lecture 5: ep and de 1 evolutionary computational intelligence lecture 5a: overview about...
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Lecture 5: EP and DE1
Evolutionary Computational Intelligence
Lecture 5a: Overview about Evolutionary Programming
Ferrante Neri
University of Jyväskylä
Lecture 5: EP and DE2
EP quick overview
Developed: USA in the 1960’s Early names: D. Fogel Typically applied to:
– traditional EP: machine learning tasks by finite state machines– contemporary EP: (numerical) optimization
Attributed features:– very open framework: any representation and mutation op’s OK– crossbred with ES (contemporary EP)– consequently: hard to say what “standard” EP is
Special:– no recombination– self-adaptation of parameters standard (contemporary EP)
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EP technical summary tableau
Representation Real-valued vectors
Recombination None
Mutation Gaussian perturbation
Parent selection Deterministic
Survivor selection Probabilistic (+)
Specialty Self-adaptation of mutation step sizes (in meta-EP)
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Historical EP perspective
EP aimed at achieving intelligence Intelligence was viewed as adaptive
behaviour Prediction of the environment was
considered a prerequisite to adaptive behaviour
Thus: capability to predict is key to intelligence
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Finite State Machine as predictor
Consider the following FSM Task: predict next input Quality: % of in(i+1) = outi Given initial state C Input sequence 011101 Leads to output 110111 Quality: 3 out of 5
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Representation
For continuous parameter optimization Chromosomes consist of two parts:
– Object variables: x1,…,xn
– Mutation step sizes: 1,…,n
Full size: x1,…,xn, 1,…,n
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Mutation
Chromosomes: x1,…,xn, 1,…,n
i’ = i • (1 + • N(0,1)) x’i = xi + i’ • Ni(0,1) 0.2 boundary rule: ’ < 0 ’ = 0
Other variants proposed & tried:– Lognormal scheme as in ES– Using variance instead of standard deviation– Mutate -last– Other distributions, e.g, Cauchy instead of Gaussian
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Recombination
None Rationale: one point in the search space
stands for a species, not for an individual and there can be no crossover between species
Much historical debate “mutation vs. crossover”
Pragmatic approach seems to prevail today
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Parent selection
Each individual creates one child by mutation Thus:
– Deterministic– Not biased by fitness
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Survivor selection
P(t): parents, P’(t): offspring Pairwise competitions in round-robin format:
– Each solution x from P(t) P’(t) is evaluated against q other randomly chosen solutions
– For each comparison, a "win" is assigned if x is better than its opponent
– The solutions with the greatest number of wins are retained to be parents of the next generation
Parameter q allows tuning selection pressure Typically q = 10
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Example application: evolving checkers players (Fogel’02)
Neural nets for evaluating future values of moves are evolved
NNs have fixed structure with 5046 weights, these are evolved + one weight for “kings”
Representation: – vector of 5046 real numbers for object variables (weights)– vector of 5046 real numbers for ‘s
Mutation: – Gaussian, lognormal scheme with -first– Plus special mechanism for the kings’ weight
Population size 15
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Example application: evolving checkers players (Fogel’02)
Tournament size q = 5 Programs (with NN inside) play against other
programs, no human trainer or hard-wired intelligence
After 840 generation (6 months!) best strategy was tested against humans via Internet
Program earned “expert class” ranking outperforming 99.61% of all rated players
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Evolutionary Computational Intelligence
Lecture 5b:Differential Evolution
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Brief historical overview
The Term Differntial Evolution has been coined in 1994 by Storn and Proce (Germany-USA)
Some important invesigations have been recently done by Lampinen
The so far only existing book has been published in 2005
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Representation
Differential Evolution in its original implementation is intended for vectors of real numbers
Nevertheless it can be employed also in the case of integer problems, probably loosing in terms of efficiency
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Population models
GA and “comma” ES employ a generational logic: offspring population replaces entirely the previous population
“plus” ES considers both parents and offspring and after having sorted them selects a predetermined number of best performing individuals
Differential Evolution (DE) emplys a steady-state logic (also used in some GAs): the successfull offspring immediately “kills” the weakest parent
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Initial Sampling
A set of vectors in sampled, usually at random with the boundaries of the decision space
And these vector represent the design variables that we are willing to optimize
Our population size must be at least four
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Parent selection
Four individuals x1, x2, x3, x4 are selected at random from the population by means of a uniformly distributed function
Like in ES there is no selection pressure for the choice of the parents undergoing variation operators (recombination and mutation)
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Recombination
A provisional offspring xoffp is generated by:
xoffp=x1+K(x2-x3)
where K is s constant value usually set equal to 0.7
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Mutation
With a certain probability some genes of the provisional offspring are replaced with some genes of x4.
The probability of happening such mutation is usually set to 0.3
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Survivor seelection
The offspring xoff is thus generated. The fitness value of xoff is calculated
and,according to a steady-state strategy, if xoff outperforms x4, it replaces x4, if on the contrary f(xoff)>f(x4), no replacement
occurs.
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Observations
The steady state logic makes the DE structure without generation loops since the replacements occurs as soon as a better solution is generated
Exploratory logic of DE has a slight analogy with Nelder Mead since it lets the search directions been led by means of existing solutions. Analogy for 2 dimension case is rather strong
The DE is very promising but the biggest limit it has is the risk of stagnation
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Premature Convergence/ Stagnation
There are the main defects in EAs Premature Convergence: It occurs when all
the population does not have any difference (one genotype) and the corrensponding fitness value is suboptimal (+ strategy)
Stagnation:It occurs when, notwithstanding a high diversity, there are no improvements (superfit individual)
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Evolutionary Computational Intelligence
Lecture 5c:Handling Multimodality
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Motivation 1: Multimodality
Most interesting problems have more than one locally optimal solution.
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Motivation 2: Genetic Drift
Finite population with global (panmictic) mixing and selection eventually convergence around one optimum
Often might want to identify several possible peaks
This can aid global optimisation when sub-optima has the largest basin of attraction
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Biological Motivation 1: Speciation
In nature different species adapt to occupy different environmental niches, which contain finite resources, so the individuals are in competition with each other
Species only reproduce with other members of the same species (Mating Restriction)
These forces tend to lead to phenotypic homogeneity within species, but differences between species
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Biological Motivation 2: Punctuated Equilbria
Theory that periods of stasis are interrupted by rapid growth when main population is “invaded” by individuals from previously spatially isolated group of individuals from the same species
The separated sub-populations (demes) often show local adaptations in response to slight changes in their local environments
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Implications for Evolutionary Optimization
Two main approaches to diversity maintenance: Implicit approaches:
– Impose an equivalent of geographical separation– Impose an equivalent of speciation
Explicit approaches– Make similar individuals compete for resources
(fitness)– Make similar individuals compete with each other
for survival