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15

AA Aa aa

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bb r2 _{2r(1-r) (1-r)}2

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5 57 6

1 8 29

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L

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r

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2

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2

r

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r

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17

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1. f(a)Ƒf(b)ƑƐøIŻäƓƨƥŷƓŖa

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4. 2-3ƫčƧŀƄſƑƐŰmƫf(x)=0ƑƓƨ

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x

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ƖǁǨDžǞǤƵǨ

(cM)

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Ŕ¦Ƣ

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ƨ

HaldaneŔ¦

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x=−1

2ln(1−2r)

x₌1

4ln 1+2r

1−2r

# $ % & ' ( 19

ą¢Ÿ ƑSRĻśƕŔ!

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Ŋa~œƕą¢Ÿ ƫĩûƄƨ

3.

LOD

&ƢSRĻśƫĩûƄƨ

4.

LOD

&ƢSRĻśƕŵƨ&ƫŕ&ƑƂƏŰ-Ŋa~ƫŃő

ď

(linkage groups)

ƔƸǤǪǕ3žƄƨ

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ƨǭ

5.

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6.

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8.

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ĜƌƉƧƂƏŰSRƕïźƦƂƀƫïıƄƨ

21

ď3žƕƭǤƺǣǀǜƕ

•

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1.

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LOD

&ƔhƂƏŕ&ƫĬ

cƄƨ

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LOD

&ƕYKƖ^ż

Ŷ&ƫðƂƉǚǪƴǪhƫLƃŃőďƔnƄƨ

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3. 1

Ƒ

2

ƫŰ-ǚǪƴǪŻ3šƀƩƨƞƐčƧŀƄ

22

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Ǭ

L1-L2-L3-L4-L5-L6

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•

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1

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Ŷ

•

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L1

L2

L3

L4

L5

L6

14.5 0.0

5.2

8.3

17.1

20.3

23

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•

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å

-=

+ +

+ +

+

+

-

-=

1

1

1 , 1

, 1

, 1 , 1

,

[

log

(

1

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log(

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)]

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l

i

i i i

i i

i i i i i

n

R

L

q

q

q

q

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å

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=

1

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l

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q

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L2

L3

L4

ſƕƙŻÄƂŶƑżƔ…

L1

L2

L3

L4

ŸƗŰ

ƙƫL1-L3-L2-L4Ƒ ŸcƂƉƑƄƨƑ…

L1

L2 L3

L4

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100 … 4.7 x 10

158

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t

k

q

p

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26

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(global optimal solution, local optimal solution)

m‘ħƔ çƧƍƠƏƂƞŷHēŠơ

jƓŽƓŶ Y‚ƉƧéƓăƐƖ…

W

Ô

Ǭ

Ÿ

Ɨ

Ű

k

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27

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Traveling salesman problem (TSP)

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combinatorial optimization problem

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# load required packages require(rgl)

require(pso)

# set x and y arrays

x <- (-50:50)/10

y <- x

# set a objective function (surface)

z <- matrix(NA, length(x), length(y))

for(i in 1:length(x)) {

for(j in 1:length(y)) { # Rastrigin function

z[i,j] <- 20 + (x[i]^2 - 10 * cos(2 * pi * x[i]))

+ (y[j]^2 - 10 * cos(2 * pi * y[j])) }

}

# show the objective surface open3d()

persp3d(x, y, z, col = "green") # optimization

o1 <- psoptim(rep(NA,2),function(x) 20+sum(x^2-10*cos(2*pi*x)),

lower=-5,upper=5,control=list(abstol=1e-8)) show(o1)

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