wide range
  of problems
• Aircraft Design, Routing in Communications
  Networks, Tracking Windshear, Game Playing,
  Robotics, Air Traffic Control, Design,
  Scheduling, Machine Learning, Pattern
  Recognition, Job Shop Scheduling, VLSI Circuit
  Layout, Strike Force Allocation, Market
  Forecasting,Egg Price Forecasting, Design of
  Filters and Barriers, Data-Mining, User-Mining,
  ResourceAllocation, Path Planning, Theme Park
  Tours

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Characteristics

• Differences to classical algorithms/optimization
  methods
• EAs search a set of possible solutions in
  parallel
• EAs do not require derivative information
• EAs use probabilistic transition rules
• EAs are generally straightforward to apply
• EAs provide a number of potential solutions
• EAs are able to apply self-adaptation

? Another useful hammer ?
? If yes, then how can that be achieved ?
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Structure of an EA
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EA Components

• Representation mechanism (definition of
  individuals)
• Evaluation function (or fitness function)
• Population as container data structure
• Parent/Survivor selection mechanism
• Variation operators (Recombination, Mutation)
• Initialization procedure / Termination condition

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General Schema EA
Evolutionary Search (Flow Chart Model)
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General Schema EA
Evolutionary Search (Pseudo Code)
procedure EA t 0 Initialize(Pop(t))
Evaluate(Pop(t)) while(!TerminalCondition(Pop(t
)) Parents(t) ParentSelection(Pop(t)) Off
spring(t) Recombination(Parents(t)) Offspring(
t) Mutation(Offspring(t)) Evaluate(Offspring(t
)) Pop(t1) Replace(Pop(t),Offspring(t)) t
t 1
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Representation x E(D(x))

• Mapping Problem context ?Problem solving space
• Phenotype space P (candidate solution,individuals)
  
• Genotype space G (chromosomes, individuals)
• Encoding E P ? G
• Decoding D G ? P
• Encoding Technical representation of individuals
  
• GABinary Encoding (1110110000100) 7556
• ES Valued vectors (ABDJEIFJDHDIE)(1365
  78924)
• EP Finite state machines
• GP Tree of objects (LISP)

(IF_THEN_ELSE(gt x 0)(SetX(( x 3) (- 4
y)))(SetY( x (- y 1))))
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Population P(t) x1t,..., xnt

• Multi-set of genotypes unit of evolution
• Invariants
• Population Size n
• static (common)
• dynamic (unusually)
• Non-overlapping (Simple GA)
• entire population is replaced each generation
• Overlapping (Steady-State GA)
• few individuals are replaced each generation
• Sometimes associated with spatial structure
• Diversity number of different solutions in P(t)
• Multi-Population approaches (Pohlheim, 1995)

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Genetic Operators
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Selection/Sampling Operators

• Distinguish between parent and survivor selection
• Typically probabilistic work on population level
• Use fitness assignment of solution candidates
• Role pushing quality improvement
• Generational selection vs. steady-state selection
• Common steady state selection methods

Elitist Selection Roulette Wheel Selection Tournament Selection Scaling Selection Rank Selection Fitness-proportionate Selection Hierarchical Selection Boltzmann Selection Remainder stochastic sampling Stochastic uniform sampling
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Mutation Operator mi G? G

• Unary operator, always stochastic
• Bit-Strings Bit-flips (00101) ? (10101)
• Tree
• Sub tree destructive
• Sub tree/Node swap
• List
• Generative/Destructive
• Node/Sequence Swap
• Array
• Destructive
• Element Flip/Swap

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Recombination ci G G ? G

• Inherit genotype traits, typically stochastic
• Often binary operator Offspring Sex(Mum, Dad)
• Bit-Strings
• k-Point Recombination
• Uniform Recombination
• Genetic Programming(seldom used)

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A Simple Example
EA for Knapsack Problem
Representation 0,1n
Recombination 1-Point Crossover
Recombination probability 70
Mutation Uniform Bit-Flip
Mutation probability pm 1/n
Parent selection Best out of random two
Survival selection Generational
Population size 500
Number of offspring 500
Initialization Random
Termination condition No improvement in last 25 generations
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Effects of Genetic Operators

• Selection alone will tend to fill the population
  with copies of the best individual
• Selection and crossover operators will tend to
  cause the algorithms to converge on a good but
  sub-optimal solution
• Mutation alone induces a random walk through the
  search space.
• Selection and mutation creates a parallel,
  noise-tolerant, hill-climbing algorithm

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Terminal Conditions

• Discovery of an optimal solution (precision e gt
  0),
• Discovery of an optimal or near optimal solution,
• Convergence on a single or set of similar
  solutions,
• A user-specified threshold has been reached,
• A maximum number of cycles are evaluated,
• EA detects the problem has no feasible solution

? often disjunction of different conditions
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Classification
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Classification - Overview

• 1948 Alan Turing genetically or evolutionary
  search
• gt1950 Idea
• simulate evolution to solve engineering and
  design problems
• Box, 1957
• Friedberg, 1958
• Bremermann, 1962

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Genetic Algorithms (GA)

• By Holland (1975), USA
• concerned with developing robust adaptive systems
• Initially as abstraction of biological evolution
• Use of bit-strings for solution representation
• First EA which uses recombination
• Recombination seen as main operator
• very successful for combinatory optimization
  problems

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Evolutionary Strategies (ES)

• By Rechenberg (1973), Schwefel (1981), Germany
• Parameter optimization of real-valued functions
• Accentuation on mutation
• Selection (µ Parents, ? Offspring)
• (µ, ?) choose fittest of ? gt µ offspring
• (µ ?) choose fittest of ? µ solutions
• Recombination (u,v parent vectors, w child
  vector)
• More soon (Implementation Example)

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Evolutionary Programming (EP)

• By Fogel, Owens, and Walsh (1966), USA
• Application Artificial Intelligence,
• Initially for evolution of finite-state machines,
• Using mutation and selection,
• Later applications to mainly real-valued
  functions
• Strong similarity to evolutionary strategies

Example Prediction of binary cycles
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Genetic Programming (GP)

• Koza (1992), developed to simulate special
  functions
• Application Function fitting f(x)
• Using parse trees of Terminal and Non-Terminals
• Assumptions
• Completeness
• Seclusion
• Problems
• Variable count
• Variable types

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Implementation and Software
void garank(void) fitness_struct temp int
pos calc_fitness() for (int pass1
passltPOP_SIZE pass) temp
rankingspass pos pass while ((pos gt 0)
temp.fitness lt rankingspos-1.fitness)
rankingspos rankingspos-1 --pos
rankingspos temp best_sol
rankings0.fitness worst_sol
rankingsPOP_SIZE-1.fitness if (best_sol lt
best_overall) best_overall best_sol if
(worst_sol gt worst_overall) worst_overall
worst_sol
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Another Simple Example

• Search Space
• Evolutionary strategy
• Solution candidate (no encoding necessary)
• Fitness-Function
• Parent selection Elitist
• Recombination 1-Point, fixed
• Non-overlapping population

? Hybrid approach evolutionary strategy and
genetic program
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Applying Self-Adaptation

• Evolution of the Evolution
• Self-adaptation specific on-line parameter
  calibration technique
• Random number from Gaussian
  distribution with zero mean and standard
  deviation s
• Mutation operator
• Extending the candidate representation

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Working of an EA

• Distinct search phases
• Exploration
• Exploitation
• Trade-Off between exploration and exploitation
• Inefficient search vs. Propensity to quick search
  focus
• Premature Convergence climbing the wrong hill
• Losing diversity ? Converge in local optimum
• Techniques to prevent this well-known effect
• Any-time behaviour

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Multiobjective EA

• Multiobjective GA (MOGA)(Fonseca und Fleming
  (1993)),
• Niched Pareto GA (NPGA)(Horn und Nafpliotis
  (1993)),
• Nondominated Sorting GA (NSGA-II)(Deb u. a.
  (2000)) ,
• Strength Pareto EA (SPEA)(Zitzler und Thiele
  (1998)),
• Strength Pareto EA (SPEA2)(Zitzler u. a. (2001))

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Parallel Implementation of EA

• Subpopulation on MIMD (Belew and Booker (1991))
• Decrease of execution time
• Migration Model
• Unrestricted migration
• Ring migration
• Neighbourhood migration
• Global Model (Worker/Farmer)
• Diffusion Model
• handles every individual separately
• selects the mating partner in a local
  neighbourhood
• diffusion of information takes place

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API Comparison
Name Language Licence Target
PGAPack Fortran / C Freeware All
EO C GNU LGPL All
GALib C BSD Lnx,Win
GAGS C Freeware Lnx,Win
JAGA Java Freeware All
JGAP Jave Freeware All
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Discussion
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EA Advantages

• Applicable to a wide range of problems
• Useful in areas without good problem specific
  techniques
• No explicit assumptions about the search space
  necessary
• Easy to implement
• Any-time behaviour

..is a good designer of complex structures that
are well adapted to a given environment or task.
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EA Disadvantages

• Problem representation must be robust
• No general guarantee for an optimum
• No solid theoretically foundations (yet)
• Parameter tuning trial-and-error Process(but
  self-adaptive variants in evolution strategies)
• Sometimes high memory requirements
• Implementation High degree of freedom

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Summary
an EA is the second best algorithm for any
problem

• EAs are different from classical algorithms
• Less effort to develop an EA which
• Delivers acceptable solutions,
• In acceptable running time,
• Low costs of men and time
• EAs are distributable (Belew and Booker (1991))
• Subpopulations on MIMD,
• Via network
• EAs are easy to implement

In order to make evolutionary computing work
well, there must be a programmer that sets the
parameters right.
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Thank You !
Questions, Concerns, Comments, Sarcasm,
Insults
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Sources

• Spears, W. M., De Jong, K. A., Bäck, T., Fogel,
  D. B., and de Garis, H. (1993). An Overview of
  Evolutionary Computation, The Proceedings of the
  European Conference on Machine Learning, v667,
  pp. 442-459.
• A.E. Eiben, Evolutionary computing the most
  powerful problem solver in the universe?
• Zbigniew Michalewicz, Genetic Algorithms Data
  Structures Evolution Programs, Springer, 1999,
  3-540-60676-9
• Lawrence J. Fogel, Alvin J. Owens, Michael J.
  Walsh Artificial intelligence through simulated
  evolution, Wiley Verlag 1966
• John R. Koza Genetic Programming on the
  programming of computers by means of natural
  selection, MIT Verlag 1992