Derivative Free Optimization G Anuradha Contents Genetic Algorithm

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. 7

Basic Idea Of Principle Of Natural Selection “Select The Best, Discard The Rest” 8

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? 1. Works with a coding of the parameter set, not the parameters themselves 2. Search for a population of point and not a single point 3. Use objective function information and not derivatives or other auxiliary knowledge 4. Uses probabilistic transition rules and not deterministic rules

Characteristics of GA

Major components of GA • • • Encoding schemes Fitness evaluation Parent selection Crossover operators Mutation operators

Crossover operators

Elitism A policy of always keeping a certain number of best members when each new population is generated is called ELITISM