Parallel Simulated Annealing with Adaptive Temperature Determined by Genetic Algorithm

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?????
LSI????

• ??????????,??????????????????????.

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

• ?????????(GA)
• ??????????????(SA)

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

• ??????????????????
• ???????????????????
• ??????
• ???????? SA??????T ???
• SA???

1. ??????? 2. ?????? 3. ??????????????? 4.
???? 5. ??????????(?????)
????????????????????
?????????????????
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SA?????????????????

• ?????????????????????????
• ??????????????????????

SA????????
Max Temperature

• ????(????)
• ????(????)
• ???????
• ???????
• ??????

Temperature
Min Temperature
Time
????????????????????????
Mark 2000
??????(????)?????????????
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SA?????????????????

• ?????????????????????????
• ??????????????????????

SA????????
Max Temperature

• ????(????)
• ????(????)
• ???????
• ???????
• ??????

Temperature
Min Temperature
Time
????????????????????????
Mark 2000
??????(????)?????????????
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??????(??????????)
- eil101 -
TSP Optimum Topt region
eil101 629 1.1 2.5
kroA200 29368 27 53
lin318 42029 20 39
pr439 107217 44 72
rat575 6773 1.7 3.9
d657 48912 14 27

• ????????????,???????????.???,??????????????.

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????

• ?????????????????????SA???
• ??????????????????

?????????(GA)???,?????????.
?????????????.

GA for Temperature
Parallel SA with Adaptive Temperature determined
by Genetic Algorithm (PSA/AT(GA))
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PSA/AT(GA)???????
SA
L ??????
SA
L
L
SA
GA operation
SA
Solution
GA operation
Temperature(??)
E N D
GA operation
SA?1?????GA?1??(??)????
0
SA??? GA??????
1
???,GA???????????
2
?SA??????????
3
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??????????
- eil101 -
???? ???? ????
????SA

• ????????????
• ??????????,???????
• ????????????,?????????????

10
?????

• ???(Fitness)?,??????????
• ??????,????L ????,???E ???????Ek ??????????
• ???,??????,?????
• ????,???????????????

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Genetic Algorithm (GA)

• ?????????????????
• ????GA????,?????(??)???
• ???GA Eshelman93 ???

GA?????
Individual
?????????????
Selection
Crossover
????????
Mutation
???????
Population
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??(Selection)

• ?????????????????.
• ????,??????????????.
• ??????????,?????????????.
• ?????????SA?????,GA??????????????????.

Important temperature
Low temperature
High temperature
Energy
Energy
Energy
Baseline
Steps
Steps
Steps
Fitness high
Fitness low
Fitness low
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??(Crossover)

• BLX-a???????GA???

BLX-a
???(p1,p2)???d ?????ad ?????????????????????
???????????????, ??T ???????X ????.
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????(Mutation)

• ????????,??????????,????????????.

????
??µ ??????????sßd
(0ltßlt1)
(???)
d
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GA??????
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PSA/AT(GA)???????
SA
SA
SA
GA operation
SA
Solution
GA operation
Temperature(??)
E N D
GA operation
L
SA?1?????GA?1??????
0
L
SA??? GA??????
1
L ??????
???,GA???????????
2
?SA??????????
3
???????????????????
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????

• ??????????????(TSP)
• ?????????????????(JSP)
• ????
• PSA/AT(GA)(????)
• ???????SA(Parallel SAPSA)
• ????SA(Temperature Parallel SA TPSA)
• ????
• ????? ????????()
• ?????????????????????

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????

• ???????SA(PSA)??????????? ??SA??????????
  ?????????????????????????
• ????SA(TPSA)???????????????,
  ???????????????????????????????????

Steps
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?????
????? TSP JSP
????? 32 32
???? ???20 1000
1??????????? ????160 32000
???? 50 50
???? ????????50?????????? ????????50??????????
???? ????????????1???????? ????????????1????????
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?????????????(TSP)
???????PSA/AT(GA)?, ?????????TPSA????,PSA?????????
???
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??????????????
PSA ???????????????????????????? TPSA????????
??,???????? PSA/AT(GA)??????,??????????
- pr439 -
Error ratio()
5
Num. of annealing steps
(10 )
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????????(?????)
- eil101 -
Temperature
Num. of annealing steps
Num. of annealing steps
Num. of annealing steps
PSA/AT(GA)??????????TPSA
?????,?????????? PSA ???????????????
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????????(??????????)
- eil101 -
Temperature
Num. of annealing steps
Num. of annealing steps
Num. of annealing steps
PSA/AT(GA)??????????TPSA
?????,?????????? PSA ???????????????
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????????(??????????)
- eil101 -
Temperature
Num. of annealing steps
Num. of annealing steps
Num. of annealing steps
PSA/AT(GA)????????,?????????
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?????????????(JSP)
???????PSA/AT(GA)????????,JSP??????????.
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? ? ?
????
?????????????????????????? ????????????????(PSA/AT
(GA))
PSA/AT(GA)???

• ???????SA????GA??????
• ?????????????????

????

• TSP,JSP?????????????,?????????
• PSA/AT(GA)?,
• PSA???,TPSA??????????????
• PSA???????????

?????????????????????????,?????????.
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????

• SA?????????????
• ?????(????????)??????
• ??????????
• ????????

• ???????????
• (????????????)

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?????????????????(JSP)

• n????(Job)?m????(Machine)???
• ?????????????????(?????)
• ?????????????????(Makespan)????????????????

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?????????????????(JSP)

• n????(Job)?m????(Machine)???
• ?????????????????(?????)
• ?????????????????(Makespan)????????????????

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GA??????(ß?)
- kroA200 -
ß??,0.05?????
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GA??????(???)
- kroA200 -
????,0.3?????
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GA??????(?????)
- kroA200 -
??????,1/32?????
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GA??????(?????)
- kroA200 -
??????,32?????
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Coding of temperature

• PSA/AT(GA) uses GA to optimize the cooling
  schedule.
• Individual Temperature on each processor
• Design variable The exponent of temperature
  function, X
• The expression of temperature in PSA/AT(GA) is
  suitable for the exponential cooling schedule in
  SA.

Real Value
Bit Array
Encoding
X
X
Temperature 10 X
Decoding
SA cooling method
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Cooling schedule (eil101)
- TPSA -
- PSA/AT(GA) -
Temperature
Temperature
Num. of annealing steps
Num. of annealing steps
A line a cooling schedule on one SA.
PSA/AT(GA) Convergence on the important
temperature region TPSA All
processes cant always have good search.
The cooling schedule of PSA/AT(GA) is more proper
than TPSAs.
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Experimental results (Error Rate) in TSPs
Error Rate ()
TSP Problems
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SA????

• ??SA??? D.R.Greening,1990

• Serial-Like ?????????????????????.
  ????????

- Altered generation ?????SA??????, ????????
?????

• Asynchronous ????????????

• ???????,????????
• ???????????SA???

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?????????
????????????
????? 10???
2.703
?? 10X
??
PSA/AT(GA)?????????
?????????????
???? 10000 ???? 0.01
??????????? -2,4
Time
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