Evolutionary Computation ( 진 화 연 산 )

Evolutionary Computation( ) E-mail: [email protected]://scai.snu.ac.kr./~btzhang/

Byoung-Tak ZhangSchool of Computer Science and EngineeringSeoul National University

This material is also available online at http://scai.snu.ac.kr/

*Outline

Basic ConceptsTheoretical BackgroundsApplicationsCurrent IssuesReferences and URLs

*1. Basic Concepts

*Charles Darwin (1859)

Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.

*Evolutionary AlgorithmsA Computational Model Inspired by Natural Evolution and GeneticsProved Useful for Search, Machine Learning and OptimizationPopulation-Based Search (vs. Point-Based Search)Probabilistic Search (vs. Deterministic Search)Collective Learning (vs. Individual Learning)Balance of Exploration (Global Search) and Exploitation (Local Search)

*Biological TerminologyGeneFunctional entity that codes for a specific feature e.g. eye colorSet of possible allelesAlleleValue of a gene e.g. blue, green, brownCodes for a specific variation of the gene/featureLocusPosition of a gene on the chromosomeGenomeSet of all genes that define a speciesThe genome of a specific individual is called genotypeThe genome of a living organism is composed of several Chromosomes PopulationSet of competing genomes/individuals

*Analogy to Evolutionary BiologyIndividual (Chromosome) = Possible SolutionPopulation = A Collection of Possible SolutionsFitness = Goodness of SolutionsSelection (Reproduction) = Survival of the FittestCrossover = Recombination of Partial SolutionsMutation = Alteration of an Existing Solution

*The Evolution Loopevaluateinitialize population

*Basic Evolutionary AlgorithmGeneration of initial solutions (A priori knowledge, results of earlier run, random)EvaluationSelectionSolutionSufficientlygood?ENDGeneration of variants by mutationand crossoverYESNO

*Procedurebegint

*General Structure of EAssolutions1100101010101110111000110110011100110001110010111010111011101100101010crossovermutation001101011101010100110011010010evaluation110010111010111010100011001001solutionsfitnesscomputationroulettewheelselectionnew populationencodingchromosomes

*Population and Fitness

*Selection, Crossover, and MutationReproductionDistinctionMutationCrossover246486610886

*Simulated Evolution

*Selection StrategiesProportionate SelectionReproduce offspring in proportion to fitness fi.

Ranking SelectionSelect individuals according to rank(fi).

Tournament SelectionChoose q individuals at random, the best of which survives.

Other Ways

*Roulette Wheel Selection intermediate parent population:01011110101000110001 Probability of reproduction pi = fi / Sk fk Selection is a stochastic process

*Genetic Operators for BitstringsReproduction: make copies of chromosome (the fitter the chromosome, the more copies) 1 0 0 0 0 1 0 0 Crossover: exchange subparts of two chromosomes Mutation: randomly flip some bits 1 0 0 | 0 0 1 0 0 1 1 1 | 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 01 0 0 0 0 1 0 01 0 0 1 1 1 1 1 1 1 1 0 0 1 0 00 0 0 0 0 0 0 0

*MutationFor a binary string, just randomly flip a bit For a more complex structure, randomly select a site, delete the structure associated with this site, and randomly create a new sub-structure Some EAs just use mutation (no crossover) Normally, however, mutation is used to search in the local search space, by allowing small changes in the genotype (and therefore hopefully in the phenotype)

*Recombination (Crossover)Crossover is used to swap (fit) parts of individuals, in a similar way to sexual reproduction Parents are selected based on fitness Crossover sites selected (randomly, although other mechanisms exist), with some prob. Parts of the parents are exchanged to produce children

*Crossover One-point crossoverparent Aparent B1 1 0 1 01 0 0 0 1offspring Aoffspring B1 1 0 111 0 0 00 Two-point crossoverparent Aparent B1 1 0 1 01 0 0 0 1offspring Aoffspring B1 10 01 00 101

*2. Theoretical Backgrounds

*Major Evolutionary AlgorithmsGenetic ProgrammingEvolution StrategiesGenetic AlgorithmsEvolutionaryProgrammingClassifier Systems Genetic representation of candidate solutions Genetic operators Selection scheme Problem domainHybrids: BGA

*Variants of Evolutionary AlgorithmsGenetic Algorithm (Holland et al., 1960s)Bitstrings, mainly crossover, proportionate selectionEvolution Strategy (Rechenberg et al., 1960s)Real values, mainly mutation, truncation selectionEvolutionary Programming (Fogel et al., 1960s)FSMs, mutation only, tournament selectionGenetic Programming (Koza, 1990)Trees, mainly crossover, proportionate selectionHybrids: BGA (Muehlenbein et al., 1993) BGP (Zhang et al., 1995) and others.

*Evolution Strategy (ES)Problem of real-valued optimizationFind extremum (minimum) of function F(X): Rn ->ROperate directly on real-valued vector XGenerate new solutions through Gaussian mutation of all componentsSelection mechanism for determining new parents

*ES: Representation One individual:The three parts of an individual:: Object variables: Standard deviations: Rotation anglesFitnessVariancesCovariances

* , where rx, r , r {-, d, D, i, I, g, G}, e.g. rdIIES: Operator - Recombination

*

m{,,} : I I is an asexual operator.n = n, n = n(n-1)/2

1 < n < n, n = 0

n = 1, n = 0

ES: Operator - Mutation

*ES: Illustration of Mutation HyperellipsoidsLine of equal probability density to place an offspring

*ES: Evolution Strategy vs. Genetic AlgorithmCreate random initial populationEvaluate populationSelect individuals for variationVaryInsert intopopulationCreate random initial populationEvaluate populationVarySelectionInsert intopopulation

*Evolutionary Programming (EP) Original form (L. J. Fogel)Uniform random mutationsDiscrete alphabets selectionExtended Evolutionary Programming (D. B. Fogel)Continuous parameter optimizationSimilarities with ESNormally distributed mutationSelf-adaptation of mutation parameters

*EP: RepresentationConstraints for domain and variances Initialization only-operators does not surveySearch space is principally unconstrained.Individual

*EP: Operator - RecombinationNo recombinationGaussian mutation does better (Fogel and Atmar).Not all situationsEvolutionary biologyThe role of crossover is often overemphasized.Mutation-enhancing evolutionary optimizationCrossover-segregating defectsThe main point of view from researchers in the field of Genetic Algorithms

*EP: Operator - MutationGeneral form (std. EP)

Exogenous parameters must be tuned for a particular taskUsuallyProblemIf global minimums fitness value is not zero, exact approachment is not possibleIf fitness values are very large, the search is almost random walkIf user does not know about approximate position of global minimum, parameter tuning is not possible

*EP: Differences from ESProcedures for self-adaptationDeterministic vs. Probabilistic selection -ES vs. -EPLevel of abstraction: Individual vs. Species

*Genetic ProgrammingApplies principles of natural selection to computer search and optimization problems - has advantages over other procedures for badly behaved solution spaces [Koza, 1992]Genetic programming uses variable-size tree-representations rather than fixed-length strings of binary values.Program tree = S-expression = LISP parse treeTree = Functions (Nonterminals) + Terminals

*GP: RepresentationS-expression: (+ 1 2 (IF (> TIME 10) 3 4))Terminals = {1, 2, 3, 4, 10, TIME}Functions = {+, >, IF}+24>31IFTIME10

*GP: Operator - Crossover+b+aab+abab+b+ab

*GP: Operator - Mutationab+b/a+b+b/a-ba

*Breeder GP (BGP) [Zhang and Muehlenbein, 1993, 1995]ES (real-vector)GA (bitstring)Breeder GA (BGA)(real-vector + bitstring)GP (tree)Breeder GP (BGP)(tree + real-vector + bitstring)Muehlenbein et al. (1993)Zhang et al. (1993)

*GAs: Theory of Simple GAAssumptionsBitstrings of fixed sizeProportionate selectionDefinitionsSchema H: A set of substrings (e.g., H = 1**0)Order o: number of fixed positions (FP) (e.g., o(H) = 2)Defining length d: distance between leftmost FP and rightmost FP (e.g., d(H) = 3)

*GAs: Schema Theorem (Holland et al. 1975) , Number of members of HProbability of crossover and mutation, respectivelyInterpretation: Fit, short, low-order schemata (or building blocks) exponentially grow.

*Convergence velocity of (+, )-ESES: Theory

*EP: Theory (1)Analysis of std. EP(Fogel)Aims at giving a proof of convergence for resulting algorithm Mutation:Analysis of a special case EP(1,0,q,1)Identical to a (1+1)-ES havingObjective functionSimplified sphere model

*EP: Theory (2)Combination with the optimal SD

When dimension is increased, the performance is worse than an algorithm that is able to retain the opt. SD

The convergence rate of a (1+1)-EP by

*Breeder GP: Motivation for GP TheoryIn GP, parse trees of Lisp-like programs are used as chromosomes.Performance of programs are evaluated by training error and the program size tends to grow as training error decreases.Eventual goal of learning is to get small generalization error and the generalization error tends to increase as program size grows.How to control the program growth?

*Breeder GP: MDL-Based Fitness FunctionTraining error of neural trees A for data set DStructural complexity of neural trees ARelative importance of each term

*Breeder GP: Adaptive Occam Method (Zhang et al., 1995)Desired performance level in errorTraining error of best progr. at gen t-1Complexity of best progr. at gen. t

*Bayesian Evolutionary Computation (1/2)The best individual is defined as the most probable model of data D given the priori knowledge

The objective of evolutionary computation is defined to find the model A* that maximizes the posterior probability

Bayesian theorem is used to estimate P(A|D) from a population A(g) of individuals at each generation.

*Bayesian process: The BEAs attempt to explicitly estimate the posterior distribution of the individuals from their prior probability and likelihood, and then sample offspring from the distribution.Bayesian Evolutionary Computation (2/2)[Zhang, 99]

*Canonical BEA(Initialize) Generate from the prior distribution P0(A). Set generation count t 0.(P-step) Estimate posterior distribution Pt(A|D) of the individuals in At.(V-step) Generate L variations by sampling from Pt(A|D).(S-step) Select M individuals from A into based on Pt(Ai |D). Set the best individual .(Loop) If the termination condition is met, then stop. Otherwise, set t t+1 and go to (P-step).

*Basic Idea behind BEA

*Evolving Neural Trees with BEAPosterior probability of a neural tree A

*Features of EAsEvolutionary techniques are good for problems that are ill-defined or difficult Many different forms of representation Many different types of EA Leads to many different types of crossover, mutation, etc. Some problems with convergence, efficiency However, they are able to solve a diverse range of problems

*Advantages of EAsEfficient investigation of large search spaces Quickly investigate a problem with a large number of possible solutions Problem independence Can be applied to many different problems Best suited to difficult combinatorial problems

*Disadvantages of EAsNo guarantee for finding optimal solutions with a finite amount of time: True for all global optimization methods.No complete theoretical basis (yes). But much process is being made.Parameter tuning is largely based on trial and error (genetic algorithms); solution: Self-adaptation (evolution strategies). Often computationally expensive: Parallelism.

*3. Applications

*Application Fields (1)Experimental optimization & optimization with subjective evaluationCoffee recipes; general food recipesBiochemical fermentation processesWind tunnel experimentsTwo-phase nozzle optimization experimentsTechnical optimizationDesign & ProductionLogisticsControl of dynamic processes

*Application Fields (2)Structure optimizationStructure & parameters of plantsConnection structure & weights of neural netsNumber of thicknesses of layers in multilayer structuresData MiningClustering (number & centers of clusters)Fitting models to dataTime series prediction

*Application Fields (3)Path PlanningTraveling Salesman ProblemRobot ControlEvolutionary RoboticsEvolvable Hardware

*Hot Water Flashing Nozzle (1)StartHot water enteringSteam and droplet at exitAt throat: Mach 1 and onset of flashingApplication Example 1Hans-Paul Schwefel performed the original experiments

*Hot Water Flashing Nozzle (2)Application Example 1

*Minimal Weight Trust Layout LoadStart

922 kp

(LP minimum)Optimum

738 kpApplication Example 2

*Concrete Shell Roofunder own and outer load (snow and wind)Height 1.34mSpherical shapeOptimal shapeHalf span 5.00mSavings : 36% shell thickness 27% armationmax minOrthogonal bending strengthApplication Example 3

*Dipole Magnet Structure (1)Application Example 4

*Dipole Magnet Structure (2)Analysis of the magnetic field by Finite Element Analysis (FEM)Minimize sum of squared deviations from the idealIndividuals: Vectors of positions (y1, , yn)Middle: 9.8% better than upper graphic; bottom: 2.7% betterApplication Example 4

*Optical Multilayers (1) Goal: Find a filter structure such that the real reflection behavior matches the desired one as close as possible. Filter layers; - Thicknesses - Materials..Substrate (Glass)ReflectionWavelengthDesiredCurrentApplication Example 5

*Optical Multilayers (2)Problem parameters;Thickness of layersLayer materials (integer values)Number of layers n. Mixed-integer, variable-dimensional problem.Application Example 5

*Optical Multilayers (3)Objective function:

: Reflection of the actual filter for wavelength Calculation according to matrix method. : Desired reflection value

Application Example 5

*Optical Multilayers (4)Example topology: Only layer thicknesses vary; n=2Application Example 5

*Optical Multilayers (5)Example structure:Application Example 5

*Optical Multilayers (6)Parallel evolutionary algorithmPer node: EA for mixed-integer representationIsolation and migration of best individualsMutation of discrete variables: Fixed pm per population


*Circuit Design (1)Difficulty of automated circuit design:A vary hard problemExponential in the number of componentsMore than 10300 circuits with a mere 20 componentsAn important problemToo few analog designersThere is an Egg-shell of analog circuitry around almost all digital circuitsAnalog circuits must be redesigned with each new generation of process technologyNo existing automated techniquesIn contrast with digitalExisting analog techniques do only sizing of components, but do not create the topologyApplication Example 6

*Circuit Design (2)Application Example 6OutInDeveloping CircuitDevelopment of a circuit with Genetic Programming

*Circuit Design (3)Each function in the circuit-constructing tree acts on a part of the circuit and changes it in some way (e.g. creates a capacitor, creates a parallel structure, adds a connection to ground, etc)A writing head points from each function to the part of the circuit that the function will act on.Each function inherits writing heads from its parent in the treeApplication Example 6

*Circuit Design (4)Example of circuit constructing program tree

(LIST (C (-0.963 (- (- -0.875 0.113) 0.880)) (series (flip end) (series (flip end) (L 0.277 end) end) (L (- -0.640 0.749) (L 0.123 end)))) (flip (nop (L 0.657 end)))))Application Example 6

*Neural Network Design (1)Introduction: EC for NNsPreprocessing of Training DataFeature selectionTraining set optimizationTraining of Network WeightsNon-gradient searchOptimization of Network ArchitectureTopology adaptationPruning unnecessary connections/unitsApplication Example 7

*Neural Network Design (2)Encoding Schemes for NNs

Bit-stringsProperties of network structure are encoded as bit-strings.RulesNetwork configuration is specified by a graph-generation grammar.TreesNetwork is represented as neural trees.Application Example 7

*Neural Network Design (3)Neural Tree ModelsNeural treesTree-structured neural networksNonterminal nodes: Neural unitsTerminal nodes: InputsLinks: connection weights wij from j to iLayer of node i: path length of the longest path to a terminal node of the substrees of i.Type of UnitsSigma unit: the sum of weighted inputsPi unit: the product of weighted inputsOutput of a neuron: sigmoid transfer functionApplication Example 7

*Neural Network Design (4)Application Example 7Tree-Structured Model

*Neural Network Design (5)Generate M TreesEvaluate Fitness of TreesCreate L New TreesSelect Fitter TreesTermination Condition?STOPPosterior DistributionModel SelectionModel Variation(Variation Operators)YesNoPrior DistributionApplication Example 7Evolving Neural Networks by BEAs

*Neural Network Design (6)Structural Adaptation by Subtree CrossoverNeuron type, topology, size and shape of networks are adapted by crossover.

Neuron types and receptive fields are adapted by mutation.Connection weights are adapted by an EC-based stochastic hill-climbing.Application Example 7

*Fuzzy System Design (1)Fuzzy system comprises Fuzzy membership functions (MF) Rules Task is to tailor the MF and rules to get best performance Every change to MF affects the rules Every change to the rules affects the MF


*Fuzzy System Design (2)Solution is to design MF and rules simultaneously Encode in chromosomes Aarameters of the MF Associations and Certainty Factors in rules Fitness is measured by performance of the Fuzzy SystemApplication Example 8

*Fuzzy System Design (3)Evolutionary Computation and Fuzzy Systems

Fuzzy Sets (Zadeh): Points have Memberships

Evolutionary Computation can be Used to Optimize Fuzzy Control SystemsEvolve Membership Functions/RulesFUZZY MEMBERSHIP FOR COOLMembership0.01.00o2.5oTemperature (C)Application Example 8

*Fuzzy System Design (4)NM=Negative Medium, NS=Negative Small, ZE=Zero, PS=Positive Small, PM=Positive Medium, _=No EntryDefuzzification is Just Weighed CentroidMutation Up/Down by One. Two-Point Xover on String Representing the 5x5 MetrixCart Centering and Fuzzy PartitionsFuzzy Control Strategy after 100 Gen.Fmx(v=x)NMNSZEPSPMApplication Example 8GA for Fuzzy Control of Cart

*Data Mining (1)Data Mining TaskTypes of problem to be solved:ClassificationClusteringDependence Modelingetc., etc.Application Example 9

*Data Mining (2)Basic Ideas of GAs in Data MiningCandidate rules are represented as individuals of a populationRule quality is computed by a fitness functionUsing task-specific knowledgeApplication Example 9

* Data Mining (3)Classification with Genetic AlgorithmsEach individual represents a rule set i.e. an independent candidate solutionEach individual represents a single ruleA set of individuals (or entire population) represents a candidate solution (rule set)


*Data Mining (4)Individual Representation In GABIL, an individual is a rule set, encoded as a bit string [DeJong et al. 93]It uses k bits for the k values of a categorical attributeIf all k bits of an attribute are set to 1 the attribute is not used by the ruleGoal attribute: Buy furnitureMarital_status: Single/Married/DivorcedHouse:Own/Rented/University Marital_status House Buy? The string 011 100 1Represents the rule IF(Marital_status=M or D) and (House = 0) THEN (Buy furniture=y)Application Example 9

*Data Mining (5)An individual is a variable-length string representing a set of fixed-length rules

rule 1 rule 2 011 100 1 101 110 0

Mutation: traditional bit inversionCrossover: corresponding crossover points in the two parents must semantically matchApplication Example 9

*Information Retrieval (1)Classification SystemInformation Filtering Systemquestionuser profilefeedbackanswerDB Template Filling& InformationExtraction SystemInformation FilteringInformation Extractionfiltered dataText ClassificationPreprocessing and IndexingApplication Example 10

*Information Retrieval (2)[Kim & Zhang, 2000]chromosomes RetrievalFitnessApplication Example 10Evolutionary Learning: Applications in IR - Web-Document Retrieval

*Information Retrieval (3)Crossover

Truncation selectionMutationchromosome Xchromosome Ychromosome Z (offspring)zi = (xi + yi ) / 2 w.p. Pcchromosome Xchromosome Xchange value w.p. PmApplication Example 10Evolutionary Learning: Applications in IR Tag Weighting

*Information Retrieval (4)DatasetsTREC-8 Web Track Data2GB, 247491 web documents (WT2g)No. of training topics: 10, No. of test topics: 10ResultsApplication Example 10Evolutionary Learning : Applications in IR - Experimental Results

*Time Series Prediction (1)Application Example 11RawTime SeriesPrepro-cessingEvolutionaryNeural Trees(ENTs)CombiningNeural TreesAutonomousModel DiscoveryCombine Neural TreesOutputsPrediction[Zhang & Joung, 2000]

*Time Series Prediction (2)Experimental Setup for the far-infrared NH3 LaserApplication Example 11

Sheet1

Design ParamentersValues Used

population size200

max generation50

crossover rate0.95

mutation rate0.1

no. of iterations100

training set size1000

test set size1000

size of committee pool10

no. of committee members3

Sheet2

Sheet3

*Time Series Prediction (3)Experimental ResultComputed ApproximationTarget FunctionApplication Example 11

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t

x(t)

laserts

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Evolutionary Computation ( 진 화 연 산 )