1. rkj@aber.ac.uk CSM6120 Introduction to Intelligent Systems Evolutionary and Genetic Algorithms

2. Informal biological terminology  Genes  Encoding rules that describe how an organism is built up from the tiny building blocks of life  Chromosomes  Long strings formed by connecting genes together  Recombination  Process of two organisms mating, producing offspring that may end up sharing genes of their parents

3. 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

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

5. 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

6. Some GA applications

7. Application: function optimisation (1) -0.8-0.6-0.4-0.200.20.40.60.81 0 0.2 0.4 0.6 0.8 1 f(x) = x 2 g(x) = sin(x) - 0.1 x + 2 h(x,y) = x.sin(4  x) - y.sin(4  y+  ) + 1

8. 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)

9. 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)

10. 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

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

12. The GA cycle selectionselection populationpopulation evaluationevaluation modificationmodification discarddiscard deleted members deleted members parents children modified children modified children evaluated children recombinationrecombination chosen parents chosen parents

13. 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...

14.  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 GENE Example: Discrete representation 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0

15. 8 bits Genotype Phenotype: Integer Real Number Schedule... Anything? Example: Discrete representation 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0

16. Phenotype could be integer numbers Genotype: 1*2 7 + 0*2 6 + 1*2 5 + 0*2 4 + 0*2 3 + 0*2 2 + 1*2 1 + 1*2 0 = 128 + 32 + 2 + 1 = 163 = 163 Phenotype: Example: Discrete representation 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0

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

18. Phenotype could be a schedule e.g. 8 jobs, 2 time steps Genotype: = 1234567812345678 2121112221211122 JobTime Step Phenotype Example: Discrete representation 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0

19.  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 Example: Real-valued representation

20. 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

21. 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)

22. Selection selectionselection populationpopulation parents

23. 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

24. Roulette wheel selection

25. 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

26. 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

27. The GA cycle selectionselection populationpopulation evaluationevaluation modificationmodification discarddiscard deleted members deleted members parents children modified children modified children evaluated children recombinationrecombination chosen parents chosen parents

28. 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…

29. 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)

30. 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)

31. Mutation: local modification 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)  Causes movement in the search space (local or global)  Restores lost information to the population

32. Mutation  Given the representation for TSPs, how could we achieve mutation?

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

34. 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?

35. 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 evaluation modified children modified children evaluated children

36. 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)

37. 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

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

39. The GA cycle selectionselection populationpopulation evaluationevaluation modificationmodification discarddiscard deleted members deleted members parents children modified children modified children evaluated children recombinationrecombination chosen parents chosen parents

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

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

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

43. TSP example: 30 cities

48. Overview of performance

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

50. Examples  Eaters  http://math.hws.edu/xJava/GA/ http://math.hws.edu/xJava/GA/  TSP  http://www.heatonresearch.com/articles/65/page1.html http://www.heatonresearch.com/articles/65/page1.html  http://www.ads.tuwien.ac.at/raidl/tspga/TSPGA.html http://www.ads.tuwien.ac.at/raidl/tspga/TSPGA.html

51. 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.

52. 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)  Your assignment will be to code a GA for a given task! Be aware of the above issues…

53.  Concept is easy to understand  Supports multi-objective optimization  Good for “noisy” environments  Always an answer; answer gets better with time  Inherently parallel; easily distributed Benefits of GAs