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 Panagiotis Stamatopoulos Random Search 4. PopsSample Department of Informatics and Telecommunications 5. PoPS National and Kapodistrian University of Athens 6. Experiments 1/19
Piece of Pie Outline Search: Confidently Exploiting Heuristics 1. Introduction Nikolaos Pothitos, Panagiotis Stamatopoulos 2. Related Work 1. Introduction 3. Bridging Systematic and Random Search 2. Related Work 3. Bridging 4. The PopsSample Module Systematic and Random Search 5. The PoPS Method 4. PopsSample 5. PoPS 6. Experiments 6. Experiments 2/19
Piece of Pie Branches and Decisions During Search Search: Confidently Exploiting Heuristics ◮ Constraint Satisfaction Problems are commonplace Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Solutions not known a priori 1. Introduction ◮ We have to search for a solution 2. Related Work 3. Bridging ◮ Decide which path to follow Systematic and Random Search 4. PopsSample 5. PoPS 6. Experiments 3/19
Piece of Pie Normal Heuristics Search: Confidently Exploiting Heuristics ◮ Decision can be an assignment Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Normal heuristics evaluate assignments 1. Introduction ◮ Map values v i to h i 2. Related Work 3. Bridging Systematic and 5 Random Search 4 4. PopsSample 3 h i 5. PoPS 2 6. Experiments 1 0 v 1 v 2 v 3 v 4 v 5 4/19
Piece of Pie Systematic Search Decision Search: Confidently Probability Exploiting Heuristics Nikolaos Pothitos, Panagiotis ◮ Select value with highest h i Stamatopoulos 1. Introduction 1 2. Related Work 0 . 8 3. Bridging P ( i ) 0 . 6 Systematic and Random Search 0 . 4 4. PopsSample 0 . 2 5. PoPS 0 v 1 v 2 v 3 v 4 v 5 6. Experiments 5/19
Piece of Pie Random Heuristics Search: Confidently Exploiting Heuristics ◮ Choose v i completely at random Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Corresponding probability P i is same 1. Introduction ◮ h i not taken into account 2. Related Work 3. Bridging Systematic and 1 Random Search 0 . 8 4. PopsSample P ( i ) 0 . 6 5. PoPS 0 . 4 6. Experiments 0 . 2 0 v 1 v 2 v 3 v 4 v 5 6/19
Piece of Pie Normal + Random Heuristics = ? Search: Confidently Exploiting Heuristics ◮ Is there a compromise? Nikolaos Pothitos, Panagiotis h conf Stamatopoulos i P conf ( i ) = i h conf � 1. Introduction i 2. Related Work 3. Bridging Systematic and ◮ h i is taken into account. . . Random Search 4. PopsSample ◮ . . . especially as conf grows 5. PoPS 6. Experiments 7/19
Piece of Pie A New Hybrid Semi-random Heuristic Search: Confidently Exploiting Heuristics ◮ Gradually makes normal heuristics random Nikolaos Pothitos, Panagiotis ◮ conf : the randomness degree level Stamatopoulos ◮ More randomness while conf → 0 1. Introduction 2. Related Work 3. Bridging Systematic and Random Search 4. PopsSample 1 5. PoPS 0 . 8 6. Experiments P ( i ) 0 . 6 0 . 4 0 . 2 5 4 0 3 v 1 2 conf v 2 v 3 1 v 4 v 5 0 8/19
Piece of Pie Heuristics as a Roulette Wheel Search: Confidently Exploiting Heuristics ◮ For conf = 1 Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Spin the wheel and select 1. Introduction 2. Related Work h 2 3. Bridging Systematic and Random Search 4. PopsSample 5. PoPS h 3 h 1 6. Experiments h 5 h 4 9/19
Piece of Pie function PopsSample ( PieceToCover , conf ) Search: Confidently if Assignments include every variable then Exploiting Heuristics return success Nikolaos Pothitos, end if Panagiotis Stamatopoulos X ← VariablesOrderHeuristic ( X ) D X init ← D X 1. Introduction CoveredPiece ← 0 2. Related Work 3. Bridging while CoveredPiece ≤ PieceToCover do Systematic and value ← ValuesOrderHeuristic ( D X , conf ) Random Search h conf 4. PopsSample CoveredPiece ← CoveredPiece + X ← value h conf � 5. PoPS v ∈ DX init X ← v Assign value to X and add it to Assignments 6. Experiments PopsSample ( PieceToCover , conf + 100 − conf ) | X | Undo the assignment D X ← D X − { value } end while D X ← D X init ⊲ Restores initial domain return failure ⊲ All alternative values are exhausted end function 10/19
Piece of Pie function PoPS Search: Confidently for i from 1 to SamplesNum do Exploiting Heuristics Sample i is activated Nikolaos Pothitos, Cover i ← 0 Panagiotis Stamatopoulos i − 1 conf i ← 100 · SamplesNum − 1 end for 1. Introduction while the available time is not exhausted do 2. Related Work 3. Bridging for each active Sample i do Systematic and if PopsSample ( Cover i , conf i ) Random Search 4. PopsSample did not return a solution then 5. PoPS Sample i is deactivated 6. Experiments end if Cover i ← Cover i + 1 d end for if every Sample i is deactivated then Activate every Sample i ⊲ to keep searching. end if end while end function 11/19
Piece of Pie PopsSample Applied to Timetabling Search: Confidently Exploiting Heuristics ◮ Solved Iternational Timetabling Competition datasets Nikolaos Pothitos, Panagiotis Stamatopoulos 950 Ing0203-2 1. Introduction 900 Ing0304-1 Ing0304-3 2. Related Work Solution Cost 850 Ing0405-2 3. Bridging Ing0506-3 Systematic and 800 Random Search Ing0708-1 4. PopsSample 750 5. PoPS 700 6. Experiments 650 600 0 20 40 60 80 100 120 140 conf ◮ As conf rises, curves are stabilized 12/19
Piece of Pie PopsSample Applied to Timetabling Search: Confidently Exploiting Heuristics ◮ The rest university timetabling instaces Nikolaos Pothitos, Panagiotis Stamatopoulos 2200 Fis0506-1 Ing0607-2 2000 1. Introduction Ing0405-3 Ing0607-3 1800 2. Related Work Let0405-1 Fis0506-2 Solution Cost 1600 3. Bridging Ing0506-1 Let0506-2 1400 Systematic and 1200 Random Search 1000 4. PopsSample 800 5. PoPS 600 6. Experiments 400 200 0 0 20 40 60 80 100 120 140 conf 13/19
Piece of Pie PopsSample for Frequency Assignment Search: Confidently Exploiting Heuristics ◮ Centre Electronique de l’Armement instances Nikolaos Pothitos, 340000 Panagiotis 320000 Stamatopoulos scen07 300000 Solution Cost (thousands) 280000 1. Introduction 12000 2. Related Work 11000 scen10 3. Bridging 10000 Systematic and 540 Random Search 520 4. PopsSample 500 scen09 480 5. PoPS 6. Experiments 190 180 scen06 170 8 . 6 scen08 8 . 4 0 20 40 60 80 100 120 conf ◮ Smaller cost = more satisfied constraints 14/19
Piece of Pie PoPS and Other Search Methods Search: Confidently Exploiting Heuristics ◮ Depth First Search (DFS) Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Limited Discrepancy Search (LDS) 1. Introduction ◮ Iterative Broadening 2. Related Work 3. Bridging ◮ . . . Systematic and Random Search 4. PopsSample 5. PoPS 6. Experiments 15/19
Piece of Pie PopsSample called with various Search: Confidently parameters Exploiting Heuristics Nikolaos Pothitos, Panagiotis ◮ For the first timetabling instance Stamatopoulos 1. Introduction 2. Related Work 3. Bridging 450 Systematic and Solution Cost 400 Random Search 350 4. PopsSample DFS 300 Iterative 250 5. PoPS Broadening 200 6. Experiments 150 LDS 100 50 1 PieceToCover 0 . 5 20 0 60 40 80 120 100 140 0 conf 16/19
Piece of Pie PoPS vs. Other Search Methods Search: Confidently Exploiting Instance PoPS LDS DFS It. Broad. Heuristics Fis0506-1 105 171 345 286 Nikolaos Pothitos, Panagiotis Ing0203-2 241 288 698 321 Stamatopoulos 307 578 353 Ing0304-1 279 1. Introduction 215 817 235 Ing0405-3 195 2. Related Work 655 X X Let0405-1 627 3. Bridging Systematic and 311 812 342 Ing0506-1 307 Random Search 283 1184 328 Ing0607-2 282 4. PopsSample 239 635 262 Ing0607-3 223 5. PoPS 294 675 370 Ing0304-3 288 6. Experiments Ing0405-2 284 877 344 265 Fis0506-2 33 486 34 12 Let0506-2 783 1621 937 713 Ing0506-3 256 660 280 231 Ing0708-1 227 660 264 223 17/19
Piece of Pie Conclusions and Future Work Search: Confidently Exploiting Heuristics ◮ Exploit the heuristic values themselves Nikolaos Pothitos, Panagiotis Stamatopoulos ◮ Introduce heuristic confidence semantics 1. Introduction ◮ Common methods cover a nodes number 2. Related Work 3. Bridging ◮ PoPS covers an heuristic pie Systematic and Random Search ◮ Can be naturally parallelized 4. PopsSample 5. PoPS 6. Experiments 18/19
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