SOFT COMPUTING (Optimization Techniques using GA)

1. SOFT COMPUTING (Optimization Techniques using GA) Dr. N.UmaMaheswari Professor/CSE PSNA CET

2. GA Quick Overview • Developed: USA in the 1970’s • Early names: J. Holland, K. DeJong, D. Goldberg • Typically applied to: • discrete optimization • Attributed features: • not too fast • good heuristic for combinatorial problems • Special Features: • Traditionally emphasizes combining information from good parents (crossover) • many variants, e.g., reproduction models, operators Dr.N.Uma Maheswari, PSNACET

3. Search Space Initialization • Initially many individual solutions are randomly generated to form an initial population, covering the entire range of possible solutions (the search space) • Each point in the search space represents one possible solution marked by its value( fitness) Selection A proportion of the existing population is selected to bread a new bread of generation. Dr.N.Uma Maheswari, PSNACET

4. Search Space cont… Reproduction • Generate a second generation population of solutions from those selected through genetic operators: crossover and mutation. Termination • A solution is found that satisfies minimum criteria • Fixed number of generations found • Allocated budget (computation, time/money) reached • The highest ranking solution’s fitness is reaching or has reached Dr.N.Uma Maheswari, PSNACET

5. Classes of Search Techniques Dr.N.Uma Maheswari, PSNACET

6. Genetics Chromosome • All Living organisms consists of cells. In each cell there is a same set of Chromosomes. • Chromosomes are strings of DNA and consists of genes, blocks of DNA. • Each gene encodes a trait, for example color of eyes. Possible settings for a trait (e.g. blue, brown) are called alleles. Each gene has its own position in the chromosome. This position is called locus. Dr.N.Uma Maheswari, PSNACET

7. Genetics Cont… Reproduction • During reproduction, recombination (or crossover) occurs first. Genes from parents combine to form a whole new chromosome. The newly created offspring can then be mutated. The changes are mainly caused by errors in copying genes from parents. • The fitness of an organism is measure by success of the organism in its life (survival) Dr.N.Uma Maheswari, PSNACET

8. Principle Of Natural Selection • “Select The Best, Discard The Rest” • Two important elements required for any problem before a genetic algorithm can be used for a solution are: • Method for representing a solution (encoding) ex: string of bits, numbers, character • Method for measuring the quality of any proposed solution, using fitness function ex: Determining total weight Dr.N.Uma Maheswari, PSNACET

9. GA Elements Dr.N.Uma Maheswari, PSNACET

10. Nature Vs Computer - Mapping Dr.N.Uma Maheswari, PSNACET

11. Dr.N.Uma Maheswari, PSNACET

12. Genetic algorithms • Holland’s original GA is now known as the simple genetic algorithm (SGA) • Other GAs use different: • Representations • Mutations • Crossovers • Selection mechanisms Dr.N.Uma Maheswari, PSNACET

13. Fitness function • Quantifies the optimality of a solution (that is, a chromosome): that particular chromosome may be ranked against all the other chromosomes • A fitness value is assigned to each solution depending on how close it actually is to solving the problem. • Ideal fitness function correlates closely to goal + quickly computable. • For instance, knapsack problem Fitness Function = Total value of the things in the knapsack Dr.N.Uma Maheswari, PSNACET

14. Encoding • Encoding of chromosomes is one of the problems, when you are starting to solve problem with GA. Encoding very depends on the problem. • Binary Encoding: In binary encoding every chromosome is a string of bits, 0 or 1. A101100101100101011100101 B111111100000110000011111 Dr.N.Uma Maheswari, PSNACET

15. Encoding contd… • Permutation Encoding: In permutation encoding, every chromosome is a string of numbers, which represents number in a sequence. Eg:Chrom A:124356765 • Real Value Encoding: In value encoding, every chromosome is a string of some values. Values can be anything connected to problem, form numbers, real numbers or chars to some complicated objects. eg: Chromosome A:  5.3243  0.4556  2.3293  2.4545 • Tree Encoding: In tree encoding every chromosome is a tree of some objects, such as functions or commands in programming language. Dr.N.Uma Maheswari, PSNACET

16. Recombination Main idea: "Select The Best, Discard The Rest”. The process that chooses solutions to be preserved and allowed to reproduce and selects which ones must to die out. • The main goal of the recombination operator is to emphasize the good solutions and eliminate the bad solutions in a population ( while keeping the population size constant) Dr.N.Uma Maheswari, PSNACET

17. 1/6 = 17% B fitness(A) = 3 A C fitness(B) = 1 2/6 = 33% 3/6 = 50% fitness(C) = 2 SGA operators: Selection • Main idea: better individuals get higher chance • Chances proportional to fitness • Implementation: roulette wheel technique • Assign to each individual a part of the roulette wheel • Spin the wheel n times to select n individuals

18. An example after Goldberg ‘89 (1) • Simple problem: max x2 over {0,1,…,31} • GA approach: • Representation: binary code, e.g. 01101  13 • Population size: 4 • 1-point xover, bitwise mutation • Roulette wheel selection • Random initialisation • We show one generational cycle done by hand

19. So, how to select the best? • Roulette Selection • Rank Selection • Steady State Selection • Tournament Selection

20. Roulette wheel selection Main idea: the fitter is the solution with the most chances to be chosen HOW IT WORKS ?

21. x2 example: selection

22. X2 example: crossover

23. X2 example: mutation

25. Crossover • Crossover- Many genetic algorithms use strings of binary symbols for chromosomes, as in our Knapsack example, to represent solutions. • Crossover means choosing a random position in the string (say, after 2 digits) and exchanging the segments either to the right or to the left of this point with another string partitioned similarly to produce two new off spring. Dr.N.Uma Maheswari, PSNACET

26. Cross Over-Single-site

27. Crossover methods • Single Point Crossover- A random point is chosen on the individual chromosomes (strings) and the genetic material is exchanged at this point. Dr.N.Uma Maheswari, PSNACET

28. Uniform Crossover using Mask

29. Two Dimensional Crossover-Matrix Crossover

31. GA Cycle

32. Outline of the Basic Genetic Algorithm • [Start] Generate random population of n chromosomes (suitable solutions for the problem) • [Fitness] Evaluate the fitness f(x) of each chromosome x in the population • [New population] Create a new population by repeating following steps until the new population is complete Dr.N.Uma Maheswari, PSNACET

33. [Selection] Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected) The idea is to choose the better parents. • [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. • [Mutation] With a mutation probability mutate new offspring at each locus (position in chromosome). Dr.N.Uma Maheswari, PSNACET

34. [Accepting] Place new offspring in a new population • [Replace] Use new generated population for a further run of algorithm • [Test] If the end condition is satisfied, stop, and return the best solution in current population • [Loop] Go to step 2 Dr.N.Uma Maheswari, PSNACET

35. Flow Diagram of the Genetic Algorithm Process Describe Problem Generate Initial Solutions Test: is initial solution good enough? Step 1 Yes Stop No Select parents to reproduce Step 2 Step 3 Apply crossover process and create a set of offspring Apply random mutation Step 4 Step 5 Dr.N.Uma Maheswari, PSNACET

38. THANK YOU Dr.N.Uma Maheswari, PSNACET