Algorithm Portfolio Design: Theory vs. Practice Carla P. Gomes ...

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L M$N

S

1000

11 12 13 14 15

0.8

relative frequency

log median number of backtracks

1 order order order order order

100

brelazs brelazr rbrelazs rbrelazr

0.6

0.4

10 0.2

1 0.1

0 0.2

0.3 0.4 0.5 fraction of pre-assigned elements

0.6

0.7

0

î³Ù7H b _D v4NRF$Z5ILeiF]p Û 4F´.DOE$4etFçXbtQdSD6hUT%vMI6`Rb _ NfDOv4´.DEG4etFQfbtDO~ _

5

10

15 20 25 30 35 40 number of backtracks for first solution

45

50

0.8

0.7

0.6

order order order order

relative frequency

1 12 13 14 15

fraction of unsolvable cases

0.8

0.6

0.5 brelazs brelazr rbrelazs rbrelazr

0.4

0.3

0.2

0.1 0.4 0 0 0.2

0 0

0.1

0.2

0.3 0.4 0.5 0.6 0.7 fraction of pre-assigned elements

0.8

0.9

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2

4 6 8 number of backtracks for first solution

10

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1

1 0.9

0.8

0.8

relative frequency

relative frequency


0.6

0.4


0.6 0.5 0.4 0.3

0.2

0.2 0.1

0 0

5

10


45

50

0

0.5


2000


0.5

relative frequency

relative frequency

0.4

0.3

0.2


0.4

0.3

0.2

0.1 0.1

0 0

2


10

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0

2

4


18

20

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1 0.98 brelazs brelazr rbrelazs rbrelazr

0.96

relative frequency

0.94 0.92 0.9 0.88 0.86

1

0.84 0.82

0.8

0.8 500


2500

0.7

3000

relative frequency

0

0.8


0.7

0.6 relative frequency

brelazs rbrelazr

0.9

0.6 0.5 0.4 0.3 0.2

0.5 0.1 0.4 0

200

400 600 number of backtracks

800

1000

0.3 0.2 0.2

brelazs rbrelazr

median number of backtracks

0.1

0 0

2


10

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0.15

0.1

0.05

0 0

50

100

150 200 number of backtracks

250

300

4î³etb F_ QRv4biDONRF±~{zÙ DNf4FND6©*Z]btz~ _©*btbiQf~D^X~4\5`RI×bt`fQf4FNR~4FI6S`R`fD6b _ h=~íXFvM+IL`fb I6_ etNRv4DFv4`P4Ûc`%DE $ X+MR°f>JX°m ¬ o DONf74btò5Qf*â E$ò6`Jätô§I6ò~òo26DOã6N/ägúò+b¢*mô§ânF4NRóF~Xö Q bi`*DIbiFDO`/eietDLFhMQfQfbtDF*~G`PI6D6EGhJ4F=bmI6e FNfDFNf~XbtQ2QR4I6E e _Nfv~4~4bt~ _ DO~4bmFNfF~Q.4NRDF`f`RDNf`]c +wFNRF©.FDO~4`f_bt4FN Qf4F ~4ILbt`fILF*QfD6btDhm~Jbt~4c 4F@F~4F~XQ=NRv4~4` ©*btQfDv4Q³bi~XQRFNf4NRDXF`f`*DE$EvU Ã]ÉM¾fÃ6Ôea:Ñ ÎdÅ ÅRÆda¾dÆd¿¢Å ÃÅ ¾f½:Ñ Æ ?½d]Á aÔea½f¿¢ÆdÎ²Ã%ÒXÅ*Ñ :Ã Å)aX6Æ²ÅPÔ Ñb`XÅRÎ²¾=Ô¢Ã:Î²aÒÅÃÆdÉmÃ½Ä2¿f]Å ÃÇ¾dÔ¢ÒÎ²½]ÒÎÄ2Ä2Æ*ÃÃ:¾faMÅ Ã?f]aÅ aÅ*ÅRÃ¾f¾=½¿MÄ2Ñ ½Ã¾fÆdÅÅ

Portfolio for 2 processors

Portfolio for 20 processors

1600

0.45 0 brelazs, 20 rbrelazr

2 brelazs, 0 rbrelazr 1400

expected number of backtracks

expected number of backtracks

0.4 1200

1000

800

600

400

0.35

0.3

0.25

0.2 1 brelazs, 1 rbrelazr

200

0 brelazs, 2 rbrelazr 20 brelazs, 0 rbrelazr 0.15 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 standard deviation (risk)

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