An Introduction to Genetic Algorithms Lecture 2 November, 2010 Ivan Garibay

3/1/2016University of Central Florida, Department of EECS 2 Motivation: learn from nature Nature evolve strikingly complex organisms in response to complex environmental adaptation problems with apparent ease Localize and extract principles from nature Apply them to design algorithms Introduction

3/1/2016University of Central Florida, Department of EECS 3 Evolution Charles Darwin (1859): “On the origin of species by means of natural selection” Reproduction does not produce a perfect copy, always minor variations (mutations) Some variations are advantageous some are not Individuals with advantageous variations are more likely to survive and reproduce (natural selection, or the survival of the fittest) The variations are inheritable Species are continuously adapting to their environment

Basic Evolutionary Process Population Birth and Dead Fitness Variational Inheritance 3/1/2016University of Central Florida, Department of EECS 4

3/1/2016University of Central Florida, Department of EECS 5 Genetics Science of heredity Gregor Mendel (1865): units of inheritance: Genes (“traits”) Organisms form by cells Each cell has information necessary to construct a new organism = genome Genome = set of chromosomes Chromosome = set of genes Genes are DNA segments associated with a characteristic (i.e. eye color) Allele is a particular gene value (blue, black, etc)

3/1/2016University of Central Florida, Department of EECS 6 DNA: Information DNA molecule is an information structure: –Store information digitally (chain of nucleotides) –Nucleotide = deoxyribose sugar + phosphate + Nitrogenous base –4 Nitrogenous bases: Adenine, Thymine, Cytosine, Guanine DNA is an amazingly efficient, highly specialized structure for information storage, replication, expression and evolution

3/1/2016University of Central Florida, Department of EECS 7 Historical perspective Evolutionary Computation Genetic Algorithms Holland, 1975 Population based Crossover and mutation Study adaptation Schema Theorem Evolutionary Strategies Rechenberg, 1965 Population of two Only mutation Real value parameter optimization Evolutionary Programming Fogel, Owens, and Walsh, 1966 Only mutation Evolving Finite State Machines

3/1/2016University of Central Florida, Department of EECS 8 GA terminology: from biology Chromosome (string) gene Population individual Generation i Generation i+1 Crossover Mutation Genetic Operators Fitness based Selection

3/1/2016University of Central Florida, Department of EECS 9 Simple Genetic Algorithm procedure GA begin initialize population; while termination condition not satisfied do begin evaluate current population members; select parents from current population; apply genetic operators to selected parents; set offspring equal to current population; end

3/1/2016University of Central Florida, Department of EECS 10 Genetic Algorithm Components Population of individuals (population) Selection Function (birth and dead) Fitness Function (fitness) Genetic Operators (variational inheritance)

3/1/2016University of Central Florida, Department of EECS 11 Individuals Each individual represent a candidate solution String of ‘1’s and ‘0’ (binary representation GAs) In general, any information structure can be subject to evolution (integers, reals, trees, etc.) Needs to be decoded to have meaning: Genotype to Phenotype allele gene

3/1/2016University of Central Florida, Department of EECS 12 Problem Representation Problem specific Different representations are different problems for a GA Map a string (structure) into a instance of a solution Representation is very important –Define the space to be explored –Define the space structure: variations are meaningful Rethinking Evolutionary Computation Genome (DNA)Organisms Computational Instance of Evolutionary Problem Structure Solution Bit StringOrdering of cities for TSP Logo instructionsAntena GenotypetoPhenotype

3/1/2016University of Central Florida, Department of EECS 13 Binary Representation Example: encoding 4 parameters Param1 value = 1000 = 8 Param2 value = 1011 = 11 Etc.,

3/1/2016University of Central Florida, Department of EECS 14 Fitness function Problem specific component Function takes as input an individual (chromosome) Function return a numerical value that determines how good the individual is Natural Selection: fitness function = environment Genetic Algorithm: fitness function is user defined Typically higher is better

3/1/2016University of Central Florida, Department of EECS 15 Selection Survival of the fittest Select the best individuals Based on fitness function Drives exploitation: exploit good genes found so far Multiple Types –Proportional –Rank –Tournament (most used)

3/1/2016University of Central Florida, Department of EECS 16 Fitness proportional Selection Holland, Expected number of times an individual is selected to reproduce is proportional to its fitness relative to the total population fitness. –where f(i) is the fitness of individual i and f is the sum of fitness of all individuals in a pop. Actual number of offspring may be far from expected number P s (i) = f(i) / f sum

3/1/2016University of Central Florida, Department of EECS 17 Rank Selection Similar to Proportional Proportional to their rank instead Rank selection is weaker than proportional in diverse populations Rank is stronger than proportional in converged populations P s (i) = r(i) / r sum

3/1/2016University of Central Florida, Department of EECS 18 Tournament Selection Computationally efficient. –Previous methods require 2 passes: Compute sum Calculate expected number of offspring. –Rank selection also requires a sort. 1.Select two individuals 2.Generate a random number, r, 0 ≤ r ≤ 1 3.If r < k,select the better of the 2 individuals else,select the worse of the 2 individuals where k is a parameter.

3/1/2016University of Central Florida, Department of EECS 19 Genetic Operators Crossover –Biologically inspired –Combine genes from two individuals to form an off-spring (sexual reproduction) Mutation –Biologically inspired –DNA is copied with errors = mutations –Most of the time mutation = problem –Some times = advantage

3/1/2016University of Central Florida, Department of EECS Parent 1: Parent 2: Offspring 1 Offspring 2 Crossover point One-point Crossover Simplest form of crossover Advantage: Fairly large change in individuals with very little disruption of information

3/1/2016University of Central Florida, Department of EECS 21 Other Crossover Ops Two point: select two points and exchange middles Uniform: with probability px exchange or not each bit

3/1/2016University of Central Florida, Department of EECS Mutation Single parent operator Mutation rate (M) is per bit –Mutation rate per individual = M * L (individual length) –As a start: M = 1/L per bit Issues –Low mutation rate: minimal exploration –High mutation rate: too disruptive

3/1/2016University of Central Florida, Department of EECS 23 Initialization Initial Populations are randomly generated Binary case are all randomly generated binary strings

3/1/2016University of Central Florida, Department of EECS 24 GA Convergence

3/1/2016University of Central Florida, Department of EECS 25 Termination Criteria Found solution Number of generations Stagnation – no more fitness improvement

3/1/2016University of Central Florida, Department of EECS 26 A GA by hand (0) (1) (2) (3) (4) (5) Population (0)Fitness Onemax problem: Maximize the number of ones [6] [2] [4] [3] [2] 20/6 = 3.33

3/1/2016University of Central Florida, Department of EECS 27 A GA by hand (0) (1) (2) (3) (4) (5) PopulationFitness Onemax problem: Maximize the number of ones [6] [2] [4] [3] [2] (2) [4] (0) [6] (4) [3] (0) [6] (1) [2] Selected parents

3/1/2016University of Central Florida, Department of EECS 28 A GA by hand Onemax problem: Maximize the number of ones X After crossover (2) [4] (0) [6] (4) [3] (0) [6] (1) [2] Selected parentsM

3/1/2016University of Central Florida, Department of EECS 29 A GA by hand Onemax problem: Maximize the number of ones After crossoverM After mutationFitness [6] [4] [5] 28/6 = 4.67

3/1/2016University of Central Florida, Department of EECS 30 A GA by hand (0) (1) (2) (3) (4) (5) Population (0)Fitness Onemax problem: Maximize the number of ones [6] [2] [4] [3] [2] 20/6 = Population (1)Fitness [6] [4] [5] 28/6 = 4.67

3/1/2016University of Central Florida, Department of EECS 31 Next Class Problem Representation Search Spaces Fitness Landscapes