1. UNIVERSITI TENAGA NASIONAL 1 CSNB234 ARTIFICIAL INTELLIGENCE Chapter 9 Genetic Algorithms Chapter 9 Genetic Algorithms Instructor: Alicia Tang Y. C. (Chapter 12, pp. 509-519, Textbook) (pp. 116-119, Ref. #3)

2. UNIVERSITI TENAGA NASIONAL 2 Genetic Algorithms - I Genetic Algorithms (GAs) Is an efficient and robust search technique in complex searching areas It normally find near optimal solutions to problems Solutions are based on the natural selection and genetic, i.e. survival of the fittest In a GA work: a number of solutions are evaluated simultaneously

3. UNIVERSITI TENAGA NASIONAL 3 Genetic Algorithms - II developed by John Holland in 1975 inspired by biological mutation & evolution stochastic (means non-deterministic) search techniques based on the mechanism of natural selection and genetics implicit parallel search of solution space

4. UNIVERSITI TENAGA NASIONAL 4 Genetic Algorithms - III Each solution is evaluated for its fitness. The better solution the greater its chance of survival use an iterative process, with better solutions normally evolving over time

5. UNIVERSITI TENAGA NASIONAL 5 Applications GAs are used for optimization problems such as maximising profits or minimising costs/time Some problem areas are: scheduling design financial management

6. UNIVERSITI TENAGA NASIONAL 6 The Algorithm …Evolutionary Algorithm Generate initial population Evaluate function Best result start stop Criteria met? yes no selectioncrossovermutation

7. UNIVERSITI TENAGA NASIONAL 7 Genetic Representation Chromosomes (Strings) an instance of the problem to be solved which is also called a genetic structure a chromosome consists of one or more bits e.g.01001001 a chromosome with n bits represents 2 n solutions (of which some may be invalid)

8. UNIVERSITI TENAGA NASIONAL 8 Chromosomes Representation bit strings (0011.. 1101) - as seen in earlier slide permutation of elements (e3 e4 e1 e7 e9.. e15) list of rules (R1 R2 R3.. R10) Tree-structured expression (+ a b) etc. GAs have been successful with chromosomes sizes of 1000’s of bit, 100’s rules and 1000’s of permutation elements

9. UNIVERSITI TENAGA NASIONAL 9 Genes A chromosome may be divided into parts (positions) called genes Each gene may represent a particular aspect or parameter of a problem And, its values is called allele As a gene is in binary a 1 bit gene can hold 1 or 2 values, a 2 bit gene can hold 3 or 4 values, a 3 bit gene 5 to 8 values, etc. using this: e.g. n bits can hold from 2 n-1 + 1 to 2 n values

10. UNIVERSITI TENAGA NASIONAL 10 Population A GA uses a number of chromosome at a time (e.g 50) called population each representing solutions for a problem The population of chromosomes compete to survive based on their fitness and are manipulated by genetic operators The population evolves over a number of generations towards a better solution

11. UNIVERSITI TENAGA NASIONAL 11 Genetic Operators Main genetic operators are reproduction crossover mutation inversion

12. UNIVERSITI TENAGA NASIONAL 12 Reproduction “Reproduce” by “Selection” of individual chromosomes that are to reproduce selecting individuals to be parents chromosomes with a higher fitness value will have a higher probability of contributing one or more offspring in the next generation

13. Roulette wheel selection technique It is one of the chromosome selection techniques. Each chromosome is given a slice of the circular roulette wheel. The area of the slice within the wheel is equal to the chromosome fitness ratio. To select a chromosome for mating, a random number is generated in the interval [0, 100], and the chromosome whose segment spans the random number is selected. UNIVERSITI TENAGA NASIONAL 13

14. UNIVERSITI TENAGA NASIONAL 14 Crossover Mixing of genetic material (mating) Two structures in the current generation are allowed to mate randomly with each pair producing two chromosomes (offspring) A crossover point is selected at random and parts of the two parent chromosomes are swapped to create two child chromosomes.

15. UNIVERSITI TENAGA NASIONAL 15 Crossover in action 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 Before crossing over After it is done Crossover can lead to effective combination of partial solutions on different chromosomes By doing this, it helps accelerates the search at an early stage of evolution Select at random pos & swap the two bits

16. UNIVERSITI TENAGA NASIONAL 16 Types of crossover Single-point multi-point arithmetic reduced surrogate uniform shuffle tree, etc.

17. UNIVERSITI TENAGA NASIONAL 17 Mutation Mutation is a small copy error from one generation to the next the mutation rate is the probability a bit changes from 0 to 1 or 1 to 0 the mutation rate must be very small (e.g. 0.001) or it may result in a random search, rather than the guided search

18. UNIVERSITI TENAGA NASIONAL 18 Mutation in action Mutation may be random or heuristics Movement can be made global or local to some sub units 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 becomes

19. UNIVERSITI TENAGA NASIONAL 19 An Example Data population: RGB colours Aim: to obtain darkest colour represented by (0, 0, 0) This is a minimisation problem, i.e. a good colour is one that fits for (colour) --> 0. We now tabulate our data as shown (see next slide):

20. UNIVERSITI TENAGA NASIONAL 20 GA: Fitness (I) Start at a random pattern like this: Colour Red Green Blue C1 80 170 689 C2 130 690 15 C3 24 8 317 Fitness for (C1) = 80 + 170 + 689 = 939 Fitness for (C2) = 130 + 690 + 15 = 835 Fitness for (C3) = 24 + 8 + 317 = 349 Fitness for (C1) = 80 + 170 + 689 = 939 Fitness for (C2) = 130 + 690 + 15 = 835 Fitness for (C3) = 24 + 8 + 317 = 349 where

21. UNIVERSITI TENAGA NASIONAL 21 GA: Fitness (II) Start at a random pattern like this: Colour Red Green Blue C1 80 170 689 C2 130 690 15 C3 24 8 317 Fitness (C1) = 80 + 170 + 689 = 939 Fitness (C2) = 130 + 690 + 15 = 835 Fitness (C3) = 24 + 8 + 317 = 349 FITTEST PLACED TOP C3 C2 C1

22. UNIVERSITI TENAGA NASIONAL 22 GA: Selection After a Selection is done on the sample: Colour Fitness C3 349 C2 835 C1 939 ** Remember, this is a minimisation problem..

23. UNIVERSITI TENAGA NASIONAL 23 GA: Reproduction & Crossover So far, we have this Colour Red Green Blue C1 80 170 689 C2 130 690 15 C3 24 8 317 Colour Fitness C3 349 C2 835 C1 939 Colour Red Green Blue C4 24 8 15 C5 24 8 689 C6 130 690 689 C4 is crossover(C3,C2)= (24, 8, 15) C5 is crossover(C3,C1)= (24, 8, 689) C6 is crossover(C2,C1)= (130, 690, 689) Next step is to reproduce the pattern, like this, by crossing over:

24. UNIVERSITI TENAGA NASIONAL 24 Mutation in GA perform mutation, and we have Colour Red Green Blue C7 24 8 13 C8 25 9 689 C9 128 688 689 C7 is obtained by mutating(4) =(24, 8, 13) C8 is obtained by mutating(5) =(25, 9, 689 ) C9 is obtained by mutating(6) =(128, 688, 689) New population of 3 chromosomes

25. UNIVERSITI TENAGA NASIONAL 25 Conclusion (up to “mutation” to get a new data set) Some solutions have improved (after first iteration): Fitness for C7 = ( 24 + 8 + 13 ) = 45 Fitness for C8 = ( 25 + 9 + 689 ) = 743 Fitness for C9 = ( 128 + 688 + 689 ) = 1505 If the process is iterated, population will converge to have fitness near to zero (colour) --> 0. Getting better rather fast Slightly improved of the answer worse here..

26. UNIVERSITI TENAGA NASIONAL 26 We shall look at the so-called ‘fitness function’ with an example

27. UNIVERSITI TENAGA NASIONAL 27 Fitness Function The GA performs a search amongst possible solutions The GA search is guided by a fitness function which returns a single numeric value indicating the fitness of a chromosome the fitness is maximised or minimised depending on the problems

28. UNIVERSITI TENAGA NASIONAL 28 Problem Description To make the best use of disk space and avoid fragmentation, files should be allocated to minimize the number of locations used. Assumptions: files must be placed in a single location So that it could free some storage for other files use

29. UNIVERSITI TENAGA NASIONAL 29 Problem Description Disk space LocationSize (KB) 01.0 11.5 24.0 30.3 Total6.8

30. UNIVERSITI TENAGA NASIONAL 30 Files to be stored are: IdentifierSize (KB) A0.2 B0.1 C1.2 D3.0 E0.9

31. UNIVERSITI TENAGA NASIONAL 31 SOLUTION Step 1: design the structure of the chromosome use one gene per file 5 genes (for this example) the first gene represent the location for file A, etc. as there are 4 locations, 2 bit genes can be used to indicate a files location (00 = 0, 01 = 1, 10 = 2, 11 = 3) - base two chromosome size = 5 * 2 = 10 bits

32. UNIVERSITI TENAGA NASIONAL 32 Step 2: determine the fitness function The fitness is to be maximised Factors affecting the fitness function Free memory locations (min = 0, max = 4) Memory overflow (disk space Kb) Valid/invalid solutions. Fitness calculation Valid solution: fitness = bonus for getting a valid solution + number of free memory The bonus in this case is the maximum that can be obtained for an invalid solution Invalid solution: fitness = total disk space - memory overflow So that all files are allocated Not being used Not ‘fit’ if there are many overflow 6.8+0 6.8+4

33. UNIVERSITI TENAGA NASIONAL 33 Genetic Algorithm - revisited Algorithm overview Initialise the population Evaluate the fitness of the population WHILE the termination condition has not been satisfied select chromosomes for the new reproduction perform crossover on the new population perform mutation on the new population evaluate the fitness of the new population make the new population the old population ENDWHILE

34. UNIVERSITI TENAGA NASIONAL 34 Procedures Step 1: Pick a population of random codes. (Population size = 4) Step 2: Evaluate the fitness of each chromosome Step 3: Select for reproduction with a probability based on the fitness value Step 4: Crossover chromosomes to form the new generation randomly select pairs crossover

35. UNIVERSITI TENAGA NASIONAL 35 Step 5: Mutation Step 6: Loop back to step 2 Control Parameters The main GA control parameters are: Number of generations and trials Population size Crossover rate Mutation rate

36. UNIVERSITI TENAGA NASIONAL 36 Exercise

37. UNIVERSITI TENAGA NASIONAL 37

38. UNIVERSITI TENAGA NASIONAL 38 Supplementary slides

39. UNIVERSITI TENAGA NASIONAL 39 Number of generations The number of cycles (generations) of processing Not all chromosomes in a population need to be evaluated in each generation as they do not change Number of trials the fitness evaluation of a chromosome takes 1 trial the number of trials is approximately equal to population size * number-of-generations Genesis default: 1000

40. UNIVERSITI TENAGA NASIONAL 40 Population size The number of chromosomes in the population Constant throughout a GA run Genesis default: 50

41. UNIVERSITI TENAGA NASIONAL 41 Crossover rate The proportion of chromosomes that are crossed over, the remainder are copied to the new population unchanged For example a crossover rate of 0.6 results in 60% of the chromosomes selected for reproduction being crossed over, and the other 40% being carried through unchanged to the new population Genesis default: 0.6

42. UNIVERSITI TENAGA NASIONAL 42 Mutation rate The probability of a bit being mutated (changed) Usually in the range 0.01 to 0.001 For example a mutation rate of 0.001 means there is a 1 in 1000 chance of a bit being changed Genesis default: 0.001

43. UNIVERSITI TENAGA NASIONAL 43 Genetic Algorithms Software Packages ANT: PC implementation of 'John Muir Trail' experiment CFS-C: Domain Independent Subroutines for Implementing Classifier Systems in Arbitrary, User-Defined Environments DGENESIS: Distributed GA EM: Evolution Machine GAucsd: Genetic Algorithm Software Package GAC: Simple GA in C GACC: Genetic Aided Cascade-Correlation GAGA: A Genetic Algorithm for General Application GAGS: Genetic algorithm application generator and C++ class library / GAL: Simple GA in Lisp/ GAME: Genetic Algorithms Manipulation Environment

44. UNIVERSITI TENAGA NASIONAL 44 Genetic Algorithms Software Packages GAMusic: Genetic Algorithm to Evolve Musical Melodies GANNET: Genetic Algorithm / Neural NETwork GAW: Genetic Algorithm Workbench GECO: Genetic Evolution through Combination of Objects GENALG: Genetic Algorithm package written in Pascal GENESIS: GENEtic Search Implementation System GENEsYs: Experimental GA based on GENESIS GenET: Domain-independent generic GA software package Genie: GA-based modeling/forecasting system GENITOR: Modular GA package with floating-point support. GENlib: Genetic Algorithms and Neural Networks mGA: C and Common Lisp implementations of a messy GA