Evolutionary Algorithms 101

Basics and Applications

Manuel Ernst

  • from Erlangen, Bavaria Franconia
  • Software Engineer @ Methodpark
  • @seriousManual on Github & Twitter

Evolution?


source: https://de.wikipedia.org/wiki/Charles_Darwin

Circleworld

Terms: Population

Terms: Recombination

Terms: Mutation

Terms: Selection

Terms: Fitness

Algorithm

Create Population

While True
    Choose Parents

    Combinate Parents (Recombination)

    Mutate Offspring (Mutation)

    Rate Offspring (Fitness)

    Add Offspring to Population

    Remove Unfittest Individual (Selection)

    If Termination Criterion Is Met: End Loop
Next

Circles

source: http://blog.eagerbug.com/circles/

Circles: Definition

  • Given: Some circles on na arbitrary playground
  • Task: Find an additional circle
    • ...that does not cross the playground border,
    • ...that does not cross another circle
    • ...that has a maximum circular area.

Circles: Trivial

Circles: Approach

Genes


{
    x: <int>,
    y: <int>,
    radius: <int>
}

Initial Population

Arbitrary circles (x- and y-coordinate, radius)

Circles: Approach

Fitness

  • Crossing the playground border? (Penalty)
  • Crossing another circle? (Penalty)
  • How big is the circle? (Bonus)

Circles: Approach

Fitness

var overlapping = number of overlapping circles
var outside = crossings with the playground border
var area = area of the circle
var fitness = area

if outside > 0 or overlapping > 0
    fitness = fitness * -1

    if overlapping > 0
        fitness = fitness * 2 * overlapping;

    if outside > 0
        fitness = fitness * 4 * outside;

Circles: Approach

Recombination

Parents:
{x: 100, y: 10, radius: 7}
{x: 331, y: 77, radius: 50}

Child:
{x: 100, y: 77, radius: 50}

Mutation

{x: 103, y: 77, radius: 49}

Circles: Implementation

Characteristics

https://de.wikipedia.org/wiki/Vitruvianischer_Mensch

characteristics

The chosen approach is never the same

characteristics

The choosen approach is not always the optimal one

characteristics

The solution is not deterministic

characteristics

Extreme conditions

characteristics

Extreme conditions

Travelling Salesman Problem

http://business-coaching-ulm24.de/seminare/burnoutberaterin.html

Travelling Salesman

TSP: Trivial

13 cities: (n - 1)! / 2 combinations
-> 239500800 possible solutions
@ 10k tests every second: 6.6h

Travelling Salesman

Genes

1 -> 2 -> 3 -> 4 -> 5 -> 1

Initial Population

Arbitrary combinations of all cities on the map

Travelling Salesman

Recombination

Parents:
5 -> 3 -> 1 -> 4 -> 2 -> 5
2 -> 4 -> 5 -> 3 -> 1 -> 2

Child:
5 -> 4 -> 1 -> 3 -> 2 -> 5

Mutation

5 -> 4 -> 1 -> 2 -> 3 -> 5

Travelling Salesman

Fitness

The complete length of a way

Travelling Salesman

Travelling Salesman

  • 18 cities
  • 1.79e+14 possible solutions
  • @ 10k tests every second: 563years

Thank you!

Questions?

Aliens!!!

changing environment

changing environment

No Mutations