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Home » 2011 » August » 21 » Optimization Algorithms
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Optimization Algorithms

 Optimization Algorithms1. Description:   An optimization algorithm is an algorithm for finding a value x such that f(x) is as small (or as large) as possible, for a given function f, possibly with some constraints on x. Here, x can be a scalar or vector of continuous or discrete values. An algorithm terminates in a finite number of steps with a solution.   An algorithm is a special case of an iterative method, which generally need not converge in a finite number of steps. Instead, an iterative method produces a sequence of iterates from which some subsequence converges to a solution.   Many authors use "algorithm" more broadly for both finitely terminating algorithms and for iterative methods.2. Conceptual Algorithm:3. Introduction:Inspired by natural evolutionPopulation of individualsIndividual is feasible solution to problemEach individual is characterized by a Fitness functionHigher fitness is better solutionBased on their fitness, parents are selected to reproduce offspring for a new generationFitter individuals have more chance to reproduceNew generation has same size as old generation; old generation diesOffspring has combination of properties of two parentsIf well designed, population will converge to optimal solutionPseudocode: Example Of Convergence: Reproduction mechanisms have no knowledge of the problem to be solvedLink between genetic algorithm and problem:CodingFitness function4. Basic Principles:Coding or RepresentationString with all parametersFitness functionParent selectionReproductionCrossoverMutationConvergenceWhen to stopAn individual is characterized by a set of parameters: GenesThe genes are joined into a string: ChromosomeThe chromosome forms the genotypeThe genotype contains all information to construct an organism: the phenotypeReproduction is a "dumb” process on the chromosome of the genotypeFitness is measured in the real world (‘struggle for life’) of the phenotype5. CodingParameters of the solution (genes) are concatenated to form a string (chromosome)All kind of alphabets can be used for a chromosome (numbers, characters), but generally a binary alphabet is usedOrder of genes on chromosome can be importantGenerally many different codings for the parameters of a solution are possibleGood coding is probably the most important factor for the performance of a GAIn many cases many possible chromosomes do not code for feasible solutions
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