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Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Piece of Pie Search: Confidently Stamatopoulos Exploiting Heuristics 1. Introduction 2. Related Work 3. Bridging Systematic and Nikolaos Pothitos

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SLIDE 1

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Piece of Pie Search: Confidently Exploiting Heuristics

Nikolaos Pothitos Panagiotis Stamatopoulos

Department of Informatics and Telecommunications National and Kapodistrian University of Athens

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SLIDE 2

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Outline

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging Systematic and Random Search
  • 4. The PopsSample Module
  • 5. The PoPS Method
  • 6. Experiments

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SLIDE 3

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Branches and Decisions During Search

◮ Constraint Satisfaction Problems are commonplace ◮ Solutions not known a priori ◮ We have to search for a solution ◮ Decide which path to follow

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SLIDE 4

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Normal Heuristics

◮ Decision can be an assignment ◮ Normal heuristics evaluate assignments ◮ Map values vi to hi 1 2 3 4 5

v1 v2 v3 v4 v5 hi

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SLIDE 5

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Systematic Search Decision Probability

◮ Select value with highest hi 0.2 0.4 0.6 0.8 1

v1 v2 v3 v4 v5 P(i)

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SLIDE 6

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Random Heuristics

◮ Choose vi completely at random ◮ Corresponding probability Pi is same ◮ hi not taken into account 0.2 0.4 0.6 0.8 1

v1 v2 v3 v4 v5 P(i)

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SLIDE 7

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Normal + Random Heuristics = ?

◮ Is there a compromise?

Pconf(i) = hconf

i

  • i hconf

i ◮ hi is taken into account. . . ◮ . . . especially as conf grows

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SLIDE 8

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

A New Hybrid Semi-random Heuristic

◮ Gradually makes normal heuristics random ◮ conf: the randomness degree level ◮ More randomness while conf → 0

conf v1 v2 v3 v4 v5

1 2 3 4 5 0.2 0.4 0.6 0.8 1

P(i)

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SLIDE 9

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Heuristics as a Roulette Wheel

◮ For conf = 1 ◮ Spin the wheel and select

h1 h2 h3 h4 h5

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SLIDE 10

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

function PopsSample(PieceToCover, conf) if Assignments include every variable then return success end if X ← VariablesOrderHeuristic(X ) DXinit ← DX CoveredPiece ← 0 while CoveredPiece ≤ PieceToCover do value ← ValuesOrderHeuristic(DX, conf) CoveredPiece ← CoveredPiece +

hconf

X←value

  • v∈DXinit

hconf

X←v

Assign value to X and add it to Assignments PopsSample(PieceToCover, conf+ 100−conf

|X |

) Undo the assignment DX ← DX − {value} end while DX ← DXinit ⊲ Restores initial domain return failure ⊲ All alternative values are exhausted end function

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SLIDE 11

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

function PoPS for i from 1 to SamplesNum do Samplei is activated Coveri ← 0 confi ← 100 ·

i−1 SamplesNum−1

end for while the available time is not exhausted do for each active Samplei do if PopsSample(Coveri, confi) did not return a solution then Samplei is deactivated end if Coveri ← Coveri + 1

d

end for if every Samplei is deactivated then Activate every Samplei ⊲ to keep searching. end if end while end function

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SLIDE 12

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PopsSample Applied to Timetabling

◮ Solved Iternational Timetabling Competition datasets 600 650 700 750 800 850 900 950 20 40 60 80 100 120 140

Solution Cost conf

Ing0203-2 Ing0304-1 Ing0304-3 Ing0405-2 Ing0506-3 Ing0708-1 ◮ As conf rises, curves are stabilized

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SLIDE 13

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PopsSample Applied to Timetabling

◮ The rest university timetabling instaces 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 20 40 60 80 100 120 140

Solution Cost conf

Fis0506-1 Ing0405-3 Let0405-1 Ing0506-1 Ing0607-2 Ing0607-3 Fis0506-2 Let0506-2

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SLIDE 14

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PopsSample for Frequency Assignment

◮ Centre Electronique de l’Armement instances 280000 300000 320000 340000 scen07 10000 11000 12000 scen10 480 500 520 540

Solution Cost (thousands)

scen09 170 180 190 scen06 8.4 8.6 20 40 60 80 100 120

conf

scen08 ◮ Smaller cost = more satisfied constraints

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SLIDE 15

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PoPS and Other Search Methods

◮ Depth First Search (DFS) ◮ Limited Discrepancy Search (LDS) ◮ Iterative Broadening ◮ . . .

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SLIDE 16

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PopsSample called with various parameters

◮ For the first timetabling instance

DFS Iterative Broadening LDS PieceToCover

0.5 1 20 40 60 80 100 120 140

conf

50 100 150 200 250 300 350 400 450

Solution Cost

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SLIDE 17

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

PoPS vs. Other Search Methods

Instance PoPS LDS DFS

  • It. Broad.

Fis0506-1 105 171 345 286 Ing0203-2 241 288 698 321 Ing0304-1 279 307 578 353 Ing0405-3 195 215 817 235 Let0405-1 655 627 X X Ing0506-1 307 311 812 342 Ing0607-2 282 283 1184 328 Ing0607-3 223 239 635 262 Ing0304-3 288 294 675 370 Ing0405-2 265 284 877 344 Fis0506-2 12 33 486 34 Let0506-2 713 783 1621 937 Ing0506-3 231 256 660 280 Ing0708-1 223 227 660 264

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SLIDE 18

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

Conclusions and Future Work

◮ Exploit the heuristic values themselves ◮ Introduce heuristic confidence semantics ◮ Common methods cover a nodes number ◮ PoPS covers an heuristic pie ◮ Can be naturally parallelized

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SLIDE 19

Piece of Pie Search: Confidently Exploiting Heuristics Nikolaos Pothitos, Panagiotis Stamatopoulos

  • 1. Introduction
  • 2. Related Work
  • 3. Bridging

Systematic and Random Search

  • 4. PopsSample
  • 5. PoPS
  • 6. Experiments

References

  • J. L. Bresina.

Heuristic-biased stochastic sampling. In W. J. Clancey and D. S. Weld, editors, AAAI 1996: 13th National Conference on Artificial Intelligence, Portland, Oregon, volume 1, pages 271–278, Menlo Park, 1996. AAAI Press.

  • V. A. Cicirello and S. F. Smith.

Enhancing stochastic search performance by value-biased randomization of heuristics. Journal of Heuristics, 11(1):5–34, 2005.

  • P. Prosser and C. Unsworth.

Limited discrepancy search revisited.

  • J. Experim. Algor., 16:1.6:1–1.6:18, 2011.
  • D. Sharma, V. Singh, and C. Sharma.

GA-based scheduling of FMS using roulette wheel selection process. In SocProS 2011: International Conference on Soft Computing for Problem Solving, volume 131, pages 931–940. Springer, 2012.

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