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Evolutionary Computation (EC)

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Presentation on theme: "Evolutionary Computation (EC)"— Presentation transcript:

1 Evolutionary Computation (EC)
eie426-ec ppt 2017/4/14 EIE426-AICV

2 Contents Basic Concepts of EC Genetic Algorithms An Example
Chromosome Representation Stopping Criteria Initial Population Selection Mechanisms Crossover and Mutation Fitness Functions Another Example Application: Routing Optimization Advantages and Disadvantages of EC 2017/4/14 EIE426-AICV

3 Evolution and Search Evolution - search through the enormous genetic parameter space for the best genetic make-up. Borrow ideas from nature to help us solve problems that have equally large search spaces or similarly changing environment. 2017/4/14 EIE426-AICV

4 Natural Evolution and Evolutionary Computation
Individual Fitness Environment Evolutionary Computing Candidate Solution Quality Problem 2017/4/14 EIE426-AICV

5 Different ECs Several classes of EC algorithms have been developed:
- Genetic algorithms (GA’s): model genetic evolution - Genetic programming: based on GA’s, but individuals are programs (represented as trees) - Evolutionary programming: from the simulation of adaptive behavior in evolution (phenotype evolution) - Evolution strategies: model the strategic parameters that control variation in evolution, i.e., the evolution of evolution - Culture evolution: models the evolution of culture of a population and how the culture influences the evolution of individuals. - Co-evolution: individuals evolve through cooperation, or in competition with one other. 2017/4/14 EIE426-AICV

6 Basic Concepts Chromosome: individual Population: many individuals
Gene: each characteristics of chromosome (one parameter) Allele: the value of a gene Crossover: generate offspring by combining parts of the parents. Mutation: introduce new genetic material into an existing individual. Fitness: the survival strength of an individual Culling (removing) and elitism (copying) 2017/4/14 EIE426-AICV

7 Evolutionary Computation
Selection Parents Recombination (Crossover) Population Mutation The evolutionary cycle Replacement Offspring 2017/4/14 EIE426-AICV

8 Genetic Algorithms The GA was the first EC paradigm developed and applied (Holland 1975). The features of the original GA’s: A bit string representation Proportional selection Cross-over as the primary method to produce new individuals. Several changes have been made: Different representation schemes Different selection methods Different GA operators (cross-over, mutation and elitism) 2017/4/14 EIE426-AICV

9 Random Search The GA is a search procedure.
Random search is possibly the simplest search procedure. Its training time may be very long before an acceptable solution is obtained. Procedure: Start from an initial search point or a set of initial points. Random perturbations to the points Repeat until an acceptable solution is reached or a maximum number of iterations is exceeded. 2017/4/14 EIE426-AICV

10 General Genetic Algorithm
Let g = 0. Initialize the initial generation Cg . While no stopping criterion is satisfied (a) Evaluate the fitness of each individual in Cg . (b) g  g+1. (c) Select parents from Cg-1. (d) Recombine selected parents through cross-over to form offspring Og (with a probability pc). (e) Mutate offspring in Og (with a probability pm). (f) Select the new generation Cg from (the previous generation Cg-1, e.g., the best individuals are copied) and the offspring Og. g: generation Note: The things in () might or might not be carried out. 2017/4/14 EIE426-AICV

11 An Example 2017/4/14 EIE426-AICV

12 2017/4/14 EIE426-AICV

13 Use a genetic algorithm to solve the problem:
Coding (chromosome representation of a solution) Generation of initial population (solutions) Fitness calculation Genetic operation 2017/4/14 EIE426-AICV

14 Coding (chromosome representation):
Use a binary string to represent x. If the solution is to be precise to 10-6, then the interval (2-(-1)) = 3 should be divided into 3× 106. At least 22 bits should be used because 2017/4/14 EIE426-AICV

15 Decoding 2017/4/14 EIE426-AICV

16 2017/4/14 EIE426-AICV

17 Generation of initial population
A set of N 22-bit binary strings can be randomly generated as the initial population. 2017/4/14 EIE426-AICV

18 Fitness calculation Since f(x) > 0 in the interval, we can directly use f(x) as a fitness function: f(s) = f(x) e.g., s1 = < >, f(s1)= s2 = < >, f(s2)= s3 = < >, f(s3)= 2017/4/14 EIE426-AICV

19 (1) Selection: based on the fitness of individuals
Genetic operation (1) Selection: based on the fitness of individuals e.g., roulette wheel selection (fitness proportionate selection) (2) Crossover (with a probability pc) e.g., s2 = <00000 | >, f(s2)= s3 = <11100 | >, f(s3)= After the crossover operation: s’2 = <00000 | >, f(s’2)= s’3 = <11100 | >, f(s’3)= 2017/4/14 EIE426-AICV

20 (3) Mutation (with a probability pm) e.g.,
s3 = < > f(s3)= After the mutation operation: s’3 = < > f(s’3)= or s3 = < > s”3 = < > f(s”3)= 2017/4/14 EIE426-AICV

21 Simulation results: N = 50, pc = 0.25, pm = 0.01, at 89 generations, the best individual was obtained: smax = < > xmax = f(xmax) = 2017/4/14 EIE426-AICV

22 The chromosome of the best individual
The best individual at each iteration (up to 150 generations) Generation The chromosome of the best individual x fitness 1 11 17 54 71 89 150 2017/4/14 EIE426-AICV

23 Summary on Basic Concepts
Evolution is an optimization process, where the aim is to improve the ability of individuals to survive. An evolutionary algorithm (EA) is a stochastic search for an optimal solution to a given problem. Evolution - search through the enormous genetic parameter space for the best genetic make-up. Borrow ideas from nature to help us solve problems that have an equally large search spaces or similarly changing environment. 2017/4/14 EIE426-AICV

24 Genotype: describes the genetic composition of an individual
Phenotype: the expressed behavioral traits of an individual in a specific environment. Selection: use the fitness evaluations to decide which are the best parents to reproduce. Crossover: generate offspring by combining parts of the parents Mutation: introduce new genetic material into an existing individual. Coding: phenotype  genotype Decoding: genotype  phenotype 2017/4/14 EIE426-AICV

25 Simple Genetic Algorithm (SGA)
Representation Binary strings Recombination (crossover) N-point (commonly used 1-point and 2-point) or uniform; pc typically in range (0.6, 0.9) Mutation Bitwise bit-flipping with fixed probability pm (typically between 1/pop_size and 1/ chromosome_length) Parent selection Fitness-Proportionate Survivor selection All children replace parents Speciality Emphasis on crossover 2017/4/14 EIE426-AICV

26 Chromosome Representation
Genotype space = {0,1}I I-bit binary strings Phenotype space Coding (encoding or (representation) Decoding (inverse representation) 2017/4/14 EIE426-AICV

27 Binary-valued variables: no extra coding required
Nominal-valued variables D-bit with 2D discrete nominal values e.g., four colors: red (00), blue (01), green (10), yellow (11) Continuous-valued variables 2017/4/14 EIE426-AICV

28 Other Representations
Gray coding of integers (still binary chromosomes) Gray coding is a mapping that means that small changes in the genotype cause small changes in the phenotype (unlike binary coding, e.g., 0111(7) and 1000 (8)). It is generally accepted that it is better to encode numerical variables directly as Integers Floating point variables 2017/4/14 EIE426-AICV

29 Stopping Criteria The maximum number of generation is exceeded
An acceptable best fit individual has evolved The average and/or maximum fitness value do not change significantly over the past g generations. 2017/4/14 EIE426-AICV

30 Initial Population The standard way of generating the initial population is to choose gene values randomly from the allowed set of values. The goal of random selection is to ensure that the initial population is a uniform representation of the entire search space. A large population covers a larger area of the search space, and may require less generations to converge. In the case of a small population, the EA can be forced to explore a large search space by increasing the rate of mutation. 2017/4/14 EIE426-AICV

31 Selection Mechanisms Selection operators Random selection
Proportional selection: roulette wheel selection Tournament selection Rank-based selection 2017/4/14 EIE426-AICV

32 Random Selection Individuals are selected randomly with no reference to fitness at all. All the individuals, good or bad, have an equal chance of being selected. 2017/4/14 EIE426-AICV

33 Proportional Selection: Roulette Wheel Selection
Individual Chromosome Fitness fi Selection probability, Pi Accumulated probability 1 8 2 5 3 4 10 7 6 12 19 9 14 2017/4/14 EIE426-AICV

34 Roulette Wheel Selection
It can be visualized as the spinning of the wheel and testing which slide ends up at the top. Fitness values are usually normalized to [0,1]. 2017/4/14 EIE426-AICV

35 Assume that the following random number sequence is generated:
Compared the random number sequence with the accumulated probabilities, we select the individuals: 1, 8, 9, 6, 7, 5, 8, 4, 6, 10. Individuals 2 and 3 were removed and replaced with individuals 8 and 6. The individuals with high fitness tends to survive but those with low fitness may be removed. 2017/4/14 EIE426-AICV

36 The pseudocode: 2017/4/14 EIE426-AICV

37 Tournament Selection A group of k individuals is randomly selected.
The individual with the best fitness is selected from the group. The advantage: the worse individuals of the population will not be selected and the best individuals will not dominate in the reproduction process. For crossover, two tournaments are held to select each of two parents. It is possible that (1) A parent can be selected to reproduce more than once; and (2) One individual can combine with itself to reproduce offspring. 2017/4/14 EIE426-AICV

38 Rank-Based Selection The rank ordering of the fitness values is used to determine the probability of selection and not the fitness values itself. Non-deterministic linear sampling Individuals are sorted in decreasing fitness value. (1) Let n = random(random(N)) where N is the total number of individuals and random(N) return a number between 1 and N. (2) Return n as the selected individual 2017/4/14 EIE426-AICV

39 Elitism Elitism involves the selection of a set of individuals from the current generation to survive to the next generation. The number of individuals to survive to the next generation, without being mutated, is referred to as the generation gap. Generation gap = k k best individuals or k individuals selected using any selection operator 2017/4/14 EIE426-AICV

40 Crossover Crossover 2017/4/14 EIE426-AICV

41 Uniform Crossover A mask (vector) of length I (I-bit binary string) is created at random for each pair of individuals selected for reproduction. A bit with value of 1 indicates that the corresponding allele (bit) has to be swapped. 2017/4/14 EIE426-AICV

42 Parent1 Parent 2 Mask Offspring 1 Offspring 2 1 2017/4/14 EIE426-AICV

43 One-point Crossover 2017/4/14 EIE426-AICV

44 Parent1 Parent 2 Mask Offspring 1 Offspring 2 1 2017/4/14 EIE426-AICV

45 Two-point Crossover 2017/4/14 EIE426-AICV

46 Parent1 Parent 2 Mask Offspring 1 Offspring 2 1 2017/4/14 EIE426-AICV

47 Arithmetic Crossover Arithmetic crossover can be used in the case of continuous-valued genes. 2017/4/14 EIE426-AICV

48 Mutation Alter each gene independently with a probability pm (the mutation rate) Real-valued representations, mutation occurs by adding a random value (usually sampled from a Gaussian distribution ) to allele. The variance is usually a function of the fitness of the individual. Individuals with a good fitness value will be mutated less, while a bad fitness value will lead to large mutations. 2017/4/14 EIE426-AICV

49 1 1 Mutation (fox) 2017/4/14 EIE426-AICV

50 The Evolution Mechanism
Increasing diversity by using genetic operators mutation crossover Decreasing diversity by selection of parents things to kill 2017/4/14 EIE426-AICV

51 Fitness Functions Common fitness functions:
Use the objective function f(x) directly (1) For a maximization problem, Fit(f(x)) = f(x) e.g., (2) For a minimization problem, Fit(f(x)) = -f(x) e.g., solution for x2 + x = 2, to minimize f(x) = x2 + x - 2 2017/4/14 EIE426-AICV

52 Clipping 2017/4/14 EIE426-AICV

53 Mapping 2017/4/14 EIE426-AICV

54 Linear transformation of fitness functions
2017/4/14 EIE426-AICV

55 Fig. ft1 Fig. ft2 2017/4/14 EIE426-AICV

56 Genetic algorithms: case study
To find the maximum of the “peak” function of two variables x and y: -3 ≤ x, y ≤ 3 2017/4/14 EIE426-AICV

57 Chromosome representation
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58 Initial population 2017/4/14 EIE426-AICV

59 The first generation 2017/4/14 EIE426-AICV

60 Local maximum 2017/4/14 EIE426-AICV

61 Global maximum 2017/4/14 EIE426-AICV

62 Evolutionary Computation: Applications
Robotics Control Design Scheduling/Routing/Resource Allocation Machine Learning Pattern Recognition Market forecasting Data Mining Game Playing - Robocode - Backgammon - Chess 2017/4/14 EIE557-CI&IA

63 Robocode An Open Source educational game started by Mathew Nelson (originally provided by IBM). Currently contributions are being made by various people; officially Flemming N. Larsen is working on Robocode to keep it current and fix the bugs. The game is designed to help people learn to program in Java and enjoy the experience. Genetic Programming (GP) Robocode 2017/4/14 EIE426-AICV

64 Application: Routing Optimization
The problem: Given a network of M switches, an origin and a destination switch, the objective is to find the best route to connect a call between the origin and destination switches (Sevenster and Engelbrecht 1996). PSTN: Public Switch Telephone Network 2017/4/14 EIE557-CI&IA

65 Chromosome representation: - variable length
- each gene representing one switch - integer values for switch numbers - the first gene and last gene representing the origin and last switches, respectively Examples: ( ) ( ) = ( ) Duplicate switches are ignored 2017/4/14 EIE557-CI&IA

66 Initialization of population:
- randomly generated with the restriction that the first gene represents the origin switch and the last gene the destination switch 2017/4/14 EIE557-CI&IA

67 Fitness function: a multi-criteria objective function was applied.
2017/4/14 EIE557-CI&IA

68 Selection: any selection operator Crossover: any crossover operator
Mutation: replacing selected genes with a uniformly random selected switch in the range [1, M]. 2017/4/14 EIE557-CI&IA

69 Real World EC Tends include:
More complex representations and operators Use of problem specific knowledge for seeding the initial population and creating heuristic operators Hybridisation with other methods 2017/4/14 EIE557-CI&IA

70 Advantages of EC Handles huge search spaces
Balances exploration and exploitation Easy to try - not knowledge intensive Easy to combine with other methods Provides many alternative solutions Can continually evolve solutions to fit with a continually changing problem 2017/4/14 EIE557-CI&IA

71 Disadvantages of EC No guarantee for optimal solution within finite time Weak theoretical basis May need extensive parameter tuning Often computationally expensive, i.e., slow 2017/4/14 EIE557-CI&IA

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