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E1

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E2
E2
E1
???? ? ??? ???? ????? ?????? ????? ????? ??? 0 ?
1.
3
Monte-Carlo ????? ??????? ?????????? ??? ????
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Genetic Algorithm ?
4
Suppose we want to convert our sward to a shovel
5
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Fast cooling
7
A bit of work
8
What had happened
Fast cooling
Samples many high energy states
Fast cooling
Freezes in high energy state
9
??? ???? ??? ????? ???? ?????? ?? ????? Annealing
10
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But when local minima exists
energy
X
13
Step 0 Energy 230.3
energy
X
14
Step 1 Energy 190.7
energy
X
15
Step 2 Energy 178.6
energy
X
16
Step 3 Energy 134.6
energy
X
17
Step 4 Energy 53.3
energy
X
18
Step 5 Energy 50.0
energy
X
19
Step 10 Energy 48.9
Minimization is not a solution anymore
energy
X
20
The task of finding a global minimum for an
arbitrary function is hard.
21
The task of finding a global minimum for an
arbitrary function is hard.
No general method exists that guarantees success
in finite time.
22
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