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## Derivative Free Optimization

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**Derivative Free Optimization**G.Anuradha**Contents**• Genetic Algorithm • Simulated Annealing • Random search method • Downhill simplex method**Characteristics of Derivative free optimization techniques**• Derivative freeness • Does not require derivatives • Rely on repeated evaluations of objective function • Intuitive guidelines • Guidelines based on simple intuition • Some concepts are based on nature’s wisdom and thermodynamics • Slowness • Comparatively slower to derivative based optimization techniques.**Characteristics of Derivative free optimization techniques**Contd… • Flexibility:- • Works well with a complex objective function also. • Randomness • Derivative free methods are stochastic in nature • They are global optimizers given enough computational time • Analytic Opacity • Difficult to do analytic studies of these methods • Most of the knowledge about these methods are empirical in nature.**Characteristics of Derivative free optimization techniques**Contd… • Iterative Nature:- • Unlike LSE these methods are iterative in nature and requires certain stopping criteria to determine when to terminate the optimization process • For eg. The stopping criteria for a maximization problem includes • Computational time • Optimization goal • Minimal improvement • Minimal relative improvement**Genetic Algorithm**• Genetic Algorithms are search and optimization techniques based on Darwin’s Principle of Natural Selection. • Proposed by John Holland at University of Michigan in 1975**Darwin’s Principle Of Natural Selection**IF there are organisms that reproduce, and IF offsprings inherit traits from their parents, 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 THEN those members with more-adaptive traits (determined by the environment) will thrive The result is the evolution of species.**Basic Idea Of Principle Of Natural Selection**“Select The Best, Discard The Rest”**Principles behind GA**• Encodes each point in solution space into binary bit string called a chromosome • Each point is associated with a fitness value • GA keeps a set of points called population or gene pool. • In each generation GA constructs a new population using crossover and mutation • Members of higher fitness values are most likely to survive and to participate in mating or crossover operations. • This is analogous to the Darwin’s model of evolution**How is it different from other optimization and search**procedures? • Works with a coding of the parameter set, not the parameters themselves • Search for a population of point and not a single point • Use objective function information and not derivatives or other auxiliary knowledge • Uses probabilistic transition rules and not deterministic rules**Major components of GA**• Encoding schemes • Fitness evaluation • Parent selection • Crossover operators • Mutation operators**Elitism**A policy of always keeping a certain number of best members when each new population is generated is called ELITISM