Presentation is loading. Please wait.

Presentation is loading. Please wait.

Evolutionary Computation

Similar presentations

Presentation on theme: "Evolutionary Computation"— Presentation transcript:

0 Genetic Algorithms and Genetic Programming

1 Evolutionary Computation
Computational procedures patterned after biological evolution Search procedure that probabilistically applies search operators to a set of points in the search space.

2 Biological Evolution Lamarck and others Darwin and Wallace
Species “transmute” over time Darwin and Wallace Consistent heritable variation among individuals in the population Natural selection of the fittest Mendel and genetics A mechanism for inheriting traits genotype -> phenotype mapping

3 Biological Terminology
gene functional entity that codes for a specific feature e.g. eye color set of possible alleles allele value of a gene e.g. blue, green, brown codes for a specific variation of the gene/feature locus position of a gene on the chromosome genome set of all genes that define a species the genome of a specific individual is called genotype the genome of a living organism is composed of several chromosomes population set of competing genomes/individuals In GA’s genome and chromosome are used as synonyms These terms are used freely in GA terminology although the biological counterparts are by far more complex and sophisticated

4 Genotype versus Phenotype
blue print that contains the information to construct an organism e.g. human DNA genetic operators such as mutation and recombination modify the genotype during reproduction genotype of an individual is immutable (no Lamarckian evolution) phenotype physical make-up of an organism selection operates on phenotypes (Darwin’s principle : “survival of the fittest” Well, I am sure you don’t regard this issue from this perspective while you have sex but that it is to which it pretty much boils down from an evolutionary perspective

5 The Genetic Algorithm Directed search algorithms based on the mechanics of biological evolution Developed by John Holland, University of Michigan (1970’s) To understand the adaptive processes of natural systems To design artificial systems software that retains the robustness of natural systems

6 The Genetic Algorithm (cont.)
Provide efficient, effective techniques for optimization and machine learning applications Widely-used today in business, scientific and engineering circles

7 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)

8 Genotype Operators recombination (crossover)
combines two parent genotypes into a new offspring generates new variants by mixing existing genetic material stochastic selection among parent genes mutation random alteration of genes maintain genetic diversity in genetic algorithms crossover is the major operator whereas mutation only plays a minor role

9 Representation Phenotype space Genotype space = {0,1}L Encoding
Decoding (inverse representation) 9

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

11 The GA Cycle of Reproduction
children reproduction modification modified children parents population evaluation evaluated children deleted members discard

12 Population population Chromosomes could be:
Bit strings ( ) Real numbers ( ) Permutations of element (E11 E3 E7 ... E1 E15) Lists of rules (R1 R2 R3 ... R22 R23) Program elements (genetic programming) ... any data structure ... population

13 Reproduction children reproduction parents population Parents are selected at random with selection chances biased in relation to chromosome evaluations.

14 Chromosome Modification
Modifications are stochastically triggered Operator types are: Mutation Crossover (recombination) children modification modified children

15 The simple GA Has been subject of many (early) studies
still often used as benchmark for novel GAs Shows many shortcomings, e.g. Representation is too restrictive Mutation & crossovers only applicable for bit-string & integer representations Selection mechanism sensitive for converging populations with close fitness values Generational population model (step 5 in SGA repr. cycle) can be improved with explicit survivor selection

16 Representing Hypotheses
(Outlook = Overcast v Rain) ^ (Wind = Strong) by Outlook Wind IF Wind = Strong THEN PlayTennis = yes Outlook Wind PlayTennis

17 SGA operators: 1-point crossover
Choose a random point on the two parents Split parents at this crossover point Create children by exchanging tails Pc typically in range (0.6, 0.9)

18 SGA operators: mutation
Alter each gene independently with a probability pm pm is called the mutation rate Typically between 1/pop_size and 1/ chromosome_length

19 Alternative Crossover Operators
Performance with 1 Point Crossover depends on the order that variables occur in the representation more likely to keep together genes that are near each other Can never keep together genes from opposite ends of string This is known as Positional Bias Can be exploited if we know about the structure of our problem, but this is not usually the case

20 n-point crossover Choose n random crossover points
Split along those points Glue parts, alternating between parents Generalisation of 1 point (still some positional bias)

21 Uniform crossover Assign 'heads' to one parent, 'tails' to the other
Flip a coin for each gene of the first child Make an inverse copy of the gene for the second child Inheritance is independent of position

22 Order 1 crossover Idea is to preserve relative order that elements occur Informal procedure: 1. Choose an arbitrary part from the first parent 2. Copy this part to the first child 3. Copy the numbers that are not in the first part, to the first child: starting right from cut point of the copied part, using the order of the second parent and wrapping around at the end 4. Analogous for the second child, with parent roles reversed

23 Order 1 crossover example
Copy randomly selected set from first parent Copy rest from second parent in order 1,9,3,8,2

24 Crossover OR mutation? Decade long debate: which one is better / necessary / main-background Answer (at least, rather wide agreement): it depends on the problem, but in general, it is good to have both both have another role mutation-only-EA is possible, xover-only-EA would not work

25 Crossover OR mutation? (cont’d)
Exploration: Discovering promising areas in the search space, i.e. gaining information on the problem Exploitation: Optimising within a promising area, i.e. using information There is co-operation AND competition between them Crossover is explorative, it makes a big jump to an area somewhere “in between” two (parent) areas Mutation is exploitative, it creates random small diversions, thereby staying near (in the area of ) the parent

26 Crossover OR mutation? (cont’d)
Only crossover can combine information from two parents Only mutation can introduce new information (alleles) Crossover does not change the allele frequencies of the population (thought experiment: 50% 0’s on first bit in the population, ?% after performing n crossovers) To hit the optimum you often need a ‘lucky’ mutation

27 Evaluation evaluation modified children evaluated children
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 evaluated children evaluation

28 Selection Schemes stochastic sampling roulette wheel selection
spin wheel N times stochastic universal sampling roulette wheel selection single spin, wheel has N equally spaced markers tournament selection choose k candidates at random with uniform probability pick best one for reproduction expected number of offspring best :  k , average  k ½ k-1 , worst  k 1/N k-1

29 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 A C 1/6 = 17% 3/6 = 50% B 2/6 = 33% fitness(A) = 3 fitness(B) = 1 fitness(C) = 2

30 Replacement Schemes generational replacement
entire population is replaced each generation non-overlapping population 10111 01000 01011 10010 01001 11001 Selection Crossover Mutation steady state replacement a single individual (worst, random) is replaced by one offspring overlapping population 10010 01001 11001 10010 01001 11001 Selection Crossover Mutation 01110

31 Deletion population discard discarded members
Generational GA: entire populations replaced with each iteration Steady-state GA: a few members replaced each generation population discarded members discard

32 An Abstract Example Distribution of Individuals in Generation 0
Distribution of Individuals in Generation N

33 A Simple Example The Traveling Salesman Problem:
Find a tour of a given set of cities so that each city is visited only once the total distance traveled is minimized

34 Representation Representation is an ordered list of city
numbers known as an order-based GA. 1) London 3) Dunedin ) Beijing 7) Tokyo 2) Venice ) Singapore 6) Phoenix 8) Victoria CityList1 ( ) CityList2 ( )

35 Crossover Crossover combines inversion and recombination:
* * Parent ( ) Parent ( ) Child ( ) This operator is called the Order1 crossover.

36 Mutation Mutation involves reordering of the list:
* * Before: ( ) After: ( )

37 TSP Example: 30 Cities

38 Solution i (Distance = 941)

39 Solution j(Distance = 800)

40 Solution k(Distance = 652)

41 Best Solution (Distance = 420)

42 Overview of Performance

43 Population Models SGA uses a Generational model:
each individual survives for exactly one generation the entire set of parents is replaced by the offspring At the other end of the scale are Steady-State models: one offspring is generated per generation, one member of population replaced, Generation Gap the proportion of the population replaced 1.0 for GGA, 1/pop_size for SSGA

44 GABIL [de Jong et al, 1993] Learn disjunctive set of propositional rules; competitive with C4.5 Fitness Fitness(h) = (correct(h))2 Representation IF a1=T ^ a2=F THEN c=T; IF a2=T THEN c=F represented by: a1 a2 c a1 a2 c Genetic operators??? want variable length rule sets want only well-formed bit-string hypotheses

45 Crossover with variable-length bit-strings
Start with: a1 a2 c a1 a2 c h h choose crossover points for h1, e.g. after bits 1, 8 now restrict points in h2 to those that produce bitstrings with well-defined semantics, e.g. 〈1,3〉, 〈1,8〉, 〈6,8〉. if we choose 〈1,3〉, the results is: a1 a2 c h3: a1 a2 c a1 a2 c a1 a2 c h4:

46 GABIL extensions Add new genetic operators, also applied probabilistically: AddAlternative: generalise constraint on a1 by changing a 0 to 1 DropCondition: generalise constraint on ai by changing every 0 to 1. And, add new field to bitstring to determine whether to allow these: a1 a2 c a1 a2 c AA DC so now the learning strategy also evolves.

47 GABIL Results Performance of GABIL comparable to symbolic rule/tree learning methods C4.5, ID5R, AQ14. Average performance on a set of 12 synthetic problems: GABIL without AA and DC operators: 92.1% accuracy GABIL with AA and DC operators 95.2% accuracy symbolic learning methods ranged from 91.2% to 96.6%

48 Extensions to the Simple GA
Encoding schemes gray encoding messy genetic algorithms Replacement schemes generational replacement steady state replacement Fitness scaling linear scaling - truncation ranking Selection schemes stochastic sampling tournament selection

49 Genetic Programming automatic generation of computer programs + X1 *
by means of natural evolution see Koza 1999 programs are represented by a parse tree (LISP expression) tree nodes correspond to functions : - arithmetic functions {+,-,*,/} - logarithmic functions {sin,exp} leaf nodes correspond to terminals : - input variables {X1, X2, X3} - constants {0.1, 0.2, 0.5 } + X1 * tree is parsed from left to right: (+ X1 (* X2 X3)) X1+(X2*X3) X2 X3

50 Genetic Programming : Crossover
- / X1 X2 X3 + * X3 X2 X1 parent A parent B - * + / offspring B offspring A X1 X2 X2 X3 - X1 X2 X3

51 Block-Stacking Problem
V E U N stack U table A L S I R V E objective: place the blocks in the correct order such that the stack forms the word universal functions: set of actions, logical operators, do-until loop terminals: set of sensors that indicate top block on stack, next suitable block on table etc. each program tree is tested on 166 different initial configurations fitness: #configurations for which the stack was correct after program execution

52 Block-Stacking Problem
CS N NN U TB A L S I R V E Sensors: CS: current stack, name of the top block of the stack TB: top correct block, name of the topmost block on the stack such that it and all blocks underneath are in correct order NN: next block needed, name of the block needed above TB

53 Block-Stacking Problem
MS TB MS NN N U A L S I R V E Functions: MS(X): move block X to the top of the stack, return value X MT(X): moves the block on top of the stack to the table if X is anywhere in the stack returns X DU(exp1, exp2): execute exp1 until the predicate exp2 becomes true NOT(exp1) : negation of expression exp1 EQ(exp1, exp2) : returns true if exp1 and exp2 are equal

54 Block-Stacking Problem
NN U CS A TB L S I R V E N (EQ (MS NN) (EQ (MS NN) (MS NN))) move next needed block to the stack three times in a row (succeeds with a stack VERSAL and U N I on the table (DU (MS NN) (NOT NN)) move next needed block to the stack until no more blocks are needed (EQ (DU (MT CS) (NOT CS)) (DU (MS NN) (NOT NN))) empty the stack on the table and then build the stack in the correct order (EQ (DU (MT CS) (EQ (CS TB))) (DU (MS NN) (NOT NN)))

55 Learned Program Trained to fit 166 test problems
Using population of 300 programs, found this after 10 generations: (EQ (DU (MT CS)(NOT CS))(DU (MS NN)(NOT NN)))

56 Genetic Programming More interesting example: design electronic filter circuits individual are programs that transform beginning cct to final cct, by adding/subtracting components and connections. Use population of 640,000 run on 64 node parallel processor Discover circuits competitive with best human desgn

57 GP for classifying images
Teller & Veloso, 1997 Fitness: based on coverage & accuracy Representation: Primitives include Add, Sub, Mult, Div, Not, Max, Min, Read, Write, If-Then-Else, Either, Pixel, Least, Most, Ave, Variance, Difference, Mini, Library Mini refers to a local subroutine that is separately co-evolved Library refers to a global library subroutine (evolved by selecting the most useful minis) Genetic operators: Crossover mutation Create “mating pools” and use rank proportionate reproduction.

58 Biological Evolution Lamarck (19th century)
believed individual genetic makeup was altered by lifetime experience but current evidence contradicts this view What is the impact of individual learning on population evolution?

59 Baldwin Effect Assume individual learning has no direct influence on individual DNA But ability to learn reduces need to “hard wire” traitsin DNA Then Ability of individuals to learn will support more diverse gene pool because learning allow individuals with various “hard wired” traits to be successful More diverse gene pool will support faster evolution of gene pool. > individual learning (indirectly) increases rate of evolution.

60 Baldwin Effect Plausible example:
New predator appears in the environment Individual who can learn (to avoid it) will be selected Increase in learning individuals will support more diverse gene pool resulting in faster evolution possibly resulting in new non-learned traits such as instinctive fear of predator

61 Computer experiements on Baldwin Effect
Evolve simple neural nets [Hinton & Nowlan, 1987] some network weights fixed during lifetime, others trainable genetic makeup determines which are fixed and their weight values Results: With no individual learning, population failed to improve over time when individual learning allowed early generations: population contained many individuals with many trainable weights later generations: higher fitness, while number of trainable weights decreased.

Download ppt "Evolutionary Computation"

Similar presentations

Ads by Google