1Genetic AlgorithmsRussell & Norvig, Cha. 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.Components of 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 have begun to converge in the last few 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.2Genetic 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 SolutionQualityProblem3Genetic 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 nchromosomes Step 2. Assign a fitness to each individual Step 3. Repeat until nchildren 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 mparameters, 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 Mutation4Production of New Chromosomes 2 parents give rise to 2 childrenGenerations As each new generation of nindividuals 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 pbest individuals based on some selection algorithm (fitness function)3. Use these pindividuals to generate cchildren4. Go to step 2, until the desired result is achieved (i.e. little difference between generations)5Encoding Individuals are encoded as vectors of real numbers (object parameters)op= (o1, o2, o3, … , om) The strategy parameters control the mutation of the object parameterssp= (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 that only the most fit individuals are allowed to reproduce (elitist selection)Forming the Next Generation Number of individuals selected to be parents (p) too many: lots of persistent bad traits too few: stagnant gene pool Total number of children produced (c) limited by computer resources more children ⇒ faster evolutionMutation Needed to add new genes to the pool optimal solution cannot be reached if a necessary gene is not present bad genes filtered out by evolution Random changes to the chromosome object parameter mutation strategy parameter mutation changes the step size used in object parameter mutationDiscrete Recombination Similar to crossover of genetic algorithms Equal probability of receiving each parameter from each parent(8, 12, 31, … ,5) (2, 5, 23, … , 14)(2, 12, 31, … , 14)Intermediate
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