28.08.2018 Why Draw Inspiration from Evolution? INF3490/4490 - PDF document

28.08.2018 Why Draw Inspiration from Evolution? INF3490/4490 Biologically inspired computing Lecture 2: Eiben and Smith, chapter 1-4 Evolutionary Algorithms - Introduction and representation Kai Olav Ellefsen 2 The Problem with Hillclimbing Evolution • Biological evolution: – Lifeforms adapt to a particular environment over successive generations. – Combinations of traits that are better adapted tend to increase representation in population. – Mechanisms: Variation (Crossover, Mutation) and Selection (Survival of the fittest). • Evolutionary Computing (EC): – Mimic the biological evolution to optimize solutions to a wide variety of complex problems. – In every new generation, a new set of solutions is created using bits and pieces of the fittest of the old. General scheme of EAs EA scheme in pseudo-code Parent selection Parents Intialization Recombination (crossover) Population Mutation Termination Offspring Survivor selection 5 6 1

28.08.2018 Scheme of an EA: Representation: EA terms Two pillars of evolution There are two competing forces locus: the position of a gene allele= 0 or 1 (what values a Decreasing population diversity Increasing population gene can have) by selection diversity by genetic operators 0 1 2 n  of parents  mutation 1 0 1 1  of survivors  recombination gene: one element of Push towards quality Push towards novelty genotype: a set of gene the array values phenotype: what could be built/developed based on the 7 genotype Main EA components: General scheme of EAs Evaluation (fitness) function Parent selection • Represents the Parents task to solve • Enables Intialization selection Recombination (provides basis (crossover) for comparison) Population Mutation • Assigns a single real-valued fitness to each Termination phenotype Offspring Survivor selection 9 10 Main EA components: General scheme of EAs Population Parent selection • The candidate solutions (individuals) of the Parents problem Intialization • Population is the basic unit of evolution, i.e., the Recombination population is evolving , not the individuals (crossover) • Selection operators act on population level Population Mutation • Variation operators act on individual level Termination Offspring Survivor selection 11 12 2

28.08.2018 Main EA components: Main EA components: Selection mechanism (1/3) Selection mechanism (2/3) • Identifies individuals Example: roulette wheel selection – to become parents 1/6 = 17% – to survive fitness(A) = 3 B • Pushes population towards higher fitness fitness(B) = 1 A C • Parent selection is usually probabilistic fitness(C) = 2 3/6 = 50% 2/6 = 33% – high quality solutions more likely to be selected than low quality, but not guaranteed – This stochastic nature can aid escape from local optima 13 14 Main EA components: General scheme of EAs Selection mechanism (3/3) Parent selection Survivor selection: Parents • N old solutions + K new solutions (offspring) -> N Intialization individuals (new population) Recombination • Often deterministic: (crossover) – Fitness based : e.g., rank old population + Population offspring and take best Mutation – Age based : make N offspring and delete all old solutions • Sometimes a combination of stochastic and Termination deterministic (elitism) Offspring Survivor selection 15 16 Main EA components: Main EA components: Variation operators Mutation (1/2) • Role: to generate new candidate solutions • Role: cause small, random variance to a genotype • Usually divided into two types according to their arity • Element of randomness is essential and (number of inputs to the variation operator): differentiates it from other unary heuristic operators – Arity 1 : mutation operators • Importance ascribed depends on representation and historical dialect: – Arity >1 : recombination operators – Binary Genetic Algorithms – background operator – Arity = 2 typically called crossover responsible for preserving and introducing diversity – Arity > 2 is formally possible, seldom used in EC – Evolutionary Programming for continuous variables – the only search operator – Genetic Programming – hardly used 17 18 3

28.08.2018 Why do we do Random Mutation? Main EA components: Mutation (2/2) before 1 1 1 1 1 1 1 after 1 1 1 0 1 1 1 19 Main EA components: Main EA components: Recombination (2/2) Recombination (1/2) Parents • Role: merges information from parents into offspring • Choice of what information to merge is stochastic cut cut • Hope is that some offspring are better by combining 1 1 1 1 1 1 1 0 0 0 0 0 0 0 elements of genotypes that lead to good traits 1 1 1 0 0 0 0 0 0 0 1 1 1 1 Offspring 21 22 Main EA components: General scheme of EAs Initialisation / Termination Parent selection • Initialisation usually done at random, Parents – Need to ensure even spread and mixture of possible allele values Intialization – Can include existing solutions, or use problem-specific Recombination heuristics, to “seed” the population (crossover) Population • Termination condition checked every generation Mutation – Reaching some (known/hoped for) fitness – Reaching some maximum allowed number of generations Termination – Reaching some minimum level of diversity Offspring – Reaching some specified number of generations without Survivor selection fitness improvement 23 24 4

28.08.2018 Typical EA behaviour: Typical EA behaviour: Typical run: progression of fitness Are long runs beneficial? • Answer: – It depends on how much you want the last bit of progress 25 26 Chapter 4: Representation, Mutation, Role of representation and variation and Recombination operators • First stage of building an EA and most difficult one: • Role of representation and variation operators choose right representation for the problem • Most common representation of genomes: • Type of variation operators needed depends on – Binary chosen representation – Integer – Real-Valued or Floating-Point – Permutation – Tree 27 28 TSP: How to represent? Binary Representation • One of the earliest representations • Genotype consists of a string of binary digits 29 30 5

28.08.2018 Binary Representation: Binary Representation: Mutation 1-point crossover • Choose a random point on the two parents • Alter each gene independently with a probability p m • Split parents at this crossover point • p m is called the mutation rate • Create children by exchanging tails 31 32 Binary Representation: Binary Representation: n-point crossover Uniform crossover • Choose n random crossover points • Assign 'heads' to one parent, 'tails' to the other • Split along those points • Flip a coin for each gene of the first child • Glue parts, alternating between parents • Make an inverse copy of the gene for the second child • Breaks more “links” in the genome 33 34 Binary Representation: Integer Representation Crossover and/or mutation? • Some problems naturally have integer variables, – e.g. image processing parameters There is co-operation AND competition between them: • Others take categorical values from a fixed set • Crossover is explorative , it makes a big jump to an area – e.g. {blue, green, yellow, pink} somewhere “in between” two (parent) areas • Mutation is exploitative , it creates random small • N-point / uniform crossover operators work diversions, thereby staying near (in the area of) the parent • Extend bit-flipping mutation to make: – “creep” i.e. more likely to move to similar value • Adding a small (positive or negative) value to each gene with probability p . – Random resetting (esp. categorical variables) • With probability p m a new value is chosen at random 35 36 6