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Fuzzy Genetic Algorithm

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Fuzzy Genetic Algorithm

  1. 1. Fuzzy Genetic Algorithm A Solution to The Problem 1
  2. 2.  Introduction  Fuzzy logic  Genetic Algorithm  Fuzzy Genetic Algorithm  Different FGA Approach  Application Sector 2
  3. 3.  After scientists became disillusioned with classical and neoclassical attempts at modeling intelligence, they looked in other directions.  Two prominent fields arose, connectionism (neural networking, parallel processing) and evolutionary computing.  It is the latter that this essay deals with - genetic algorithms and genetic programming.  Fuzzy logic is a form of many-valued logic  A Fuzzy Genetic Algorithm (FGA) is considered as a GA that uses fuzzy logic based techniques 3
  4. 4.  Definition of fuzzy   Fuzzy – “not clear, distinct, or precise; blurred” Definition of fuzzy logic A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts.  Compared to traditional binary sets fuzzy logic variables may have a truth value that ranges in degree between 0 and 1 Membership Function   The membership function represents the degree of truth as an extension of valuation. 4
  5. 5.  The term "fuzzy logic" was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh.  Fuzzy logic has been applied to many fields, from control theory to artificial intelligence.  Fuzzy logics however had been studied since the 1920s as infinite-valued logics notably by Łukasiewicz and Tarski. 5
  6. 6.  A point on that scale has three "truth values"—one for each of the three functions.  red arrow points to zero, this temperature may be interpreted as "not hot“  The orange arrow (pointing at 0.2) may describe it as "slightly warm“  The blue arrow (pointing at 0.8) "fairly cold" 6
  7. 7.  A genetic algorithm (or GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems.  Genetic algorithms are categorized as global search heuristics.  Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover (also called recombination). 7
  8. 8.  The new population is then used in the next iteration of the algorithm.  Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population.  If the algorithm has terminated due to a maximum number of generations, a satisfactory solution may or may not have been reached. 8
  9. 9. Initial Population Selection • The evolution usually starts from a population of randomly generated individuals Mating • Individual solutions are selected through a fitness-based process Crossover Mutation • This generational process is repeated until a termination condition has been reached. • improve the solution through repetitive Terminate application of the mutation, crossover, inversion and selection operators 9
  10. 10.  The use of FL based techniques for either improving GA behaviour and modeling GA components, the results obtained have been called fuzzy genetic algorithms (FGAs),  The application of GAs in various optimization and search problems involving fuzzy systems.  An FGA may be defined as an ordering sequence of instructions in which some of the instructions or algorithm components may be designed with fuzzy logic based tools  A fuzzy fitness finding mechanism guides the GA through the search space by combining the contributions of various criteria/features that have been identified as the governing factors for the formation of the clusters. 10
  11. 11. A single objective optimization model cannot serve the purpose of a fitness measuring index because we are looking at multiple criteria that could be responsible for stringing together data items into clusters. This is true; not only for the clustering problem but for any problem solving using GA that involves multiple criteria. In multi-criteria optimization, the notion of optimality is not clearly defined. A solution may be best w.r.t. one criterion but not so w.r.t. the other criteria. Pareto optimality offers a set of nondominated solutions called the P-optimal set where the integrity of each of the criteria is respected. 11
  12. 12. The algorithm has two computational elements that work together. i) The Genetic Algorithm (GA) and ii) The Fuzzy Fitness Finder (FFF). 12
  13. 13. Cossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based. Cross over is a process of taking more than one parent solutions and producing a child solution from them. 13
  14. 14.  Mutation is a genetic operator used to maintain genetic diversity from one generation of a population of genetic algorithm chromosomes to the next.  It is analogous to biological mutation. Mutation alters one or more gene values in a chromosome from its initial state.  In mutation, the solution may change entirely from the previous solution. Hence GA can come to better solution by using mutation.  Mutation occurs during evolution according to a user-definable mutation probability.  This probability should be set low. If it is set too high, the search will turn into a primitive random search. 14
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  16. 16. FGA Fuzzy GA · A genetic representation for potential solutions to the problem. While the population of the genetic algorithm undergoes evolution at every generation, the relatively ‘good’ solutions reproduce while the relatively ‘bad’ solutions die. · Method to create an initial population of potential solutions To distinguish between solutions, an objective (evaluation) function is used. In the simple cases, there is only one criterion for optimization for example, maximization of profit or minimization of cost. · Selection of individuals for the next generation But in many real-world decision making problems, there is a need for simultaneous optimization of multiple objectives. · An evaluation function to rate solutions in terms of their “fitness” · Genetic operators that alter the composition of the children In order to make a successful run of a GA, the values for the parameters of the GA have to be defined like the population size, parameters for the genetic operators and the terminating condition. 16
  17. 17. • The Fuzzy Fitness Finder • Input and Output Criteria • Fuzzification of Inputs • Fuzzy Inference Engine • Defuzzification of Output 17
  18. 18. Pittsburgh Approach Iterative Rule Learning Approach Michigan Approach The Nagoya Approach 18
  19. 19. Electrical Engg. Mechanical Engg. Economics Artificial Intelligence Approx. in all sectors of life. 19
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