ARTIFICIAL INTELLIGENCE Evolutionary computing Lecturer: Silja - PowerPoint PPT Presentation

Utrecht University INFOB2KI 2019-2020 The Netherlands ARTIFICIAL INTELLIGENCE Evolutionary computing Lecturer: Silja Renooij These slides are part of the INFOB2KI Course Notes available from www.cs.uu.nl/docs/vakken/b2ki/schema.html

What is it? Evolutionary computing (EC) = the use of evolutionary algorithms (EAs):  Population‐based, stochastic search algorithms based on mechanisms of natural evolution. – Evolution viewed as search algorithm or problem solver – Natural evolution only used as metaphor for computational system design

Why the metaphor?  Ability to efficiently guide a search through a large solution space  Ability to adapt solutions to changing environments  Goal: design high quality solutions through “emergent” behavior

Darwinian process characteristics 5 key requirements of a Darwinian system: 1. Structures carry information (e.g. DNA) 2. Structures are copied (next generation) 3. Copies partially vary from the original (inheritance) 4. Structures compete for limited resources (Struggle for life  selection) 5. Relative reproductive success depends on environment (Survival of the fittest) There is no evolution without competition.

Darwinian characteristics in EC 1. Structures  e.g. binary strings, real‐valued vectors, programs,… 2. Structures are copied  Selection algorithm: e.g. tournament selection, … 3. Copies partially vary from the original  Mutation & crossover operators 4. Structures compete for limited resources  New offspring (partly) replaces parents in fixed size population 5. Relative reproductive success depends on environment  User‐defined fitness function

EC streams EC unites four traditionally distinct streams, based on historical differences in representation :  Genetic algorithms (GA) – Solutions encoded as discrete structures, e.g. bit‐strings  Evolution strategies (ES) – Encoding using real‐valued vectors  Evolutionary programming (EP) – Encoding with finite state machines  Genetic programming (GP) – Encoding using trees Nowadays we just use what seems most appropriate.

EAs: Main idea  Take a population of candidate solutions to a given problem  Use operators inspired by the mechanisms of natural genetic variation  Apply selective pressure toward certain properties (what does “fit” mean?)  Evolve a more fit solution

General Scheme of EAs generation Based upon replacement strategy

Evolutionary terminology Inspired by biology:  Individuals: candidate solutions  Phenotypes: solutions in the real world  Genotypes: individuals within the EA  Population: – (representations of) possible solutions – usually fixed size multiset of genotypes – Diversity of a population refers to the number of different fitness’s / phenotypes / genotypes present (note not the same thing)  Also: genes, chromosomes, …

Design of an Evolutionary Algorithm

The Steps - I In order to build an evolutionary algorithm we have to perform various steps. External to the evolving system:  Design a representation for individuals: – A data‐structure – A mapping between phenotype and genotype (encoding and decoding)  Decide how to initialize a population  Decide when to stop the algorithm

The Steps - II In order to build an evolutionary algorithm we have to perform various steps. Internal to the evolving system:  Design a way of evaluating an individual  Decide how to select parent individuals  Design suitable recombination operator(s)  Design suitable mutation operator(s)  Decide how to select surviving individuals Variation operators

The external design steps

Initialisation Usually done at random  Uniformly on search space if possible – Binary strings: 0 or 1 with probability 0.5 – Real‐valued representations: uniformly on a given interval Or: seed the population with previous results or those from heuristics.  With care: – Possible loss of genetic diversity – Possible unrecoverable bias

Stopping criterion Termination condition checked every generation  Reaching some (known/hoped for) fitness optimum  Limit on CPU resources:  Reaching some maximum allowed number of generations  Reaching some minimum level of diversity  Limit on user’s patience:  Reaching some specified number of generations without fitness improvement

Designing a Representation  Method/ data structure for representing an individual as a genotype (encoding) – often takes the form of a bit string in GAs – usually different parts of structure represent different aspects of solution  Choice depends on – the problem to solve – how genotypes will be evaluated – what genetic operators might be used/suitable

Discrete Representation  an individual can be represented using discrete values – binary; integer; any other system with discrete set of values CHROMOSOME Example: binary representation GENE

Discrete Representation  for each genotype there must be a phenotype Example: Phenotype: • Integer 8 bits Genotype • Real Number • Schedule • ... • Anything?

Example: genotype to phenotype  Phenotype could be integer numbers Genotype: Phenotype: = 163 1*2 7 + 0*2 6 + 1*2 5 + 0*2 4 + 0*2 3 + 0*2 2 + 1*2 1 + 1*2 0 = 128 + 32 + 2 + 1 = 163  Phenotype could be real numbers Phenotype: (between 2.5 and 20.5) Genotype: = 14.00 163       x 2 . 5 20 . 5 2 . 5 14 . 00 255

Example: genotype to phenotype  Phenotype could be a schedule Time Job Step 1 2 Genotype: 2 1 3 2 4 1 = Phenotype 5 1 6 1 7 2 8 2  Phenotype could be …

The internal design steps

Evaluating an Individual  Often based upon fitness – A measure of the goodness of the organism – The more values the fitness function distinguishes the better for selection – Can also be based on results of some external process: e.g. competing models for a game  This is by far the most costly step for real applications  You could use approximate fitness ‐ but not for too long

Parent Selection Mechanism  Selection pressure: ensure that selection of better individuals is more probable than of less good individuals  drives population forward  ! less good individuals may still include some useful genetic material  Methods (a.o): – Proportionate selection  typical textbook method; not often used in practice – Rank‐based selection • Truncation selection • Tournament selection

Fitness proportionate selection I Selection based on absolute fitness values  Given a population of N individuals, individual i is � selected with probability � � � ���  Selecting again N parents  expected number of times individual i is selected for mating is: f where is average fitness � �

Fitness proportionate selection II Best Better (fitter) individuals have:  more space in population pool  more chances to be selected Worst Disadvantages:  Danger of premature convergence: (seemingly) outstanding individuals take over entire population very quickly  Low selection pressure when fitness values are near each other  local optima

Truncation selection  Rank based selection: use relative rather than absolute fitness  Individuals are sorted on their fitness value from best to worse.  Select the top τ %  Copy each selected solution 100/ τ times (for fixed population size)

Tournament selection For a tournament of size k :  Select k random individuals for tournament (with or without replacement)  Select only the best individual as parent Hold N tournaments to get a population of N

Variation operators with examples for discrete structures (GAs)

Recombination/Crossover We can have one or more recombination operator for a representation.  Mimics biological recombination – Some portion of genetic material is swapped between chromosomes – Typically the swapping produces offspring  Offspring inherits parts from each of m ≥ 2 parents  Recombination should produce m valid chromosomes  Stochastic: – n cross‐over point(s) selected randomly – Operator applied with a certain probability

1-point cross-over Whole Population: . . . Each chromosome is cut into 2 pieces (at same cutpoint) which are recombined: cut cut parents 1 1 1 1 1 1 1 0 0 0 0 0 0 0 offspring 1 1 1 0 0 0 0 0 0 0 1 1 1 1

n-point & uniform cross-over  n‐point cross‐over: each chromosome is cut into n+1 pieces which are recombined  Uniform cross‐over: for each position, swap with a certain probability

Mutation We can have one or more mutation operators for a representation.  Mechanism for preserving variety in the population  At least one mutation operator should allow every part of the search space to be reached  Mutation should produce valid chromosome  Stochastic: – Alters the structure in a position with some probability – Operator applied with a certain probability

Mutation parent before 1 1 1 1 1 1 1 after 1 1 1 0 1 1 1 offspring mutated gene Mutation usually happens with small probability p m for each ` gene’