CSM6120 Introduction to Intelligent Systems

1. CSM6120Introduction to Intelligent Systems Evolutionary and Genetic Algorithms

2. Basic ideas of EAs • An EA is an iterative procedure which evolves a population of individuals • Each individual is a candidate solution to a given problem • Each individual is evaluated by a fitness function, which measures the quality of its candidate solution • At each iteration (generation): • The best individuals are selected • Genetic operators are applied to selected individuals in order to produce new individuals (offspring) • New individuals are evaluated by fitness function

3. Taxonomy Search Techniques Uninformed Informed DFS BFS Evolutionary Algorithms Simulated Annealing A* Hill Climbing Evolutionary Strategies Swarm Intelligence Genetic Programming Genetic Algorithms

4. The Genetic Algorithm • Directed search algorithms based on the mechanics of biological evolution • Developed by John Holland, University of Michigan (1970s) • To understand the adaptive processes of natural systems • To design artificial systems software that retains the robustness of natural systems • Provide efficient, effective techniques for optimization and machine learning applications

5. Some GA applications

6. Application: function optimisation (1) 1 0.8 0.6 0.4 0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 g(x) = sin(x) - 0.1 x + 2 f(x) = x2 h(x,y) = x.sin(4x) - y.sin(4y+ ) + 1

7. Application: function optimisation (2) • Conventional approaches: • Often requires knowledge of derivatives or other specific mathematical technique • Evolutionary algorithm approach: • Requires only a measure of solution quality (fitness function)

8. Components of a GA A problem to solve, and ... • Encoding technique (gene, chromosome) • Initialization procedure (creation) • Evaluation function (environment) • Selection of parents (reproduction) • Genetic operators (mutation, recombination) • Parameter settings (practice and art)

9. GA terminology • Population • The collection of potential solutions (i.e. all the chromosomes) • Parents/Children • Both are chromosomes • Children are generated from the parent chromosomes • Generations • Number of iterations/cycles through the GA process

10. Simple GA initialize population; evaluate population; while TerminationCriteriaNotSatisfied { select parents for reproduction; perform recombination and mutation; evaluate population; }

11. The GA cycle chosen parents recombination children selection modification modified children parents evaluation population evaluated children deleted members discard

12. Population Chromosomes could be: • Bit strings (0101 ... 1100) • Real numbers (43.2 -33.1 ... 0.0 89.2) • Permutations of element (E11 E3 E7 ... E1 E15) • Lists of rules (R1 R2 R3 ... R22 R23) • Program elements (genetic programming) • ... any data structure ...

13. Example: Discrete representation • Representation of an individual can be using discrete values (binary, integer, or any other system with a discrete set of values) • The following is an example of binary representation: CHROMOSOME 1 0 1 0 0 0 1 1 GENE

14. ... • Anything? Example: Discrete representation 8 bits Genotype Phenotype: • Integer • Real Number • Schedule 1 0 1 0 0 0 1 1

15. Example: Discrete representation Phenotype could be integer numbers Genotype: Phenotype: = 163 1 0 1 0 0 0 1 1 1*27 + 0*26 + 1*25 + 0*24 + 0*23 + 0*22 + 1*21 + 1*20= 128 + 32 + 2 + 1 = 163

16. Example: Discrete representation Phenotype could be real numbers e.g. a number between 2.5 and 20.5 using 8 binary digits Genotype: Phenotype: = 13.9609 1 0 1 0 0 0 1 1

17. Example: Discrete representation Phenotype could be a schedule e.g. 8 jobs, 2 time steps Phenotype Job Time Step 1 2 3 4 5 6 7 8 2 1 2 1 1 1 2 2 Genotype: = 1 0 1 0 0 0 1 1

18. Example: Real-valued representation • A very natural encoding if the solution we are looking for is a list of real-valued numbers, then encode it as a list of real-valued numbers! (i.e., not as a string of 1s and 0s) • Lots of applications, e.g. parameter optimisation

19. Representation • Task – how to represent the travelling salesman problem (TSP)? Find a tour of a given set of cities so that • Each city is visited only once • The total distance travelled is minimised

20. Representation One possibility - an ordered list of city numbers (this is known as an order-based GA) 1) London 3) Dunedin 5) Beijing 7) Tokyo 2) Venice 4) Singapore 6) Phoenix 8) Victoria Chromosome 1 (3 5 7 2 1 6 4 8) Chromosome 2 (2 5 7 6 8 1 3 4)

21. Selection selection parents population

22. Selection • Need to choose which chromosomes to use based on their ‘fitness’ • Why not choose the best chromosomes? • We want a balance between exploration and exploitation

23. Roulette wheel selection

24. Rank-based selection • 1st step • Sort (rank) individuals according to fitness • Ascending or descending order (minimization or maximization) • 2nd step • Select individuals with probability proportional to their rank only (ignoring the fitness value) • The better the rank, the higher the probability of being selected • It avoids most of the problems associated with roulette-wheel selection, but still requires global sorting of individuals, reducing potential for parallel processing

25. Tournament selection • A number of “tournaments” are run • Several chromosomes chosen at random • The chromosome with the highest fitness is selected each time • Larger tournament size means that weak chromosomes are less likely to be selected • Advantages • It is efficient to code • It works on parallel architectures 

26. Crossover: recombination P1 (0 1 1 0 1 0 1 1) (1 1 0 1 1 0 1 1) C1 P2 (1 1 0 1 1 0 0 1) (0 1 1 0 1 0 0 1) C2 Crossover is a critical feature of GAs: • It greatly accelerates search early in evolution of a population • It leads to effective combination of sub-solutions on different chromosomes • Several methods for crossover exist…

27. Crossover • How would we implement crossover for TSPs? Parent 1 (3 5 7 2 1 6 4 8) Parent 2 (2 5 7 6 8 1 3 4)

28. Crossover Parent 1 (3 5 7 2 1 6 4 8) Parent 2 (2 5 7 6 8 1 3 4) Child 1 (3 5 7 6 8 1 3 4) Child 2 (2 5 7 2 1 6 4 8)

29. Mutation: local modification • Causes movement in the search space(local or global) • Restores lost information to the population Before: (1 0 1 1 0 1 1 0) After: (0 1 1 0 0 1 1 0) Before: (1.38 -69.4 326.44 0.1) After: (1.38 -67.5 326.44 0.1)

30. Mutation • Given the representation for TSPs, how could we achieve mutation?

31. Mutation Mutation involves reordering of the list: ** Before: (5 8 7 2 1 6 3 4) After: (5 8 6 2 1 7 3 4)

32. Note • Both mutation and crossover are applied based on user-supplied probabilities • We usually use a fairly high crossover rate and fairly low mutation rate • Why do you think this is?

33. Evaluation of fitness • The evaluator decodes a chromosome and assigns it a fitness measure • The evaluator is the only link between a classical GA and the problem it is solving modified children evaluation evaluated children

34. Fitness functions • Evaluate the ‘goodness’ of chromosomes • (How well they solve the problem) • Critical to the success of the GA • Often difficult to define well • Must be fairly fast, as each chromosome must be evaluated each generation (iteration)

35. Fitness functions • Fitness function for the TSP? • (3 5 7 2 1 6 4 8) • As we’re minimizing the distance travelled, the fitness is the total distance travelled in the journey defined by the chromosome

36. Deletion • Generational GA:entire populations replaced with each iteration • Steady-state GA:a few members replaced each generation population deleted members discard

37. The GA cycle chosen parents recombination children selection modification modified children parents evaluation population evaluated children deleted members discard

38. Stopping! • The GA cycle continues until • The system has ‘converged’; or • A specified number of iterations (‘generations’) has been performed

39. An abstract example Distribution of Individuals in Generation 0 Distribution of Individuals in Generation N

40. Good demo of the GA components • http://www.obitko.com/tutorials/genetic-algorithms/example-function-minimum.php

41. TSP example: 30 cities

46. Overview of performance

47. Example: n-queens • Put n queens on an n × n board with no two queens on the same row, column, or diagonal

48. Examples • Eaters • http://math.hws.edu/xJava/GA/ • TSP • http://www.heatonresearch.com/articles/65/page1.html • http://www.ads.tuwien.ac.at/raidl/tspga/TSPGA.html • Good demo of the GA components • http://www.obitko.com/tutorials/genetic-algorithms/example-function-minimum.php

49. Exercise: The Card Problem • You have 10 cards numbered from 1 to 10. You have to choose a way of dividing them into 2 piles, so that the cards in Pile0 *sum* to a number as close as possible to 36, and the remaining cards in Pile1 *multiply* to a number as close as possible to 360 • Encoding • Each card can be in Pile0 or Pile1, there are 1024 possible ways of sorting them into 2 piles, and you have to find the best. Think of a sensible way of encoding any possible solution. • Fitness • Some of these chromosomes will be closer to the target than others. Think of a sensible way of evaluating any chromosome and scoring it with a fitness measure.

50. Issues for GA practitioners • Choosing basic implementation issues: • Representation • Population size, mutation rate, ... • Selection, deletion policies • Crossover, mutation operators • Termination criteria • Performance, scalability • Solution is only as good as the fitness function (often hardest part)