Evolutionary Algorithms Keith L. Downing The Norwegian University - PowerPoint PPT Presentation

Evolutionary Algorithms Keith L. Downing The Norwegian University of Science and Technology (NTNU) Trondheim, Norway keithd@idi.ntnu.no February 4, 2014 Keith L. Downing Evolutionary Algorithms

Malthus and Darwin Thomas Malthus (1789) Population growth rate = f(pop size) ⇒ Exp. Growth Limited Resources Competition for those resources = Malthusian Crunch As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring Struggle for Existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected (Charles Darwin, On the Origin of Species by Means of Natural Selection (1859), pg. 5) Keith L. Downing Evolutionary Algorithms

3 Prerequisites for Evolution Selection - some environmental factors must favor certain 1 traits over others. Variation - individuals must consistently arise that are 2 significantly (although not necessarily considerably) different from their ancestors. Heritability - children must, on average, inherit a good 3 many traits from their parents to insure that selected traits survive generational turnover. Keith L. Downing Evolutionary Algorithms

Basic Cycle of Evolution Aging & Death Competition Maturation Mating Mating Immature Adult Ptypes Ptypes Ptypes Selection Variation Selection Mitosis & Development Meiosis Inheritance + Selection Reproduction: Gamete Pairing Gtypes Gametes Keith L. Downing Evolutionary Algorithms

Basic Cycle of an Evolutionary Algorithm .<%CD0&%+ :)*"%1)2< =%*%6")42 :)"2%&& =%*%6")42 ;%&")2< .+/*", -01%2", '()*+, .+/*" -01%2" -"#$%& -"#$%& -"#$%& =%*%6")42 52(%1)"026% !"#$% 7%8%*4$9%2" '4$#)2< 301)0")42 >%$14+/6")42? -01%2" !"#$%& >%649@)20")42,A !"#$%& B/"0")42 Keith L. Downing Evolutionary Algorithms

Evolutionary Algorithm Flowchart P 3 P 7 Test Fitness of G G Phenotypes Adult Selection P 2 P 5 G G P P 5 P 7 P G G G G Young Adults P P 6 P P 8 G G G G Retain Some Adults Development: Generate Parent Selection Phenotypes from Genotypes 6 P P 8 G G G G 5 P P 8 G G G G Begin Next Generation G G Reproduction Initialize child G G genotype population Keith L. Downing Evolutionary Algorithms

Essential Components of an Evolutionary Algorithm Genotype representation 1 Phenotype representation 2 Translator of genotypes into phenotypes ( Development ) 3 Genetic operators for forming new genotypes from existing 4 ones ( e.g. crossover and mutation ) Fitness assessment procedure 5 Selection strategy for child → adult phenotypes 6 Selection strategy for adult → parent phenotypes 7 Keith L. Downing Evolutionary Algorithms

Short Taps Puzzle: A Simple Example Dennis Shasha, Scientific American , August 2003 Problem: A CIA official must send N messages (of varying length) within a time 1 interval T. Several messages can have overlapping sending periods. 2 A spy is tapping signals, but to avoid detection, the spy can tap for at 3 most K consecutive time units during the T-step interval. To be intercepted, a message’s entire duration must be within the tap 4 window. 5 The sender is willing to allow at most M messages to be tapped. Goal: Assign start times to the N messages such that, no matter when the K-step tap interval occurs, no more than M messages will be tapped. Example Scenario N = 7 messages of durations 2, 3, 4 .. 8 T = 15, K = 10, M = 3 Keith L. Downing Evolutionary Algorithms

Genotype & Phenotype Genotype 0000 1011 1010 0111 0011 0000 0011 Start sending Start sending Start sending mesage 1 mesage 3 mesage 7 at time 0 at time 10 at time 3 Phenotype 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 2 4 6 8 10 12 14 Keith L. Downing Evolutionary Algorithms

Genetic Operators Parents Children 1 1 1 1 1-Point 0 0 0 5 9 13 0 Crossover 1 1 0 0 1 0 1 0 1 0 1 0 1 0 4 1 3 1 0 0 1 3 4 0 0 1 0 0 0 Parents Children 0 1 2-Point 0 1 0 1 Crossover 15 4 1 0 7 12 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 2 4 5 0 3 1 0 0 1 0 0 0 0 Main operators for binary chromosomes crossover, mutation, inversion Keith L. Downing Evolutionary Algorithms

Fitness K-Step Window Message Message 3 Message 5 2 Message 4 Message 1 Message 7 Message 6 Vulnerability (V) = # K-unit windows in which M or more messages are intercepted. 1 Fitness = 1 + V Keith L. Downing Evolutionary Algorithms

Adult and Parent Selection Adult Selection: Full Generational Replacement Die Adults Children Parent Selection: Fitness Proportionate Fitness Individual Roulette Wheel Keith L. Downing Evolutionary Algorithms

Evolving a Broadcast Schedule Scenario N = 10 messages of durations 2, 3, 4, 4, 4, 4, 5, 6, 7, 8 T = 20, K = 10, M = 3 GA population size = 20 1 M ax Avg 0.9 M in 0.8 0.7 0.6 Fitness 0.5 0.4 0.3 0.2 0.1 0 0 5 10 15 20 25 30 35 40 45 Generation Keith L. Downing Evolutionary Algorithms

The Evolved Schedule 11 10 10 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 2 4 6 8 10 12 14 16 18 Keith L. Downing Evolutionary Algorithms

Genotype Classifications Syntactic - based on how they look - DeJong (2006) Fixed-Length Linear Objects 1 Fixed-Size Nonlinear Objects 2 Variable-Length Linear Objects 3 Variable-Size NonLinear Objects 4 Semantic - based on what they encode Data Oriented - these encode several data values whose 1 usage in the phenotype may vary but does not include actual data manipulation or program control. Program Oriented - these encode explicit data processing 2 and control information - supplementary data may also be encoded - to form the kernel of an executable program at the phenotypic level. Keith L. Downing Evolutionary Algorithms

Program-Oriented Genotypes + * + * + * - * X -3 2 3 3 -2 X X X + * * * X X X + 3 3 + * -2 X - -3 2 (lambda (X) (+ (* (* (* X X) X) (+ 3 3)) (+ (* -2 X) (- -3 2)))) Keith L. Downing Evolutionary Algorithms

Crossover in Program-Oriented Genotypes (lambda (X) (- (* (+ X 1) X) (+ X 3))) (lambda (X) (* (+ X X) (- 2 3))) - * * + + - + X X X X 3 2 3 X 1 * - + * - + X + X X X 3 2 3 1 X (lambda (X) (- (- 2 3) (+ X 3))) (lambda (X) (* (+ X X) (* (+ X 1) X))) Keith L. Downing Evolutionary Algorithms

Crossover in Linear Program-Oriented Genotypes Main trick: find valid subtrees in the linear chromosome Complete Subtree + * * * X X X + 3 3 + * -2 X - -3 2 1 2 3 2 1 0 1 0 -1 Keith L. Downing Evolutionary Algorithms

Fitness Biology Ability to produce offspring Or even....ability to produce viable offspring → ability to produce grandchildren! Evolutionary Computation Performance level on a problem or set of problems Used as basis for reproduction: biases adult and parental selection. Keith L. Downing Evolutionary Algorithms

Fitness Variance Biology: Fundamental Theorem of Natural Selection Evolutionary rate ∝ Population fitness variance ⇒ Evolutionary rate ∝ Reproduction-rate variance ⇒ No significant change in the population if all individuals have same reproduction rate. Evolutionary Algorithms: Selection Mechanisms Early in Runs: Too much fitness variance ⇒ Premature Convergence Late in Runs: Mastery Effect - all individuals are good ⇒ Low fitness variance Selection mechanisms enable regulation of reproductive variance by scaling fitness values prior to choosing of parents. Keith L. Downing Evolutionary Algorithms

Selection Pressure Biology: Ruthlessness level of the world Degree to which superior phenotypes dominant the inferior w.r.t. reproductive rates Evolutionary Computation: Fitness scaling Degree to which individuals with higher (lower) fitness have higher (lower) reproductive rates. High Slightly higher (lower) fitness ⇒ Drastically higher (lower) reproduction rate. Low Drastically higher (lower) fitness ⇒ Only slightly higher (lower) reproduction rate. Keith L. Downing Evolutionary Algorithms

Fitness-Landscape F AS Genotype Space − → Phenotype Space − → Fitness Landscape Keith L. Downing Evolutionary Algorithms

Selection Pressure = Fitness-Landscape Morph Early in an EA Run Fitness Fitness Phenotype Phenotype Late in an EA Run Fitness Fitness Phenotype Phenotype (Early) ⇓ variance via low selection pressure. (Late) ⇑ variance via high selection pressure. Keith L. Downing Evolutionary Algorithms

Selection in Evolutionary Computation a b b Children Old Adults b Adults a Fitness Scaling Reproduction Global Competition c 1 2 1 2 5 3 4 Parents 3 4 5 d Local Tournaments 1 5 3 4 3 4 Sizes of rectangles denote relative fitness. Keith L. Downing Evolutionary Algorithms

Adult Selection 7 Full Generational Replacement 20 Death Child Pool Adult Pool 10 12 3 18 11 12 Over-Production Replacement 7 20 Death Adult Pool Child Pool 10 13 12 7 18 6 11 12 3 10 Generational Mixing 10 Death Adult Pool Child Pool 7 13 20 7 18 6 12 11 12 3 10 Keith L. Downing Evolutionary Algorithms