Download presentation

Presentation is loading. Please wait.

Published byMichelle Wagner Modified over 3 years ago

1
Evolutionary Algorithms Nicolas Kruchten 4 th Year Engineering Science Infrastructure Option

2
What are they? EAs are stochastic techniques used to search multidimensional spaces for points, according to some criteria. They operate by mimicking reproduction & selection processes More on this in a bit…

3
What are they good for? EAs are used to solve optimization problems of various types: Find the vector x such that f(x) is min or max A huge variety of engineering or science problems can be reduced to, or expressed as, optimization problems

4
A black-box example Say you have a black box, with n knobs, and a light bulb, what set of knob positions will make the bulb glow brightest?

5
What if… n=1? n=10000? knobs are continuous? discrete? mixed? some combinations are invalid? (i.e. knob 1 must be less than knob 2) an analytical expression exists?

6
Traditional methods Direct Calculus Gradient descent or hill climbing Frank Wolfe (!) Simplex Simulated Annealing SPSA Etc.

7
Unfortunately they… Sometimes simply dont apply Only work for specific problems Dont scale well (NP-Hard, NP-Complete) Get trapped in local optima

8
EAs… Dont have all of these problems Scale reasonably well Work for a huge variety of problems Dont require gradients but can use them

9
How EAs work 1)Pick a population of feasible points 2)Generate new points from the better ones 3)Throw out the worse ones 4)Thats one generation: rinse & repeat Lo and behold! The points in your population are getting better and better!

10
Back to our example Our feasible points were sets of knob positions, we call these chromosomes Individual knob positions are genes The brightness we call the fitness, were looking for chromosomes with good fitness

11
How to get new points This is where the genetic comes in Given some parent chromosomes, how do we mix them up and get a child? Various schemes are possible depending on how we represent the parents (binary, real, integer etc)

12
Mutation If we only ever blend or mix and match genes, we can only ever explore combinations of our initial gene pool To explore new parts and find new optima, we periodically change, or mutate, genes. Again, various processes are possible.

13
Which parents to use Various schemes exist for selection: –Pick the best ones –Pick random ones –Pick them based on relative fitness –Pick them based on relative rank –Pick them based on how different they are –etc

14
Which points to keep Various schemes exist to decide which children and/or parents to keep at each generation –Keep only the children –Select from a pool of children and parents Best Random Rank Fitness, etc

15
When to stop You can stop an EA whenever is appropriate, but typical convergence criteria include: –A number of generations –A given standard deviation of fitnesses –A period of time –Total convergence –Etc.

16
Putting it all together Let t = 0; Initialize P(t) Evaluate C(t) Let t = t + 1; Assemble P(t) from P(t-1) and C(t-1) Stop? no End yes Evaluate P(t) Generate C(t) from P(t)

17
EA Limitations EAs are extremely flexible, but they have their own problems: –Can be very slow, requiring many potentially long evaluations –Are tough to design and configure, many many parameters –No guarantee of global optimum

18
Some history You may have heard of GAs, which are a subset of EAs Much confusion and conflicting terminology exists A huge body of operators, combinations and approaches have been proposed

19
Evolutionary Programming Traditional: –Credited to Fogel, US, published in 66 –Single parents (so not genetic) –Basically pure mutation Since then: –EP approaches themselves mutated independently towards general EA practice

20
Evolutionary Strategies Traditional: –Credited to Rechenberg and Schwefel, Switzerland, published in 73 –Tiny populations (1 or 2) –Sophisticated adaptive mutation scheme Since then: –Adaptive mutation has gone mainstream

21
Genetic Algorithms Traditional: –Credited to Holland, US, published in 72 –Binary coding –Keep only the children Since then: –Has grown to be loosely interchangable with EA, with real-coded GA, crowding GA etc

22
State of the art No hard and fast rules about the best EA flavour for a given problem Some heuristics exist EAs have been successfully applied to many problems in various fields, but with few general results

23
Advanced EAs Parallelization Distribution –Master/Slave –Peered Demes (see parallelization) –Hybrid Hybridization

24
ITS Applications Model calibration is a great example of a challenging transportation-related optimization: Minimize an error term by varying some model parameters

25
ITS Example: GAID Genetic Adaptive Incident Detection Use of a GA to train a neural network: perfect example of ANN + EA = ITS The problem: automatically detecting incidents on the freeway, using traffic loop data

26
GAID: Basics GAID uses a probabilistic neural network (PNN) which takes 16d vectors and classifies them into two piles Traffic loop data -> incident/normal The PNN is defined by 16 parameters

27
GAID: Diagram PNN = f(parameters) Loop Data Incident Normal 16 Parameters EA

28
GAID: Fitness Fitness: correct classifications/number of vectors We quiz the PNN with known data to score it We are looking for the set of 16 real parameters which make GAID the most accurate

29
GAID: Initialization Initialization: –Pick population size: 50 –Pick 50 random sets of 16 real parameters between 0 and 1000 –Score the chromosomes

30
GAID: Generation Generation: –Pick the child population (generation) size: 50 –Select 2 parents at random –Each child gene is either mom or dads –Mutate every gene: add some uniformly distributed random number between -50 and 50 –Score the children

31
GAID: 2d view

34
One alternative

35
GAID: Assembly Assembly of children and parents: –Choose the 50 best from the combined pool of children and parents Convergence: repeat, stopping when the STD is less than 0.005

36
GAID: Summary Real representation, 16 genes Popsize = Gensize = 50 Random Initialization 2 parents, random selection real crossover, creep mutation on all genes Crowding assembly, best selection STD convergence

Similar presentations

OK

D Nagesh Kumar, IIScOptimization Methods: M8L5 1 Advanced Topics in Optimization Evolutionary Algorithms for Optimization and Search.

D Nagesh Kumar, IIScOptimization Methods: M8L5 1 Advanced Topics in Optimization Evolutionary Algorithms for Optimization and Search.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different solid figures and nets Ppt on magnetic field lines class 10 Ppt on restaurant business plan Ppt on data handling for class 7 cbse Ppt on home automation and security for mobile devices Ppt on series and parallel circuits problems Ppt on girl child abortion Liquid crystal on silicon display ppt on tv Ppt on pet domestic and wild animals Ppt on environmental pollution in india