CS321 HS 2009 Autonomic Computer Systems Evolutionary Computation I November 17, 2009

1S321 HS 2009: Evolutionary Computation I, L. Yamamoto, M. Sifalakis, 17 Nov. 2009

CS321 HS 2009CS321 HS 2009

Autonomic Computer SystemsAutonomic Computer Systems

Evolutionary Computation IEvolutionary Computation I

November 17, 2009November 17, 2009

Lidia Yamamoto and Manolis SifalakisUniversity of Basel http://cn.cs.unibas.ch


OverviewOverview

Part I (today)• Genetic Algorithms (GA)• Genetic Programming (GP)

Part II (Thursday)• Representations• Dynamic environments


Overview of Today’s LectureOverview of Today’s Lecture

Evolutionary Computation, Part I• Introduction

– (Self-)Optimization– Basic definitions from genetics

• Evolutionary Computation– Common definitions, basic algorithm– Genetic Algorithms (GA)– Genetic Programming (GP)

• Example: Symbolic regression with TinyGP


TextbooksTextbooks

Melanie Mitchell, “An Introduction to Genetic Algorithms”, MIT Press, 1998.

W. Banzhaf, P. Nordin, R. E. Keller, and F. D. Francone. "Genetic Programming, An Introduction". Morgan Kaufmann Publishers, Inc., 1998.

R. Poli, W. B. Langdon, and N. F. McPhee. "A Field Guide to Genetic Programming". Published via http://lulu.com, 2008. http://www.gp-field-guide.org.uk/.


Optimization and Self-OptimizationOptimization and Self-Optimization

Optimization (Operations Research)• maximize/minimize objective function subject to constraints• search for a solution in a vast search space or solution space

(space of all possible solutions)• linear/non-linear

Self-Optimization (IBM Autonomic Computing)• ability of the system to optimize its operations based on a

given target operation profile (objectives and constraints)• system continually seeks to improve its performance and

efficiency, in order to meet end-users' needs with minimal human intervention

• also able to track and respond to profile changes


Optimization (Operations Research)Optimization (Operations Research)

General formulation of an optimization problem:

f(x) = objective function gi(x) = constraints

Simple example:

1 variable (x),

no constraints

maximize:

subject to:

f(x)

x

globaloptimum local

optima

searchspace

best solution


Heuristic OptimizationHeuristic Optimization

Search space often discrete, and too large for exhaustive search Heuristic optimization seeks to explore promising regions of the

search space through a beamed search:• refinement of promising solutions seen so far• do not guarantee that a global optimum will be found• might be trapped in local optima• goal is to provide a satisfactory solution in reasonable time

Some heuristic optimization algorithms:• Evolutionary algorithms: Inspired by genetics and Darwinian

evolution• Swarm algorithms: Inspired by the behavior of social insects

(ants, bees...), flocks of birds, fish, etc.


Evolutionary ComputationEvolutionary Computation

Heuristic optimization method• Beamed search in a vast space of possible solutions

Inspired by Darwinian evolution:• Biological evolution by natural selection• Survival of the fittest

Advantages:• Simplicity• Potential parallelism• Able to work with limited information: only fitness improvement

Disadvantages:• Computation cost (e.g. large populations, complex fitness)• No guarantees (like all heuristics)


An Eukaryotic CellAn Eukaryotic Cell

(Prokaryotic = without nucleus, e.g. bacteria) Eukaryotic = with nucleus, e.g. plant and animal cells

nucleus

membrane

organellesand othercell components(e.g. mitochondria, ribosomes...)

cytoplasm

genome(genetic material)


The GenomeThe Genome

Each cell nucleus contains one or more chromosomes A chromosome contains a number of genes A gene is a region of genomic (DNA) sequence defining a

functional block Chromosomes may occur in one or more copies within a cell:

• Diploid cell: has two copies of each chromosome (e.g. in humans and most animals)

• Haploid cell: only one copy (e.g. gametes)• Polyploid cell: several copies (typically a power of 2, e.g.

tomatoes, crops)



cell nucleus

chromosomes

chromosome pair(diploid organism)

chromosomes genes

gene

A T

G C

DNA

double helix



A gene is the basic unit of heredity in a living organism• region of genomic sequence• can be seen as a functional block• typical encodes a protein, which leads to a trait, e.g. eye color Locus is the position of a gene in the chromosome Allele: each possible alternative DNA sequence for a given

gene locus (e.g. leading to different traits such as red or white flowers)



Genotype: the genetic material of an individual Phenotype: the ensemble of observable traits (e.g. flower color,

leaf shape) resulting from the genotype of an individual

homologouschromosomes

allelefor red flowers

allele forwhite flowers


Recombination and MutationRecombination and Mutation

The DNA is able to replicate with a high fidelity (with the help of enzymes)

However, mutations (errors in the copy process) might still occur, e.g. due to chemical agents, radiations, etc.

Recombination (crossover) during sexual reproduction: chromosomes swap genes


Darwinian EvolutionDarwinian Evolution

Reproduction = replication + (unlimited) heritable variation• Replication of the DNA sequence• Cell replication• Organism reproduction• Variation: mutation, recombination

Fitness = Reproduction rate• how fast an organism (or species) is able to reproduce

Selection: survival of the fittest• exponential growth + finite resources = competition• outcome: competitive exclusion (survival of the fittest)


OverviewOverview






Evolutionary ComputationEvolutionary Computation

Genetic Algorithms (GA)• goal: find an optimum solution (e.g. combination of

parameters) to an instance of a problem• candidate solutions are typically strings

Genetic Programming (GP)• goal: find an optimum program able to solve any instance of

the problem• candidate solutions are programs, e.g. linear (e.g. assembly

language), tree (e.g. LISP), graph (dataflow, cartesian GP) Other variants not covered in this course:

• Evolution Strategies (ES), Evolutionary Programming (EP)


Evolutionary Computation: Basic ConceptsEvolutionary Computation: Basic Concepts

Individual: a candidate solution to the problem to be solved Population: set of candidate solutions Genotype: (compact) representation of individuals; can be broken

down into chromosomes, genes, alleles,...• GA: string of bits, integers, characters, etc., examples:

bin: 01101011 hex: 39fe87ac3b46

dec: 2039384757 alpha: addbadbaaccd• GP: program, e.g. linear, tree, graph,...

linear: I1: R1 = R2 + R3; I2: R3 = R4 * R1; I3: Jump I2

LISP tree: (* (+ 3 a) (if (< a b) (- x y) (/ x 3)))



Genetic operators: variation functions that transform a set of individuals (parents) into a new set (offspring) Common operators:

• Mutation: random change in genotype, with low probability

• Crossover: recombine portions of two genotypes

01010101001

offspringmutation

01010010001

parent

1011 1100101

0010 011100010

1011

11001010010

011100010crossover

offspring 1

offspring 2

parent 1

parent 2 crossover point



Phenotype: (expanded) individual that can be evaluated for fitness (e.g. program)• can be the same as the genotype (direct encoding)• or different: indirect encoding: genotype-phenotype map

0 23 198 54

if (a > 10) then x = 20else print b

genotype

phenotype

map



Fitness: measure of how good a candidate solution is• tested on a number of test cases (training set)• expressed as a fitness function: e.g. error between ideal and

obtained solution (on training case); absolute or relative performance measure

Selection strategy: Algorithm that selects individuals in the population that will build the next generation

• Principle: "survival of the fittest": best fit individuals have a higher chance of being selected

• Selected individuals undergo variation through genetic operators to form the next generation


Evolutionary Computation: Basic AlgorithmEvolutionary Computation: Basic Algorithm

pop = initial population generation = 0 evaluate(pop) while bestfit(pop) not good enough, and not stop:

• parents = select(pop)• children = recombine(parents) with probability pr• mutate(children) with probability pm• pop = children + select(pop)• evaluate(pop)• generation = generation + 1


Fitness LandscapeFitness Landscape

n-dimensional

landscape:• fitness function is the

objective function:

• is the genotype to be optimized

• peaks: local optima 3-D case: intuitive

visualization: z = f (x, y)

z

xy

example of an initial population(red dots) on a fitness landscape


Fitness LandscapeFitness Landscape

Convergence example:

z

xy

z

xy


Fitness EvaluationFitness Evaluation

Examples of fitness functions:

Error fitness function: sum of distances (error) between expected (pi) and obtained (oi) solution on training case i out of n cases, for individual p:

in this case, best fitness = 0

Relative performance measure, e.g. success rate (best fitness = 100%)

Absolute performance measure, e.g. amount of credits won, amount of food found (best fitness = infinite)


Selection StrategiesSelection Strategies

Selection is typically stochastic: "survival of the fittest":• best individuals have a higher chance of being selected• selected individuals become "parents" and produce "offspring”• offspring form the next generation of individuals to be

evaluated Examples of selection strategies:

• Fitness-proportional selection (Roulette wheel)• Ranking selection• Tournament selection


Selection StrategiesSelection Strategies

Fitness-proportional or Roulette Wheel selection: the probability of selection (pi) of individual i (out of a population of m

individuals) is proportional to its fitness:

Ranking selection: probability of selection is a function of rank of individual from worst to best fitness.

Tournament selection: a group of randomly selected individuals "compete" in a tournament; winners (best fitness) produce offspring which will replace losers.


OverviewOverview






Genetic AlgorithmsGenetic Algorithms

Genetic Algorithms: goal: find an optimum solution (e.g. combination of parameters) to an instance of a problem

Became popular via John Holland, 1970s Example: solving the Travelling Salesman Problem (NP-hard):

given a set of cities and connections (roads) between them, find the shortest tour that visits all cities (and each city only once).

individual = candidate tour (sequence of cities) fitness = length of tour (the shorter the better) initial population = set of randomly generated tours iterate by evaluating, selecting, mutating and recombining tours

until stop criterion (e.g. max number of generations,


Sample IterationSample Iteration

Ci = individuals (chromosomes) with two genes: X and Y

Fitness function:

parents:C4-C3, C4-C1recombine byswapping genes


Simple GA Example: Discover the hidden sentenceSimple GA Example: Discover the hidden sentence

Goal: Find out what's the hidden sentence: e.g. "this is a test" (without blanks); only the length of the target sentence is known to the GA• (generalization of the OneMax problem: maximize the number of ones in a

bitstring) Fitness: Similarity measure between obtained and target string, using a string

alignment (edit distance) algorithm : • 100% similarity = identical strings = optimum

Fixed-length genotype (character string) Mutations:

• point mutation (letter replacement, e.g. "ABCD" "ABXD");• shift (rotate) left/right (e.g. "ABCD" "BCDA")

Two-point crossover Tournament selection, size 4 (two best remain in population, and their

offspring replace the two worst)


Simple GA Example: Typical runSimple GA Example: Typical run

> ./strga "thisisatest"

gen= 1, fit= -27, best=qthakeqsfzt

gen= 2, fit= 9, best=ophrispstet

gen= 3, fit= 9, best=ophrispstet

gen=10, fit= 45, best=qthisattest

gen=15, fit= 81, best=thisisatesc

gen=18, fit= 100, best=thisisatest

Size of search space=3.670344e+15

Population size=1000 tested=45070

Percent of search space explored: 5.176626e-10 % Size of search space = number of all possible strings of same length as target

(11 characters in example) using alphabet a-z = 2611 possible strings Typically only a small fraction of (huge) search space is explored But this problem is quite (too) easy for a GA (smooth fitness landscape)


Search for solutions aggressivelySearch for solutions aggressively

Hill climbing: always chooses best solution so far Always reaches a hilltop But maybe not the highest top:

can be trapped in a local maximum

E.g. Steepest Ascend


Search for solutions with a GASearch for solutions with a GA

Solution discovered probabilistically

Problem: Can not guarantee discovery of hilltop

May reach global maxima by wandering through search space

GA


GA: Real-World ApplicationsGA: Real-World Applications

Numerical and Combinatorial Optimisation• Job-Shop Scheduling, Traveling salesman

Economic• Biding and trading strategies, stock trends

Ecology• Host-parasite co-evolution, resource flow, biological arm races

Population Genetics• Viability of gene propagation

Social systems• Evolution of social behavior in insect colonies

Computer art• Automatic generation of graphics, music


GA for Computer ArtGA for Computer Art

Interactive evolution: user (computer artist) determines fitness Examples by Karl Sims, http://www.karlsims.com/

Genetic Images1993

Galapagos(3D animated forms)

1997

Competingvirtual creatures

1994


OverviewOverview





Documents

CS321 HS 2009 Autonomic Computer Systems Evolutionary Computation I November 17, 2009