10. Lecture Stochastic Optimization

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1 Soft Control (AT 3, RMA) 10. Lecture Stochastic Optimization Genetic Algorithms

2 10. Structure of the lecture 1. Soft control: the definition and limitations, basics of epert" systems 2. Knowledge representation and knowledge processing (Symbolic AI) application: epert systems 3. Fuzzy Systems: Dealing with Fuzzy knowledge application: Fuzzy Control 4. Connective systems: neural networks application: Identification and neural controller 5. Genetic Algorithms: Stochastic Optimization Genetic Algorithms Simulated Annealing Differential Evolution Application: Optimization 6. Summary and Literarture reference 271

3 Contents of 10 th Lecture Classification in the lecture Conjunction with the other methods Overview of Evolutionary Algorithms The basic idea of genetic algorithms Idea Properties Genetic algorithms in detail Development Elements Sample Applications in automation technology Genetic Programming Summary 272

4 Classification in the lecture Natural development Looking at the considered systems in the past lectures we can say that we have had intelligent top-down views : Technical Development and procedures in the lecture Epert systems (abstract mathematical thinking) are a further development of Fuzzy-Systems ( natural Fuzzy-Close) This could only be developed on the basis of the neural structure of the brain Neural Networks (Learning and adaptation) Originated from the course of evolution of simpler structures Genetic Algorithms ( survival of the fittest ) 273

5 Overview of evolutionary algorithms Evolutionäre Algorithmen Genetische Programmierung Genetische Algorithmen Evolutionsstrategien Typical features of the different algorithms: Representation of individuals Operators used Size of individuals Selection Mechanism Genetic Algorithms Bit-String Recombination*, Mutation Genetic Synta trees Recombination*, Programming Mutation Evolutions Floating point vector Mutation*, strategies Recombination Operators marked with an * play the biggest role Constant Variable Constant Probabilistic Probabilistic Deterministic 274

6 The basic idea of Genetic algorithms Genetic algorithms are numerical optimization algorithms on the basis of two concepts of nature : Genetic Natural selection Initial ideas in 1950, a breakthrough in the 1960s with John Holland Basic concepts of GA There are a large number population of possible solutions to a problem There is a method to determine how well or bad a solution is There is a recombination method, the elements of the good solutions connects to generate new or better solutions There is a mutation operator, to prevent the permanent loss of diversity within the solutions 275

7 Properties of GA Analogous to the evolution theory in biology Evolution is a successful, robust method for adaptation of biological systems GA can search premises of hypotheses The comple, interacting elements where the influence of each part on the overall hypothesis is unclear GA can be easily parallelized GA are not deterministic GA does not optimize a single individual, but always a whole population. It is possible to find several local optima and finish with the selection of global optimum 276

8 Cycle of GA 1. Define the coding 2. Defining a fitness function 3. Initialization of a population 4. Calculation of fitness for the population 5. Selection of elements for the recombination 6. Recombination 7. Mutation 8. Composition of the new generation of 1. The Offspring 2. Elements of the parent generation(not always Elitism) 9. Net up-to 4 to a termination criterion is reached 277

9 Coding Most will use a binary encoding Bit strings are easy to manipulate (simple implementation of the genetic operators) If there are problems in several variables, the bit strings hanged together One speaks in analogy to the biology of genotype and phenotype 278

10 Fitness function Describes the goodness of a solution Fitness function should differ well between individuals, otherwise the only possibility of the search more or less randomly and converges to bad genetic algorithm It would be desirable fitness function that individuals with significantly similar characteristics also have similar fitness levels Should be easy to calculate, since they very often applied 279

11 Selection methods Monte-Carlo (Roulette-Wheel-Selection) Each individual will be allocated sector of Roulettrads proportional to fitness Selection Ranking-Selection Selection on the basis of seniority (the fitness value) within the population Tournament-Selection Random choice of 2 (or more) individuals, with predefined takeover of better likely 280

12 Roulette-Wheel-Selection Build the sum of the individuals of all fitness levels F sum Generate a random number R between 0 and F sum Add the fitness values of individuals one by one until the sum eceeds the value of R Select the most recently added individual 281

13 Rank based Selection N individuals in the population will be sorted in accordance with their fitness levels The best individual receives N Score, the net N-1, the worst 1 rating point With those rating points instead of the actual fitness will be assessed in accordance with the roulette wheel selection procedures Advantage in comparison to the roulette-wheel selection: Strong preference for less capable individuals Weaker deprivation of the most vulnerable individuals Simplified procedures: it is randomly chosen from individuals with a high rank (fied number) selected Only the best % allowed to participate in the recombination 282

14 Eample for comparison 1000-mal Roulette-Wheel-Selection mal Rank based Seletion 283

15 Recombination or crossover From two previously selected individuals (parents) are two new crossover individuals generated (descendants) It is coincidentally a certain position on the selected bit string At this point, the strings cut and the ends are swapped Variations with several crossover points are possible 284

16 Mutation From the newly formed individuals; candidates with a low probability are selected for mutations Mutation: There will be a randomly chosen bit inverted Caution: depending on the chosen coding different mutation has high influence Take into consideration that variations are possible in the selection of bits to be mutated 285

17 Composition of the New Generation Basically you can specify whether a certain percentage of parents' generation takes over to the net generation Often it renounces : the detriment that can happen is that the maimum fitness in the new generation is lower Possible methods: Elitism A fied proportion of the new generation consists of the best representatives of parents' generation, the rest being regenerated (selection, crossover, mutation) Another way: After the recombination the offspring are selected not automatically but the best individuals are selected 286

18 Applications in automation technology Optimization of controller parameters Optimization of parameters in models (approimation of curves) Optimization of controller structures (encoding is difficult Genetic Programming) Optimization of many parameters in a fuzzy controller Rules Membership functions Optimization of many parameters in a neural network Weights Structure 287

19 Genetic Programming Special case of a genetic algorithm Instead of bit strings the individuals are represented by trees The trees are synta trees and provide programs which + + si n ^ 8 * 2 + y Represents the function: f (, y) sin 2 y Represents the function: f ( )

20 Genetic Programming Mutation: * becomes 8 + f ( ) 2 8 becomes f ( )

21 Genetic Programming Recombination: E1: E2: + + si n ^ K1: + K2: + si n + 8 ^ 2 290

22 Genetic Programming with Block diagrarms Recombination Mutation 291

23 Summary and learning from the 10th Lecture Basic idea of GA Comparison of GA s with other optimization methods Individual elements of the GA and know their significance and may illustrate eemplary: Selection Crossing Mutation Possible applications relating to automation technology Relation to Neuro-fuzzy Approach of genetic programming 292

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