Evolutionary Algorithms · Evolutionary Algorithms is not just Genetic Algorithms. EA tries to mimic the Darvinian evolution EA is signiﬁcantly different from SA and TABU and thus

1Thomas Stidsen

DTU-Management / Operations Research

Evolutionary Algorithms– simulated evolution

Thomas Stidsen

[email protected]

DTU-Management

Technical University of Denmark

2Thomas Stidsen


Outline1Heuristics and Meta-heuristics

General information on EA’s

The standard EA

EA for Facility Location

EA disected

Different EA types

Advanced topics

Why and why not use EA

Parameters

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Specialised heuristics vs. metaheuristicsThis part of the course is termed: Metaheuristics,what is a metaheuristic ?

A general skeleton to an algorithm applicable toa wide range of optimisation problems.

A meta-heuristic often “evolve” into a morespecialised heuristic when it is specialised to aparticular problem

Approximation algorithms and very largeneighbourhood searches are very specialisedtechniques which have a more limited scope

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Specialised heuristics vs. metaheuristicsEfficiency

Specialisation

Heuristics

Meta−heuristics

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General InformationEvolutionary Algorithms is not just GeneticAlgorithms.

EA tries to mimic the Darvinian evolution

EA is significantly different from SA and TABUand thus complements these.

EA is difficult to use:Many parametersParameters are hidden and dependsnon-linearly on each other.

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HistoryInvented independently three different places, inthe 60’ies:

Michigan: John Holland, Genetic Algorithms.Germany: Schwefel and Rechenberg,Evolution Strategies.California: Edward Fogel: EvolutionaryProgramming.

First dedicated conference: ICGA-85.

Popularised by D. Goldberg, 1989 (GeneticAlgorithms).

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The Standard EA

Initialise the entire populationrepeat

Select promising individuals from current populationReproduce selected individualsMutate reproduced individualsEvaluate created individualsCreate new/updated population

until finished()return best from population

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Application of EAWhen applying EA’s to a certain problem we needto:

Define problem dependent parts

Select type of EA to use

Select parameters for EA

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Problem dependent partsThis is where the modelling of a real world problembegins, three different parts needs to be specified:

Evaluation

Crossover and Mutation operators (andRepresentation)

Let’s look at the simple and classic problem ...

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Representation: A Bit vectorVery simple: Boolean vector, corresponding to e.g.binary variables ...

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Mutation

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1 2 3 4 5

1 0 0 10

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Exactly like the neighborhood

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CrossoverThe simple 1-point crossover:

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OperatorsThe bit-mutation operator and the 1-point crossoverare general non-problem dependent operators.Generally these are not the best operators forspecific problems. What could be the alternative ?

Problem dependent crossovers ???

PMX crossover to Christmas Lunch problem

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ReproductionWhat is a good crossover ? Difficult to quantify but:

Avoid epistasis: Related genes should be“close”.

Avoid collateral mutation, keep the geneticmaterial.

New genetic material should be created by themutation operator.

Choose the best material (a little dangerous).

Creating good reproduction operators is an art not ascience.

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Optimisation algorithm choiceChoosing the right Evolutionary Algorithm for theoptimization problem then becomes the next issue,the components are:

Population, several current solutions instead ofjust one.

Selection, which individuals should the nextpopulation consist of.

Stopping Criteria, when are we finished ?

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The Components II: PopulationThe population is necessary for thereproduction.

Makes the algorithm robust, but increases theneed for computer power and memory.

The trade off: Prob. of getting a good solutionvs. time.

The size determines this trade off and isproblem dependent.

Important measure: Convergense, is thedegree of similarity of the solutions in thepopulation.

The crossover requires a non-converged populationto work.

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The Components III: SelectionA much overlooked component which is veryimportant.

Takes one population to a reduced population.

Can be compared to the temperature of theSimulated Annealing.

Three important types:Proportional selection, the classic method,but problematic ...Tournament selection, the simplest method.Stochastic Universal Sampling after LinearFitness ranking.

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Selection: Proportional Selection

P3

P4

P1

P2

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Selection: Proportional SelectionThis classical method is the basis for most of thetheory, but there are two problems:

Premature convergence: A good initialindividual may quickly spread into the entirepopulation.

Slow finishing: In the end, the individualsusually have almost identical fitness values

For these reasons, proportional selection is neverused ...

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Selection: Tournament selectionA simple and efficient approach: Select twodifferent individuals randomly and choose the best:

Avoids the premature convergence and slowfinishing.

Easy to use in parallel

Random fluctuations may cause problems

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Selection: LFR-SUSLFR-SUS: Linear Fitness Ranking with StochasticUniversal Sampling. Works in several stages:

Sort the entire population

Assign selection value linearly

Use stochastic universal sampling to copyindividuals

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LFR

1

1.0

2.0

NIndividual Ranking

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SUS

P2

P1

P4

P3

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Selection: LFR-SUSThe most “fair” method, with the least noise inthe sampling of new individuals.

More computational demanding, but that’susually not a problem

Difficult to parralellise

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The Components IIII: ReproductionThe biggest difference compared to otheralgorithms: Create a new individual/solution bycombining material from two previous solution:

Intuitively: Create new solutions by combiningexisting solutions in a new way.

Very problemdependent.

Standard types: 1-point, 2-point.

Traditionally considered the most importantcomponent.

If you cannot create a good crossover, don’t useEA.

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The Components IIII: MutationTraditionally a background operator.

Corresponds to the traditional neighbourhoodupdate: sm ∈ N (sl).

Possibility for guided mutations.

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Two recomandable EA’sTwo good algorithms worth considering are:

Generational EA with LFT-SUS (bacteriaevolution)

Steady State EA with tournament selection(elephant evolution)

Depending on the problem, these are excellentalgorithms.

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Generational EAP ← RandomIndividuals()repeat

P ′ := LFR− SUS(P )P ′′ ← {}while P ′ 6= {}

p1, p2 := RandomRemove2(P ′)o1, o2 := Crossover(p1, p2)P ′′ ← o′

1, o′

2:= Mutate(o1, o2)

endwhileP := P ′′

until finished()return Best(P )

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Steady State EAP ← RandomIndividuals()repeat

p1, p2, p3, p4 := RandomSelect4dif(P )o1, o2 := Crossover(Best(p1, p2), Best(p3, p4))o′

1, o′

2:= Mutate(o1, o2)

r1, r2, r3, r4 := RandomSelect4different(P )Replace(P,Worst(r1, r2), o1)Replace(P,Worst(r3, r4), o2)

until finished()

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Convergence ?What did I mean by converged ? Depending on therepresentation, we may look on the similarity of thedifferent individuals:

Binary strings: Hamming distance

Permutation ???

Real valued arrays: Euclidian distance

Special structures: ???

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Advanced TopicsThere are MANY variations of EA’s, just to name afew:

Island EA.

Hill climber inclusion: Baldwin and Lamarcianevolution.

Parallel implementations.

Multi-criteria optimisation.

Co-evolutionary EA.

Automatic operator probability adjustment.

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EA TheoryAs for the other metaheuristics, the EA theory isvery limited:

The Schemata theorem, in your notes.

Price’es theorem. Comes from populationbiology, and has been transferred to EA’s byLee Altenberg. Very complicated mathematics.

Goldberg’s work on population sizing.

In practice none of theories are useable. Note,contrary to SA there is no convergence theory.

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The first theory book ...Is the book: “Genetic Algorithms - Principles andPerspectives”, C.R. Reeves & J. E. Rowe.

The first (to my knowledge) theory book onevolutionary algorithms.

The lack of theory is acknowledged ...

... but not ignored !

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Many bad articles ...“The number of papers devoted to GA’s isenormous - and increasing - but sadly, too many ofthem have titles like: A New Genetic Algorithm forthe Multi-Resource Travelling GravediggerProblem with Variable Coffin Size”, “GeneticAlgorithms - Principles and Perspectives”, C.R.Reeves & J. E. Rowe.

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When to use EA ?When should you consider EA ?

If the problem is REALLY hard:If the problem is very multimodal.If the problem is a multi criteria problem.If the standard neighbourhood is bad ...

If you have a good reproduction operator.

If your problem is multi-objective

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When not use EADon’t use EA if:

Your problem is too simple.

Your (single solution) neighbourhood operator isefficient

Your reproduction cannot produce goodindividuals.

Time is critical.

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ParametersThere are more parameters in EA than in SA andmost TABU algorithms. Further some parametersare hidden:

Population size.

Selection pressure, Important but hiddenparameter.

Operator probability: Which operator should thealgorithm use ?

Stopping criteria.

Generation gap.These are just the basic parameters, many othersmay show up ...

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Tips and tricksA few general advices:

The most important: Get the representation andreproduction operator right.

Use a large population initially.

Be carefull about the selection pressure, use alow selection pressure initially.

Tune your evaluation function, this is where thebulk of the work is performed by the computer.

Watch the convergens.

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Evolutionary Algorithms · Evolutionary Algorithms is not just Genetic Algorithms. EA tries to mimic the Darvinian evolution EA is signiﬁcantly different from SA and TABU and thus