GA Applications

1
(No Transcript)
2
GA Applications

• Peaks function
• C- code
• GOAT package for MATLAB
• minimization and maximization
• Traveling Salesman Problem
• genotype and phenotype encoding
• customizing operators
• rankscaling
• Hillis Sorting Problem
• Sequence Alignment
• Floating point GAs
• Constraint optimization
• Multi-objective optimization
• The schemata theorem

3
Components of binary GA in Feature Selection
R2 Goodness of fit
Problem max R2
Selected Population
0.1
Fitness
Population
Selection
110101 111111 000000
f1 0.60 f2 0.30 f3 0.10
110101 110101 000000
0.3
0.6
Crossover point
111100 000011
111111 000000
Crossover
Selected gene
Mutated gene
Mutation
111111
111110
4
Genetic Operators
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
Traveling Salesman Problem
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
void main(int argc, char argv) char
mombassa80, root80 data
b double alpha, beta
//user data int num_cities MATRIX
distances Container box
//user data to objective function
in box double ( fptr) (data, VECTOR)
//function pointer to objective fnctn genotype
pop fptr Salesman3 MatrixAllocate(distan
ces, 500, 500) userData(b, box)
// tells pointer of userdata in data
struct for b Read_User_Data(alpha, beta,
num_cities, distances) box.pop pop
box.alpha alpha box.beta beta
box.num_cities num_cities box.distances
distances if (argc 2) strcpy( mombassa,
argv1) Allocate_GA(pop, b, argc, mombassa,
root, fptr) b.print_flag0 Loop_GA(b,
pop, root, fptr) Write_User_Data(b, pop,
root, fptr) De_Allocate_GA(pop, b, root,
fptr) MatrixFree(distances, 500)
25
double Salesman2(data a, VECTOR x) int
i, isum0double tour 0, pen10, pen20 double
alpha, betaint num_cities, one, two,
help Container box (Container )(a-gtud)
alpha box-gtalpha beta box-gtbeta
num_cities box-gtnum_cities help
num_cities/2(num_cities-1) if (num_cities2
1) help helpnum_cities2 for (i 0 i
lt num_cities-1i) one (int) xi
two (int) xi1 tour tour
box-gtdistancesonetwo one (int)
xnum_cities-1 two (int) x0 tour
tour box-gtdistancesonetwo for (i 0
i lt num_citiesi) isum (int) xi if
(isum!help) pen1alpha getche()
box-gtpenn1pen1 box-gtpenn2pen2 return
tour pen1
26
SCHEMATA THEOREM (Holland)

• h(i) raw fitness for population sample i
• f(i) normalized fitness f(i) h(i)/Sh(i)
• A schema denotes a set of substrings that have
  identical
• values at certain loci 1101 10101, 11101
• m(S,t) number of scheme exemplars in pop at
  generation t
• Number of schema of inividual S present in next
  generation is
• proportional to chance of an individual being
  picked that has
• the schema according to
• m(S,t1) m(S,t) n f(S)/Sf m(S,t) f(S)/fave
  m(S,t) fave (1c)
• m(S,t1) m(S,0) (1c)t
• Better than average schemata grow exponentially

27
Partially Mapped Crossover
28
Genetic Algorithm cycle
29
Note In the plot, fitnesses are plotted as
(1-R2) and The problem can be thought as a
minimization.
30
Source A. Yasri and D. Hartsough, Toward an
Optimal Procedure for Variable Selection and QSAR
Model Building J. Chem. Inf. Comput. Sci. 2001
Vol. 41, No.5, pp. 1218-1227.
31
Search space in feature selection
A data set with 10 features
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)