Using genetic algorithms to solve complex problems
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Using genetic algorithms to solve complex problems
Using genetic algorithms to solve complex problems. Julius van der Werf. School
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Using genetic algorithms to solve complex problems Julius van der Werf School of Rural Science and Agriculture University of New England Armidale, Australia
Complex Problems • • • • • • •
Multi-dimensional Multi-objective Multiple local optima Flat surfaces Non-differentiable Variables are highly interactive Messy
complex (animal) production problems • Optimal resource allocation – Feeding strategies – Logistics of supply
– Total Resource Management: TRM
complex animal breeding problems • Breeding program design – Mate selection – Development of synthetics / genetic resources TGRM
• Breeding objectives – Non-linear profit space – Selection index weights (incl. QTL)
Linear programming Dynamic Programming Optimal Control Theory Simplex algorithm
tedious
Solving complex problems • All deterministic search algorithms – Need to break the ‘curse of multidimensionality’
• Exhaustive (finite) search algorithms – Job increases exponentially with problem size
Random search or stochastic algorithms • Efficient • Optimal solution not guaranteed – But…….. Perform better than other algorithms in complex problems à Real Time solutions
Genetic Algorithms • GA = “Get away with Algebra” • 30 years old • Fitness = f(x)
– x = vector with parameters – Repeated cycles of
mutation recombination selection mating of parents
The Theory of Evolution • Fitness selection • Mutation
As geneticists we know how – To create variation powerful the – Need just enough, but limited concept is! – Can it work by itself? • The value of sex
• Recombination helps • Selection…………………….etc
Genetic Algorithm (= 'locus')
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Recombination
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Mutation 'Allele' = male allocated for breeding
• Each individual is a ‘genotype’ = possible solution • Each genotype leads to a certain outcome (phenotype)
‘chromosome’
‘locus’ Female No.
Evolutionary algorithms Female No. (= 'locus')
• Genetic Algorithm – 70-ties
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Mutation
• Differential Evolution – Price and Storn, 1997: “Dr. Dobbs Journal” – Simple and powerful – (19 lines of C++ code)
'Allele' = male allocated for breeding
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Differential Evolution • Propagation is through haploids with only some sex – Each candidate is replaced by the best of • itself • mix of itself and a competitor
• Mutation
– It perturbates specific variance for each variable! i.e. not a ‘standard random noise’ around each variable
• Recombination – For each allele change the proportions in the mix – Complementary means of creating viable vectors
• Select highest function value
The DE Algorithm Sample base population For generation = 1 to maxgens
Next generation
The DE Algorithm Sample base population For generation = 1 to maxgens For individual = 1 to N_individuals Draw a challenger (from 3 pop’n members)
Compare fitness of challenger and individual Replace individual if challenger wins Next individual Next generation
The DE Algorithm Sample base population For generation = 1 to maxgens For individual = 1 to N_individuals Draw a challenger (from 3 pop’n members) For j = 1 to N_loci Draw allele from challenger or individual Next Locus Compare fitness of challenger and individual Replace individual if challenger wins Next individual Next generation
The DE Algorithm • Sample base population 7 individuals 3 6 -1 2 -4
5 loci
The DE Algorithm • Evaluate this generation
3 6 -1 2 -4 34.56
21.67
13.05
45.98 28.23 41.68 25.74
Fitness
The DE Algorithm • Next generation: Each individual is challenged X1……….. XC 3 6 -1 2 -4 34.56
XA
XB
Xi = target Competes with
XT = trial, XT = XC + F.(XA-XB) Replace Xi with XT If higher fitness
The DE Algorithm Xi = target Xi
Competes with XT = XC + F.(XA-XB) XC
XA
XB
3
2 -4 34.56
F= 0.4 ~ 1.2
Xi(i) à XT(i)
6 -1
Mutator
=
+F
-
If rnd > CR Xi(i) à Xi(i) If rnd target Generation 0 x1 2.055 0.795 6.220 -4.860 3.145 -4.546 3.626 2.046 3.714 4.496
Differential Evolution • Mutation – It perturbates specific variance for each variable! ‘population derived noise’ – Not a ‘standard random noise’ around each variable
• Recombination – ‘knowledge sharing operator’ • Efficiently shuffle information about successful combination • à focus on most promising area of a solution space
– Complementary means of creating viable vectors – Uniform vs non-uniform crossover
Applying the DE Algorithm Sample base population For generation = 1 to maxgens For individual = 1 to N_individuals Draw a challenger (from 3 pop’n members) For j = 1 to N_loci Draw allele from challenger or individual Next Locus Compare fitness of challenger and individual Replace individual if challenger wins Next individual Next generation
The problem is evaluated in a subroutine
Which Problems are good for a DE to solve? • Complex • When f(x1, x2, …xn) is relatively easy to evaluate, but not easy to optimize (need derivatives etc.) • Problem representation is usually the challenge! – – – –
Minimize vs maximize Avoid redundancy Efficiently use sample space Can use ranks in allocation problems