GRASP

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????????????????????????????????(???)

• ??????
• ??????
• ?? ??

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????(???)

• ????????
• ?????
• Local Search?????
• Simulated Annealing?????
• Genetic Algorithm
• Tabu Search
• Quicker

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????????(???)
4
????????

• F ????????(??)
• f F ? R (Z) (????)
• ??? or ??? f(x)
• ?? x ? F

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?????????????

• ??
• ????,????,????????????
• ??(??1)
• ?????????????????
• ????(?????????)
• ?????????(???????)

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?????????????

• ??(??2)
• ???(?????????????)
• Simulated Annealing? (???????)
• Tabu Search (????)
• Genetic Algorithm (??)
• ??(??3)
• ????????????????????????? any time ??????
• Knuth?METAFONT???

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????????(???)
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?????

• ????F??F?????????
• N F ? 2 F
• ? x ??(?????????)??????????.

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??????????????????????
?????? 1,2,3,4
???????? 1,2,3,4???????4!????
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??????????????????????
???? ?????????(???)
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?????(??) 1234 ?????
J1
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????????????????????
?? ??????????
1 2 4 3
????? 1 2 3 4 ???
1 3 2 4
2 1 3 4
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???????????????????????
1234
??????
2134
6
6
?????
1243
1324
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7
7
6
5
6
5
8
7
4
10
4
5
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10
8
3
7
8
5
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Local Search(?????,???)
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????????????
x
?? N(x)
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??????(??????)
?????
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Local Search

• ??(x) y? N(x)f(y)gtf(x)

x ?????????? while ??(x) ? do x
??(x)????????
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Local Search?????
??????? (x,y) f(x)gtf(y)
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Local Search?????
????(???)
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Multiple Start Local Search (????????)
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Multiple Start Local Search(????????)

• while ?????? ? yes do
• x ??????????
• while ??(x) ? do
• x ??(x)????????

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???????

• ???(intensification)
• ????????????????????????(proximate optimality
  property)????,?????????????????.
• ???(diversification)
• ????????????????????????,????????????????????????.

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??? intensification
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??? diversification
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GRASP (Greedy Randomized Adaptive Search
Procedure)
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Iterated Local Search(???????)

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Iterated Local Search (???????)

• x ??????????
• while ?????? ? yes do
• while ??(x) ? do
• x ??(x)????????
• x ??????? N'(x)????????

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Simulated Annealing ? (????????)

• ?????(annealing)???????????.

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Simulated Annealing?
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Simulated Annealing?

• x1 ??????????
• for k1 to 8 do
• y N(x)????????
• ? min. f(y)-f(xk),0
• ?? exp ?/Tk? xk1 y (??)
• ?????? xk1 xk (??)

?? T1?T2? ?T8 0
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????????????
????
1
??
??
0
?f(y)-f(x)
?????????
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???

• ????? (logarithmic cooling)
• Tk T1/log2 (1k)
• ??????? (geometric cooling)
• ????? ????????(16????)????????? T T
  ??(0.95????)???.

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Simulated Annealing????

• ???????????????,??????????????.
• ??????????(blind search)?????.
• ???????????????,?????????????????.
• ?????.(????????????.)

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Genetic Algorithm(?????????)

• ??(?????????)?????????.
• ????????(??population)?????????.
• ?????????????,??(crossover)???????(mutation)??????
  ?????.

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Genetic Algorithm

• ??(X) ?? X ?????????????????????????.
• ??(X) ?? X ??????????????(????)??????????.

P(0) ?????? for t0 to T do Y??( P(t) )
P(t1) ??( Y )
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???????
??(crossover)
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Genetic Algorithm???

• ?????????????.
• Local Search?????
• ??????(premature convergence)
• ?????????????????.
• ???????????????????.
• ?????,?????

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?????
?????????????????????
38
?????
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Tabu Search (?????)

• ????????????????.
• ??
• ????????? (steepest ascent mildest descent
  method)
• ???????(adaptive memory programming)
• ?????????????,??????,????????(?????????????????)??
  ??.

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Tabu Search(???)
TL2
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Tabu Search 1
????????
????????????!
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Tabu Search 2
TL2
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Tabu Search 3
TL2
FIFO
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Tabu Search 4
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Tabu Search 5
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Tabu Search 6
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Tabu Search 7
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Tabu Search 8
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Tabu Search 9
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Tabu Search 10
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Tabu Search

• TL (Tabu List) ?????
• ????????????????????.
• ???????????????????,?????(short term
  memory)??????.
• Best(x) arg max.f(y) y? N(x)-TL

x ?????????? while ??????? yes do x
Best(x) x?TL????,??????????.
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?? attribute
???
??
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?? attribute

• TL?????????.
• ?????????????,???????????????????.
• Tabu Search???????

?? ?????????????????????
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Tabu Search????? 1
???
1234
6
1243
6
7
1234
1243
7
7
6
5
6
5
8
7
4
10
3?4???????? ??????
4
5
10
6
10
8
3
7
8
5
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Tabu Search????? 2
6
7
7
8
7
10
6
10
10
8
8
6
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Tabu Search????? 3
6
7
8
10
6
8
6
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Tabu Search????? 4
6
6
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TL3??? ????
8
4
10
6
8
3
5
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Tabu Search????? 5
6
6
7
8
4
6
8
3
5
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?????
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????????(???)
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Quicker

• ???????????k????(Tabu Search??????)
• ??????, ??????? Genetic Algorithm
• ?????????????????? ?????????
• ????(rejection free)???????Simulated Annealing

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Quicker
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????????...

• ????? ???????????IV
• (?????)
• ?5? ????????????

???????.