Genetic algorithms

Genetic algorithms

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  Genetic Algorithms BY RIMPLE DHAMIJA
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  Genetic Algorithms •Genetic Algorithmsare part of evolutionary computing. •Genetic Algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. It is frequently used to find optimal or near-optimal solutions to difficult problems which otherwise would take a lifetime to solve. • Optimization is the process of making something better. In any process, we have a set of inputs and a set of outputs •Optimization refers to finding the values of inputs in such a way that we get the “best” output values. •The definition of “best” varies from problem to problem, but in mathematical terms, it refers to maximizing or minimizing one or more objective functions, by varying the input parameters.
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  Search Space If Weare solving some problem, we are usually looking for solutions best among others. The space of all feasible solutions is called Search Space( State space). Each point in the Search space represent one feasible solution. Each feasible solution can be marked by its value of fitness for the problem. Various techniques to find suitable solution are Hill Climbing, Best-First Search etc. The solution is often considered as good solution because it is not possible to prove what is real optimum. NP-Hard Problems are kind of difficult problems which cannot be solved by traditional way. It is difficult to find solution but once we have it, it is easy to check the solution. This fact led to NP-Complete Problem.
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  Search Space(contd.) NP- meansNon-Deterministic Polynomial  It means that it is possible to guess the solution( by some non-deterministic algorithm) and then check it, both in polynomial time.  NP-Complete problems are of type for which answer is simply ‘Yes’ or ‘No’.  The problems with complicated outputs are called NP-Hard problems.  To find a solution, simply try all the alternatives but this is very slow and sometimes not usable at all.  Genetic Algorithms are alternative method to solve NP-Problem. E.g. Travelling Salesman Problem
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  Principle behind GeneticAlgorithms •SELECT THE BEST, DISCARD THE REST •It is based on Darwin’s principle of natural selection. • If there are Organisms that reproduce, and • If Offsprings inherit traits from there progenitors, and • If there is variability of traits, and • If the environment cannot support all members of a growing population, • Then those members of the population with less adaptive traits( determined by the environment) will die out, and • Those members with more adaptive traits( determined by the environment ) will thrive. • The Result is evolution of Species.
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  Evolution through NaturalSelection Initial Population of Animals Struggle for existence, survival of the fittest Surviving individuals reproduce, propagate favourable characteristics Millions of Years Evolved Species [Favourable characteristic now a trait of Species.]
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  Nature to ComputerMapping NATURE Population Individual Fitness Chromosome Gene Reproduction COMPUTER Set Of Solutions Solution to a Problem Quality of a Solution Encoding for a Solution Part of encoding Crossover
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  Requirements to implementGenetic Algorithm Two important elements required for any problem before a genetic algorithm can be used for a solution are •Method for representing a solution ex: a string of bits, numbers, character ex: determination total weight. •Method for measuring the quality of any proposed solution, using fitness function. Basi
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  GA Genetic Algorithm isstarted with a set of solutions(represented by Chromosomes) called population. Solutions from one Population are taken and used to form a new population.( This is motivated by hope that the new population will be better than the old one) Solutions which are selected to form new solutions(Offsprings) are selected according to their fitness value( the more suitable they are, the more chances they have to reproduce.) This process is repeated until some condition is satisfied. E.g. No of Populations or improvement of the best solution.
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  Genetic Algorithm Step 1-[START] Generate random population of n Chromosomes i.e. suitable solutions to the problem. Step 2- [Fitness] Evaluate the fitness f(x) of each Chromosome x in the Population. Step 3-[New Population] Create a new population by repeating following steps until the new population is complete. ◦ (a) [Selection] Select two parent Chromosomes from a Population according to their fitness.(the better fitness, the bigger chances to be selected) ◦ (b)[Crossover] With a crossover probability, cross over the parents to form a new offspring(children). If no crossover was performed, offspring is an exact copy of parents. ◦ ( c)[Mutation] With a mutation probability, mutate new offspring at each locus( position in chromosome)
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  Genetic Algorithm(contd.) ◦ (d)[Accepting] Place new offspring in a new Population. Step 4- [Replace] Use new generated population for a further run of algorithm. Step 5- [Test] If the end condition is satisfied, Stop, and return the best Solution in current Population. Step 6- [Loop] Go To Step 2.
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  Genetic Algorithm( analternate) Simple_Genetic_Algorithm() { Initialize the Population; Calculate Fitness Function; While( Fitness Value != Optimal Value) { ◦ Selection; // Natural Selection, Survival of Fittest ◦ Crossover; //Reproduction, Propagate favourable characteristics ◦ Mutation; // Mutation ◦ Calculate Fitness Function; } }