Evolutionary Algorithms: How to Go Darwin

[email protected] @BWKnopper github.com/bknopper Evolutionary Algorithms: How to Go Darwin

[email protected] @BWKnopper github.com/bknopper 2

[email protected] @BWKnopper github.com/bknopper Let me introduce myself… • Bas W.
Knopper • Dutch • JavaOne, J-Fall, GeeCon, JFokus Speaker • AI enthousiast • Soft spot for EvolutionaryAlgorithms • (Java) Developer • Managing Partner @ JCore

[email protected] @BWKnopper github.com/bknopper By Developers. For Developers. De missie van
JCore is om ambitieuze Java Developers een traject te bieden waarmee ze sneller en beter Senior Java Developers kunnen worden. Wat (Java Consultancy) -> We helpen klanten met het realiseren van complexe IT projecten. Hoe Met ambitieuze en enthousiaste Java Consultants die een bijdrage leveren bij de klant. Waarom Vanuit een passie voor IT en het oplossen van complexe problemen.

[email protected] @BWKnopper github.com/bknopper What I would like to accomplish… •
Interest • Understanding • How & when • Add to toolbox • Attention @DevFestNL #EvolutionaryAlgorithms #golang @BWKnopper

[email protected] @BWKnopper github.com/bknopper Agenda • Introduction • NASA • Evolution
Concepts • Puzzle Solving Time: Traveling Salesman Problem • Evolutionary Algorithm Design • Go Code • Demo! • Frameworks • Checklist

[email protected] @BWKnopper github.com/bknopper NASA • Space Technology 5 mission •
launched March 22, 2006, and completed June 20, 2006 • Three full service 25-kilogram-class spacecraft

[email protected] @BWKnopper github.com/bknopper NASA Continued • Needs even smaller antenna
• That still functions according to spec • Need forsolution that’s not easy to engineer • So they used an EA that made these:

[email protected] @BWKnopper github.com/bknopper

[email protected] @BWKnopper github.com/bknopper Recap • Powerfulexample • First evolved object
to travel through space • How?

[email protected] @BWKnopper github.com/bknopper Evolution

[email protected] @BWKnopper github.com/bknopper Evolution - “Survival of the fittest” Finite
Resources Lifeforms with a basic instinct towards Reproduction Natural Selection

[email protected] @BWKnopper github.com/bknopper Recombination Mutation

[email protected] @BWKnopper github.com/bknopper From evolution to problem solving Environment Problem
Individual Candidate Solution

[email protected] @BWKnopper github.com/bknopper Puzzle solving time! • More down to
earth example • TravellingSalesman Problem

[email protected] @BWKnopper github.com/bknopper Travelling Salesman Problem • Given n cities
• n = number of cities to visit • Find (optimal) route for visiting all cities • Visit every city only once • Return to origin city • Search space is huge • For 30 cities there are 30! ≈ 10^32 possible routes That’s 100.000.000.000.000.000.000.000.000.000.000 possible routes! Brute force might not be the best solution…

[email protected] @BWKnopper github.com/bknopper Puzzle solving time! • More down to
earth example • TravellingSalesman Problem • Use case to show you • EvolutionaryAlgorithm Design • Plain Go Code • Demo

[email protected] @BWKnopper github.com/bknopper • No GoPro(pun intended) • Big thanks
to Rob Brinkman • Why then? Disclaimer

[email protected] @BWKnopper github.com/bknopper EA Algorithm (Pseudocode) INITIALISE population with random
candidate solutions;

[email protected] @BWKnopper github.com/bknopper Candidate Solution - Representation • n =
6 • Label cities 1,2,3,4,5,6 • And base city 1 • Candidate Solution • Signifyingthe route • for n = 10 • Enables • Calculatingdistance (fitness function) • Mutation • Recombination 1 5 6 3 4 2 1 1 10 9 4 7 3 5 6 8 2 1

candidate solutions;

candidate solutions; EVALUATE each candidate;

[email protected] @BWKnopper github.com/bknopper Evaluation Function (Fitness Function) • Summed distance:
• d1,2 + d2,4 + … + d5,1 • Used golang-geofor calculations • Minimize! 1 5 6 3 4 2 1

[email protected] @BWKnopper github.com/bknopper /** * Calculates the total distance of
the whole route * and stores it as this candidate solution's fitness */ func (candidateSolution *CandidateSolution) calculateFitness() { }

the whole route * and stores it as this candidate solution's fitness */ func (candidateSolution *CandidateSolution) calculateFitness() { totalDistance := float64(0) for i := 0; i < (len(candidateSolution.Route) - 1); i++ { } candidateSolution.Fitness = totalDistance }

the whole route * and stores it as this candidate solution's fitness */ func (candidateSolution *CandidateSolution) calculateFitness() { totalDistance := float64(0) for i := 0; i < (len(candidateSolution.Route) - 1); i++ { city := candidateSolution.Route[i] nextCity := candidateSolution.Route[i + 1] totalDistance += city.calculateDistance(nextCity) } candidateSolution.Fitness = totalDistance }

candidate solutions; EVALUATE each candidate;

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { }

[email protected] @BWKnopper github.com/bknopper Figures from “Introduction toEvolutionary Computing” byA.E. Eiben
& J.E. Smith (Springer) Termination Condition • EA’s are stochastic • May never find optimum

[email protected] @BWKnopper github.com/bknopper Termination Condition • Combination • Sure to
terminate • Time • Max number of runs (generations) • Goal • Fitness threshold • Fitness improvementstagnation Figure from “Introduction to Evolutionary Computing” by A.E. Eiben & J.E. Smith (Springer)

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; }

[email protected] @BWKnopper github.com/bknopper Parent Selection • Where x is the
number of parents: • Pick x best • Random x • Best xout of random y • In our example: • Best x out of random y

[email protected] @BWKnopper github.com/bknopper func (algorithm *Algorithm) parentSelection() CandidateSolutions {

[email protected] @BWKnopper github.com/bknopper func (algorithm *Algorithm) parentSelection() CandidateSolutions { tempPopulation
:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize)

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { /* pick random candidates */

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { randomIndex := rand.Intn(len(tempPopulation)) randomCandidateSolution := tempPopulation[randomIndex]

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { randomIndex := rand.Intn(len(tempPopulation)) randomCandidateSolution := tempPopulation[randomIndex] randomCandidates[i] = randomCandidateSolution

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { randomIndex := rand.Intn(len(tempPopulation)) randomCandidateSolution := tempPopulation[randomIndex] randomCandidates[i] = randomCandidateSolution /* delete the candidate from the temp population, so we can't pick it again */ tempPopulation[randomIndex] = tempPopulation[len(tempPopulation)-1] tempPopulation = tempPopulation[:len(tempPopulation)-1] }

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { randomIndex := rand.Intn(len(tempPopulation)) randomCandidateSolution := tempPopulation[randomIndex] randomCandidates[i] = randomCandidateSolution /* delete the candidate from the temp population, so we can't pick it again */ tempPopulation[randomIndex] = tempPopulation[len(tempPopulation)-1] tempPopulation = tempPopulation[:len(tempPopulation)-1] } /* Sort the population so that the best candidates are up front */ sort.Sort(randomCandidates)

:= make(CandidateSolutions, algorithm.populationSize) copy(tempPopulation, algorithm.population) randomCandidates := make(CandidateSolutions, algorithm.parentPoolSize) for i := 0; i < algorithm.parentPoolSize; i++ { randomIndex := rand.Intn(len(tempPopulation)) randomCandidateSolution := tempPopulation[randomIndex] randomCandidates[i] = randomCandidateSolution /* delete the candidate from the temp population, so we can't pick it again */ tempPopulation[randomIndex] = tempPopulation[len(tempPopulation)-1] tempPopulation = tempPopulation[:len(tempPopulation)-1] } /* Sort the population so that the best candidates are up front */ sort.Sort(randomCandidates) /* return a list with size parentSelectionSize with the best CandidateSolutions */ return randomCandidates[0:algorithm.parentSelectionSize] }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; }

[email protected] @BWKnopper github.com/bknopper Recombination • In our example: • half-half
does not work • “Cut-and-crossfill” 1 6 5 3 4 2 1 1 4 2 1 1 2 4 5 6 3 1 1 5 4 2 1 1 3 5 4 2 1 1 6 3 5 4 2 1 1 4 2 5 6 3 1 1 2 4 5 6 3 1 1 2 4 5 6 3 1 1 2 4 5 6 3 1

[email protected] @BWKnopper github.com/bknopper func (candidateSolution *CandidateSolution) recombine(otherParent CandidateSolution) CandidateSolutions {

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1)))

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1))) /* initialize the routes for the children */ childRoute1 := make(Cities, len(parentRoute1)) childRoute2 := make(Cities, len(parentRoute1))

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1))) /* initialize the routes for the children */ childRoute1 := make(Cities, len(parentRoute1)) childRoute2 := make(Cities, len(parentRoute1)) /* get the first part of both parent routes using the cut index */ partRoute1 := parentRoute1[0:cutIndex] partRoute2 := parentRoute2[0:cutIndex]

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1))) /* initialize the routes for the children */ childRoute1 := make(Cities, len(parentRoute1)) childRoute2 := make(Cities, len(parentRoute1)) /* get the first part of both parent routes using the cut index */ partRoute1 := parentRoute1[0:cutIndex] partRoute2 := parentRoute2[0:cutIndex] /* copy the first part of the parents cut into the children */ copy(childRoute1, partRoute1) copy(childRoute2, partRoute2)

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1))) /* initialize the routes for the children */ childRoute1 := make(Cities, len(parentRoute1)) childRoute2 := make(Cities, len(parentRoute1)) /* get the first part of both parent routes using the cut index */ partRoute1 := parentRoute1[0:cutIndex] partRoute2 := parentRoute2[0:cutIndex] /* copy the first part of the parents cut into the children */ copy(childRoute1, partRoute1) copy(childRoute2, partRoute2) candidateSolution.crossFill(childRoute1, parentRoute2, cutIndex) candidateSolution.crossFill(childRoute2, parentRoute1, cutIndex)

/* get routes of both parents */ parentRoute1 := candidateSolution.VisitingCities parentRoute2 := otherParent.VisitingCities /* randomize cutIndex for "cross-and-fill point" */ cutIndex := int32(rand.Intn(len(parentRoute1))) /* initialize the routes for the children */ childRoute1 := make(Cities, len(parentRoute1)) childRoute2 := make(Cities, len(parentRoute1)) /* get the first part of both parent routes using the cut index */ partRoute1 := parentRoute1[0:cutIndex] partRoute2 := parentRoute2[0:cutIndex] /* copy the first part of the parents cut into the children */ copy(childRoute1, partRoute1) copy(childRoute2, partRoute2) candidateSolution.crossFill(childRoute1, parentRoute2, cutIndex) candidateSolution.crossFill(childRoute2, parentRoute1, cutIndex) /* create new children using the new children routes */ child1 := NewCandidateSolution(getBaseCity(), childRoute1); child2 := NewCandidateSolution(getBaseCity(), childRoute2); /* put the children in a list and return it */ return CandidateSolutions{child1, child2} }

[email protected] @BWKnopper github.com/bknopper /** * Check the rest of the
route in the crossing parent and add the cities that are not yet in the child * (in the order of the route of the crossing parent) */ func (candidateSolution *CandidateSolution) crossFill(childRoute Cities, parentRoute []City, cutIndex int32) {

route in the crossing parent and add the cities that are not yet in the child * (in the order of the route of the crossing parent) */ func (candidateSolution *CandidateSolution) crossFill(childRoute Cities, parentRoute []City, cutIndex int32) { /* * traverse the parent route from the cut index on and add every city * not yet in the child to the child */ childRouteIndex := cutIndex for i := cutIndex; i < int32(len(parentRoute)); i++ { nextCityOnRoute := parentRoute[i] if (!childRoute.contains(nextCityOnRoute)) { childRoute[childRouteIndex] = nextCityOnRoute childRouteIndex++ } } 1 4 2 5 6 3 1

route in the crossing parent and add the cities that are not yet in the child * (in the order of the route of the crossing parent) */ func (candidateSolution *CandidateSolution) crossFill(childRoute Cities, parentRoute []City, cutIndex int32) { /* * traverse the parent route from the cut index on and add every city * not yet in the child to the child */ childRouteIndex := cutIndex for i := cutIndex; i < int32(len(parentRoute)); i++ { nextCityOnRoute := parentRoute[i] if (!childRoute.contains(nextCityOnRoute)) { childRoute[childRouteIndex] = nextCityOnRoute childRouteIndex++ } } /* * traverse the parent route from the start of the route and add every * city not yet in the child to the child */ for i := 0; i < int(cutIndex); i++ { nextCityOnRoute := parentRoute[i] if (!childRoute.contains(nextCityOnRoute)) { childRoute[childRouteIndex] = nextCityOnRoute childRouteIndex++ } } } 1 4 2 5 6 3 1 1 4 2 5 6 3 1

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; }

[email protected] @BWKnopper github.com/bknopper 1 6 5 3 4 2 1
Mutation • Change of nr won’t work • Infeasiblecandidate solution • Swap to the rescue! 1 6 5 3 4 2 1 1 2 5 3 4 6 1

[email protected] @BWKnopper github.com/bknopper func (candidateSolution *CandidateSolution) mutate() { 1 6
5 3 4 2 1

[email protected] @BWKnopper github.com/bknopper func (candidateSolution *CandidateSolution) mutate() { /* randomly
select two indices in the route */ indexFirstCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) indexSecondCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) 1 6 5 3 4 2 1 1 6 5 3 4 2 1

select two indices in the route */ indexFirstCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) indexSecondCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) /* Make sure they are different */ for (indexFirstCity == indexSecondCity) { indexSecondCity = int32(rand.Intn(len(candidateSolution.VisitingCities))) } 1 6 5 3 4 2 1 1 6 5 3 4 2 1

select two indices in the route */ indexFirstCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) indexSecondCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) /* Make sure they are different */ for (indexFirstCity == indexSecondCity) { indexSecondCity = int32(rand.Intn(len(candidateSolution.VisitingCities))) } /* Retrieve the cities */ firstCity := candidateSolution.VisitingCities[indexFirstCity] secondCity := candidateSolution.VisitingCities[indexSecondCity] 1 6 5 3 4 2 1 1 6 5 3 4 2 1

select two indices in the route */ indexFirstCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) indexSecondCity := int32(rand.Intn(len(candidateSolution.VisitingCities))) /* Make sure they are different */ for (indexFirstCity == indexSecondCity) { indexSecondCity = int32(rand.Intn(len(candidateSolution.VisitingCities))) } /* Retrieve the cities */ firstCity := candidateSolution.VisitingCities[indexFirstCity] secondCity := candidateSolution.VisitingCities[indexSecondCity] /* Changer! */ candidateSolution.VisitingCities[indexFirstCity] = secondCity candidateSolution.VisitingCities[indexFirstCity] = firstCity } 1 2 5 3 4 6 1 1 6 5 3 4 2 1 1 6 5 3 4 2 1

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; 4 EVALUATE new candidates; }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; 4 EVALUATE new candidates; 5 SELECT individuals for the next generation; }

[email protected] @BWKnopper github.com/bknopper Survivor Selection • Replacement Strategy • Do
nothing • Replace Worst

[email protected] @BWKnopper github.com/bknopper /** * Selects the survivors by removing
the worst candidate * solutions from the list, so we have the original * population size again */ func (algorithm *Algorithm) selectSurvivors() { }

the worst candidate * solutions from the list, so we have the original * population size again */ func (algorithm *Algorithm) selectSurvivors() { sort.Sort(algorithm.population) }

the worst candidate * solutions from the list, so we have the original * population size again */ func (algorithm *Algorithm) selectSurvivors() { sort.Sort(algorithm.population) algorithm.population = algorithm.population[:algorithm.populationSize] }

candidate solutions; EVALUATE each candidate; WHILE ( TERMINATION CONDITION is not satisfied ) { 1 SELECT parents; 2 RECOMBINE pairs of parents; 3 MUTATE the resulting offspring; 4 EVALUATE new candidates; 5 SELECT individuals for the next generation; }

[email protected] @BWKnopper github.com/bknopper Tuning… • Mutation probability • Population size
• Nr of offspring • Termination condition (# runs or fitness) • Parent selection • Survival selection • Initialisation • Random

[email protected] @BWKnopper github.com/bknopper EA Behavior Figures from “Introduction to Evolutionary
Computing” by A.E. Eiben & J.E. Smith (Springer)

[email protected] @BWKnopper github.com/bknopper Demo! https://github.com/bknopper/TSPEvolutionaryAlgorithmsDemo.git

[email protected] @BWKnopper github.com/bknopper With great power comes great responsibility •
I’m sure I cannot find a solution using a brute-force approach? • (within a reasonable amountof time) • Am I facing an optimization or search problem? • Can I encode a candidate solution to the problem? • Representationpossible? • Can I determine the fitness of a candidate solution?

[email protected] @BWKnopper github.com/bknopper Literature

[email protected] @BWKnopper github.com/bknopper Additional questions? • Contact me on @BWKnopper
• Google it! • There’slotstofind… • Papers • Demo’s

[email protected] @BWKnopper github.com/bknopper Slide 83 of 68

Evolutionary Algorithms: How to Go Darwin

Evolutionary Algorithms: How to Go Darwin

More Decks by Bas W. Knopper

Other Decks in Technology

Featured

Transcript