Genetic AlgorithmsWhat is Evolutionary Computation?The ArgumentEvolutionary ComputingNatural SelectionWhen changes occur ...Genetic Change in IndividualsGenetic Change in IndividualsRecombination (Crossover)The Nature of Computational ProblemsWhy Evolution Proves to be a Good Model for Solving these Types of ProblemsThe MetaphorSlide 13Encoding the ProblemBasic Genetic AlgorithmFitness FunctionSample Search SpaceGenetic OperatorsProduction of New ChromosomesGenerationsThe Evolutionary CycleUltimate GoalDynamic EvolutionBasic Evolution StrategyEncodingFitness FunctionsForming the Next GenerationMutationDiscrete RecombinationIntermediate RecombinationExample: Find the max value of f(x1, …, x100).Evolution Processp,cSlide 34p+cTuning a GADomains of ApplicationLocal Beam SearchStochastic Beam SearchGA vs. Local Beam SearchGA vs. Stochastic Beam SearchGA suitable for Rugged TerrainDrawbacks of GAWhy use a GA?When NOT to use a GA?TaxonomyGenetic Algorithms22c: 145, Chapter 4.3What is Evolutionary Computation?An abstraction from the theory of biological evolution that is used to create optimization procedures or methodologies, usually implemented on computers, that are used to solve problems.The ArgumentEvolution has optimized biological processes;thereforeAdoption of the evolutionary paradigm to computation and other problems can help us find optimal solutions.Evolutionary ComputingGenetic Algorithmsinvented by John Holland (University of Michigan) in the 1960’sEvolution Strategiesinvented by Ingo Rechenberg (Technical University Berlin) in the 1960’sStarted out as individual developments, but converged in the later yearsNatural SelectionLimited number of resourcesCompetition results in struggle for existenceSuccess depends on fitness --fitness of an individual: how well-adapted an individual is to their environment. This is determined by their genes (blueprints for their physical and other characteristics).Successful individuals are able to reproduce and pass on their genesWhen changes occur ...Previously “fit” (well-adapted) individuals will no longer be best-suited for their environmentSome members of the population will have genes that confer different characteristics than “the norm”. Some of these characteristics can make them more “fit” in the changing environment.Genetic Change in IndividualsMutation in genesmay be due to various sources (e.g. UV rays, chemicals, etc.)Start:1001001001001001001001Location of MutationAfter Mutation:1001000001001001001001Genetic Change in Individuals Recombination (Crossover)occurs during reproduction -- sections of genetic material exchanged between two chromosomesRecombination (Crossover)Image from http://esg-www.mit.edu:8001/bio/mg/meiosis.htmlThe Nature of Computational ProblemsRequire search through many possibilities to find a solution(e.g. search through sets of rules for one set that best predicts the ups and downs of the financial markets)Search space too big -- search won’t return within our lifetimesRequire algorithm to be adaptive or to construct original solution(e.g. interfaces that must adapt to idiosyncrasies of different users)Why Evolution Proves to be a Good Model for Solving these Types of ProblemsEvolution is a method of searching for an (almost) optimal solutionPossibilities -- all individualsBest solution -- the most “fit” or well-adapted individualEvolution is a parallel processTesting and changing of numerous species and individuals occur at the same time (or, in parallel)Evolution can be seen as a method that designs new (original) solutions to a changing environmentThe MetaphorEVOLUTIONIndividualFitnessEnvironmentPROBLEM SOLVINGCandidate SolutionQualityProblemGenetic AlgorithmsClosely follows a biological approach to problem solvingA simulated population of randomly selected individuals is generated then allowed to evolveEncoding the ProblemExample: Looking for a new site which is closest to several nearby cities. Express the problem in terms of a bit stringz = (1001010101011100)where the first 8 bits of the string represent the X-coordinate and the second 8 bits represent the Y-coordinateBasic Genetic AlgorithmStep 1. Generate a random population of n chromosomesStep 2. Assign a fitness value to each individualStep 3. Repeat until n children have been producedChoose 2 parents based on fitness proportional selectionApply genetic operators to copies of the parentsProduce new chromosomesFitness FunctionFor each individual in the population, evaluate its relative fitnessFor a problem with m parameters, the fitness can be plotted in an m+1 dimensional spaceSample Search SpaceA randomly generated population of individuals will be randomly distributed throughout the search spaceImage from http://www2.informatik.uni-erlangen.de/~jacob/Evolvica/Java/MultiModalSearch/rats.017/Surface.gifGenetic OperatorsCross-overMutationProduction of New Chromosomes2 parents give rise to 2 childrenGenerationsAs each new generation of n individuals is generated, they replace their parent generationTo achieve the desired results, typically 500 to 5000 generations are requiredThe Evolutionary CycleRecombinationMutationPopulationOffspringParentsSelectionReplacementUltimate GoalEach subsequent generation will evolve toward the global maximumAfter sufficient generations a near optimal solution will be present in the population of chromosomesDynamic EvolutionGenetic algorithms can adapt to a dynamically changing search spaceSeek out the moving maximum via a parasitic fitness functionas the chromosomes adapt to the search space, so does the fitness functionBasic Evolution Strategy1. Generate some random individuals2. Select the p best individuals based on some selection algorithm (fitness function)3. Use these p individuals to generate c children4. Go to step 2, until the desired result is achieved (i.e. little difference between generations)EncodingIndividuals are encoded as vectors of real numbers (object parameters)op = (o1, o2, o3, … , om)The strategy parameters control the mutation of the object parameterssp = (s1, s2, s3, … , sm)These two parameters constitute the individual’s chromosomeFitness FunctionsNeed a method for determining if one solution is more optimal than anotherMathematical formulaMain difference from genetic algorithms is